# Faculty Profile

## Eduardo H Fradkin

### Primary Research Area

- Condensed Matter Physics - Condensed Matter Physics (theoretical)

### Profile Sections

### Biography

Professor Eduardo Fradkin received his Licenciado (master's) degree in physics from Universidad de Buenos Aires (Argentina) and his PhD in physics from Stanford University in 1979. He came to the University of Illinois in 1979 as a postdoctoral research associate, and became an assistant professor of physics at Illinois in 1981. He was promoted to associate professor in 1984, and became a full professor in 1989. Professor Fradkin is an internationally recognized leader in theoretical physics, who has contributed to many problems at the interface between quantum field theory (QFT) and condensed matter physics (CMP).

In his early work, he pioneered the use of concepts from CMP and statistical physics, such as order parameters and phase diagrams, to problems of QFT and high energy physics, in particular to the non-perturbative behavior of gauge theories. Perhaps his most important result in this area was the proof that when matter fields carry the fundamental unit of charge, the Higgs and confinement phases of gauge theories are smoothly connected to each other and are as different as a liquid is from a gas. This result remains one of the cornerstones of our understanding of the phases of gauge theories and represents a lasting contribution to elementary particle physics.

Professor Fradkin's unique perspective has allowed him to invoke and apply results from QFT to CMP. He was one of the first theorists to use gauge theory concepts in the theory of spin glasses and to use concepts of chaos and non-linear systems in equilibrium statistical mechanics of frustrated systems. Professor Fradkin has pioneered the application of QFT methods to the physics of correlated disordered electronic systems and the quantum stability of the spontaneously dimerized state of polyacetylene.

Professor Fradkin also pioneered the use of Dirac fermions for CMP problems, particularly in two space dimensions. A prime example is his work on Dirac fermions on random fields (which he began with former graduate student Dr. Matthew Fisher), which is now regarded as the universality class of the transition between quantum Hall plateaus in the integer Hall effect. This work is also important for the description of quasiparticles in disordered d-wave superconductors. He also applied, quite early on, these ideas to the physics of what nowadays are known as topological insulators, showing that in the presence of lattice topological defects, these systems exhibit a non-trivial electronic spectrum with a parity anomaly.

A major achievement of Professor Fradkin's recent research has been the development, in collaboration with former graduate student Dr. Ana Lopez, of the fermion Chern-Simons field theory of the fractional quantum Hall effect. This theory has played a central role in the current research effort in this exciting problem in CMP. Professor Fradkin and his collaborators have extended this theory to the more challenging problem of the non-Abelian quantum hall states and developed a theory of a non-Abelian interferometer to study the unusual properties of the vortices of these quantum fluids.

More recently Professor Fradkin and his collaborators introduced the notion of electronic liquid crystal states, which are phases of quantum fermionic strongly correlated systems exhibiting properties akin to those of classical complex fluids. These ideas play a crucial role in the current understanding of the pesudogap regime of high temperature superconductors.

### For more information

### Other Professional Employment

- Member of the International Scientific Board of the International Center for Advanced Studies (Buenos Aires, Argentina), since 2015.
- Director, Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign (since Spring 2011)
- Member of the Board of Scientific Directors of the Journal of Statistical Mechanics (JSTAT) (since 2011)
- Visiting Professor, Department of Physics, Faculty of Exact and Natural Sciences, University of Buenos Aires, Argentina, July 2010.
- Program Organizer and Visiting Scientist, Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, CA 93106 (Summer 2009).
- Member of the Scientific Advisory Board Committee of the Institute of Theoretical Physics of the University of Amsterdam, The Netherlands.
- Visiting Scientist at the Program on Frontiers in Quantum Computation at the Princeton Center for Theoretical Physics, February 2008.

### Research Statement

Professor Fradkin is an internationally recognized leader in theoretical physics, who has contributed to many problems at the interface between quantum field theory (QFT) and condensed matter physics (CMP). He pioneered the use of concepts from CMP and statistical physics, such as order parameters and phase diagrams, to problems of QFT and high energy physics. Perhaps his most important result in this area was the proof that when matter fields carry the fundamental unit of charge, the Higgs and confinement phases of gauge theories are smoothly connected to each other and are as different as a liquid is from a gas. This result remains one of the cornerstones of our understanding of the phases of gauge theories and represents a lasting contribution to elementary particle physics. Professor Fradkin's unique perspective has allowed him to invoke and apply results from QFT to CMP. He was one of the first theorists to use gauge theory concepts in the theory of spin glasses and to use concepts of chaos and non-linear systems in equilibrium statistical mechanics of frustrated systems.

Professor Fradkin has pioneered the application of QFT methods to the physics of correlated disordered electronic systems and the quantum stability of the spontaneously dimerized state of polyacetylene. Professor Fradkin also pioneered the use of Dirac fermions for CMP problems, particularly in two space dimensions. A prime example is his work on Dirac fermions on random fields, which is now regarded as the universality class of the transition between quantum Hall plateaus in the integer Hall effect. This work is also important for the description of quasiparticles in disordered d-wave superconductors. A major achievement of Professor Fradkin's recent research has been the development of the fermion Chern-Simons field theory of the fractional quantum Hall effect. This theory has played a central role in the current research effort in this exciting problem in CMP. He has recently developed a theory of electronic liquid crystal phases in strongly correlated systems and formulated a mechanism of high temperature superconductivity based on this new concept. This theory plays a central role in the interpretation of experiments in these systems of foremost importance. He is also a leader in the theory of topological phases in condensed matter and on the role of quantum entanglement at quantum critical points.

### Research Areas

### Books Authored or Co-Authored (Original Editions)

- E. H. Fradkin. Field Theories of Condensed Physics, Second Edition. Cambridge University Press. (2013).
- E. H. Fradkin. Field Theories of Condensed Matter Systems. (Addison-Wesley Advanced Book Program: Redwood City). Frontiers in Physics Series (1991).

### Selected Articles in Journals

- Shichao Yan, Davide Iaia, Emilia Morosan, Eduardo Fradkin, Peter Abbamonte, and Vidya Madhavan. The influence of domain walls in the incommensurate charge density wave state of Cu intercalated 1T-TiSe
_{2}. Physical Review Letters**116**, 106405 (2017). - Krishna Kumar, Hitesh J. Changlani, Bryan K. Clark, and Eduardo Fradkin. Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at m=2/3 magnetization. Physical Review B 94, 134410 (2016).
- Peng Ye, Taylor L. Hughes, Joseph Maciejko, and Eduardo Fradkin. Composite particle theory of three-dimensional gapped fermionic phases: Fractional topological insulators and charge-loop excitation symmetry. Physical Review B 94, 115104 (2016).
- Yu Gan, Gilberto A. de la Peña, Anshul Kogar, Bruno Uchoa, Diego Casa, Thomas Gog, Eduardo Fradkin, and Peter Abbamonte. Reexamination of the effective fine structure constant of graphene as measured in graphite. Physical Review B93, 195150 (2016).
- Yizhi You, Gil Young Cho, Eduardo Fradkin. Nematic quantum phase transition of composite Fermi liquids in half-filled Landau levels and their geometric response. Physical Review B 93, 205401 (2016).
- Yuxuan Wang, Gil Young Cho, Taylor L. Hughes, and Eduardo Fradkin. Topological superconducting phases from inversion symmetry breaking order in spin-orbit-coupled systems. Physical Review B 93, 134512 (2016).
- AtMa P. O. Chan, Thomas Kvorning, Shinsei Ryu, and Eduardo Fradkin.Effective hydrodynamic field theory and condensation picture of topological insulators. Physical Review B 93, 155122 (2016).
- Luiz H. Santos and Eduardo Fradkin. "Instanton effects in lattice models of bosonic symmetry-protected topological states". Phys. Rev. B 93, 155145 (2016).
- Xiao Chen, Xiongjie Yu, Gil Young Cho, Bryan K. Clark, and Eduardo Fradkin. Many-body Localization Transition in Rokhsar-Kivelson-type wave functions. Physical Review B 92, 212204 (2015).
- N. Samkharadze, K. A. Schreiber, G. C. Gardner, M. J. Manfra, E. Fradkin and G. A. Csáthy. Observation of a transition from a topologically ordered to a spontaneously broken symmetry phase. Nature Physics 12, 191 (2016).
- Kai Sun, Krishna Kumar, and Eduardo Fradkin. A discretized Chern-Simons gauge theory on arbitrary graphs. Physical Review B 92, 115148 (2015). (Editor's suggestion)
- X. M. Chen, A. J. Miller, C. Nugroho, G. A. de la Peña, Y. I. Joe, A. Kogar, J. D. Brock, J. Geck, G. J. MacDougall, S. L. Cooper, E. Fradkin, D. J. Van Harlingen, P. Abbamonte. Influence of Ti doping on the incommensurate charge density wave in 1T-TaS
_{2}. Physical Review B 91, 245113 (2015). - Jeffrey C. Y. Teo, Taylor L. Hughes, and Eduardo Fradkin. Theory of Twist Liquids: Gauging and Anyonic Symmetry. Annals of Physics 360, 349 (2015).
- Eduardo Fradkin, Steven A. Kivelson, and John M. Tranquada. Colloquium: Theory of intertwined orders in high temperature superconductors. Reviews of Modern Physics 87, 457 (2015)
- S. L. Gleason, Y. Gim, T. Byrum, A. Kogar, P. Abbamonte, E. Fradkin, G. J. MacDougall, D. J. Van Harlingen, Xiangde Zhu, C. Petrovic, and S. L. Cooper. Structural contributions to the pressure-tuned charge-density-wave to superconductor transition in ZrTe
_{3}: Raman scattering studies. Physical Review B 91, 155124 (2015). - Rodrigo Soto-Garrido, Gil Young Cho, and Eduardo Fradkin. Quasi-one-dimensional pair density wave superconducting state. Physical Review B 91, 195102 (2015).
- Xiao Chen, Gil Young Cho, Thomas Faulkner, and Eduardo Fradkin. Scaling of entanglement in 2+1-dimensional scale-invariant field theories. Journal of Statistical Mechanics, 2015, P02010 (2015).
- Andrey Gromov, Gil Young Cho, Yizhi You, Alexander G. Abanov, and Eduardo Fradkin. Erratum: Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect [Phys. Rev. Lett. 114, 016805 (2015)]. Physical Review Letters 114, 149902 (2015).
- Andrey Gromov, Gil Young Cho, Yizhi You, Alexander G. Abanov, and Eduardo Fradkin. Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect. Physical Review Letters 114, 016805(2015). (Editor's Suggestion)
- Yizhi You, Gil Young Cho and Eduardo Fradkin. Theory of the Nematic Fractional Quantum Hall State. Physical Review X 4, 041050 (2014).
- Gil Young Cho, Rodrigo Soto-Garrido and Eduardo Fradkin. Topological Pair-Density-Wave Superconducting States. Physical Review Letters 113, 256405 (2014).
- Krishna Kumar, Kai Sun, and Eduardo Fradkin. Chern-Simons theory for magnetization plateaus of the spin-1/2 XXZ quantum Heisenberg model on the kagome lattice. Physical Review B 90, 174409 (2014).
- Gil Young Cho, Yizhi You and Eduardo Fradkin. Geometry of fractional quantum Hall Fluids. Physical Review B 90, 115139 (2014).
- Rodrigo Soto Garrido and Eduardo Fradkin. Pair-Density-Wave Superconducting States and Electronic Liquid Crystal Phases. Physical Review B 89, 165126 (2014).
- Eduardo Fradkin, Enrique F. Moreno and Fidel A. Schaposnik. Bosonization of fermions coupled to topologically massive gravity. Physics Letters B 730, 284 (2014).
- Stefanos Papanikolaou, Daniel Charrier, and Eduardo Fradkin. Ising nematic fluid phase of hard-core dimers on the square lattice. Physical Review B 89, 035128 (2014).
- Yizhi You and Eduardo Fradkin. Field theory of nematicity in the spontaneous quantum anomalous Hall effect. Physical Review B 88, 235124 (2013). (Editor's Suggestion)
- Xiao Chen and Eduardo Fradkin. Quantum entanglement and thermal reduced density matrices in fermion and spin systems on ladders. J. Stat. Mech. (2013) P08013
- Hugo Aita, Liliana Arrachea, Carlos Naón, and Eduardo Fradkin, Heat transport through quantum Hall edge states: Tunneling versus capacitive couplings to reservoirs. Physical Review B 88, 085122 (2013).
- Ariel Dobry, Akbar Jaefari, and Eduardo Fradkin, Inhomogeneous superconducting phases in the frustrated Kondo-Heisenberg chain, Physical Review B 87, 245102 (2013)
- AtMa Chan, Taylor L. Hughes, Shinsei Ryu, and Eduardo Fradkin. Effective field theories for topological insulators by functional bosonization. Phys. Rev. B 87, 085132 (2013).
- Benjamin Hsu and Eduardo Fradkin. Dynamical stability of the quantum Lifshitz theory in 2+1 Dimensions. Phys. Rev. B 87, 085102 (2013).
- Eduardo Fradkin and Steven A. Kivelson. High-temperature superconductivity: Ineluctable complexity. Nature Physics 8, 864 (2012).
- Xiao Chen, Benjamin Hsu, Taylor Hughes and Eduardo Fradkin, The Renyi Entropy and the Multifractal Spectrum of Systems Near the Localization Transition. Phys. Rev. B 86, 134201 (2012).
- B. Uchoa, J. P Reed, Y. Gan, Y. I. Joe, E. Fradkin, P. Abbamonte, and D. Casa. The electron many-body problem in graphene. Physica Scripta T 2012, 014014 (2012).
- A. Jaefari and E. Fradkin. Pair-density-wave superconducting order in two-leg ladders. Phys. Rev. B 85, 035104 (2012).
- L. Arrachea and E. Fradkin. Chiral heat transport in driven quantum Hall and quantum spin Hall edge states. Phys. Rev. B 84, 235436 (2011).
- D. G. Barci and E. Fradkin. Role of nematic fluctuations in the thermal melting of pair-density-wave phases in two-dimensional superconductors. Phys. Rev. B 83, 100509(R) (2011).
- D. Schuricht, F. H. L. Essler, A. Jaefari, and E. Fradkin. Boundary effects on the local density of states of one-dimensional Mott insulators and charge density wave states. Phys. Rev. B 83, 035111 (2011).
- M. Kim, X. M. Chen, Y. I. Joe, E. Fradkin, P. Abbamonte, and S. L. Cooper. Mapping the magnetostructural quantum phases of Mn3O4. Phys. Rev. Lett. 104, 136402 (2010).
- A. Jaefari, S. Lal, and E. Fradkin. Charge-density wave and superconductor competition in stripe phases of high-temperature superconductors. Phys. Rev. B 82, 144531 (2010).
- E. Berg, E. Fradkin, and S. A. Kivelson. Pair-density-wave correlations in the Kondo-Heisenberg model. Phys. Rev. Lett. 105, 146403 (2010).
- B. Hsu and E. Fradkin. Universal behavior of entanglement in 2D quantum critical dimer models. J. of Stat. Mech.: Theo. and Exp. P09004 (2010).
- B. Fregoso and E. Fradkin. Unconventional magnetism in imbalanced Fermi systems with magnetic dipolar interactions. Phys. Rev. B 81, 214443 (2010).
- E. Fradkin and S. A. Kivelson. Electron nematic phases proliferate. Science 327:5962 155-156 (2010).
- T. L. Hughes, R. G. Leigh, and E. Fradkin. Torsional response and dissipationless viscosity in topological insulators. Phys. Rev. Lett. 107, 075502 (2011).
- J. P. Reed, B. Uchoa, Y. I. Joe, Y. Gan, D. Casa, E. Fradkin, and P. Abbamonte. The effective fine structure constant of freestanding graphene measured in graphite. Science 330, 805-808 (2010).
- B. Hsu and E. Fradkin. Universal behavior of entanglement in 2D quantum critical Models. J. of Stat. Mech.: Theo. and Exp. P09004 (2010).
- E. Fradkin, S. A. Kivelson, M. J. Lawler, J. P. Eisenstein, and A. P. Mackenzie. Nematic Fermi fluids in Condensed Matter Physics. Annual Reviews of Cond. Matter Phys. 1, 153 (2010).
- B. M. Fregoso and E. Fradkin. Unconventional magnetism in imbalanced Fermi systems with magnetic dipolar interactions. Phys. Rev. B 81, 214443 (2010).
- M. Kim, H. Barath, X. Chen, Y. -I Joe, E. Fradkin, P. Abbamonte, and S. L. Cooper. Magnetic field and pressure controlled phases in complex materials. Adv. Mat. 22, 1148 (2010).
- M. Kim, X. Chen, Y.-I. Joe, E. Fradkin, P. Abbamonte and S. L. Cooper. Mapping the magneto-structural quantum phases of Mn
_{3}O_{4}. Phys. Rev. Lett. 104, 136402 (2010). - B. Hsu, E. Grosfeld, and E. Fradkin. Quantum noise and entanglement generated by a local quantum quench. Phys. Rev. B 80, 235412 (2009). (Editor's Suggestion)
- B. M. Fregoso and E. Fradkin. Ferro-nematic ground state of the dilute dipolar Fermi gas. Phys. Rev. Lett. 103, 205301 (2009).
- E. Fradkin. Scaling of entanglement entropy at 2D quantum Lifshitz fixed points and topological fluids. J. of Phys. A 42, 504011 (2009). (Special issue on Entanglement Entropy: P. Calabrese, J. Cardy, and B. Doyon, editors)
- E. Berg, E. Fradkin, and S. A. Kivelson. Charge 4e superconductivity from pair density wave order in certain high temperature superconductors. Nature Physics 5, 830-833 (2009).
- E. Berg, E. Fradkin, S. A. Kivelson and J. M. Tranquada. Striped superconducting order: How the cuprtaes intertwine spin, charge, and superconducting orders. New J. of Phys. 11, 115004 (2009).
- B. M. Fregoso, K. Sun, E. Fradkin, and B. L. Lev. Biaxial nematic phases in ultracold dipolar Fermi gases. New J. of Phys. 11, 103003 (2009).
- K. Sun, H. Yao, E. Fradkin, and S. A. Kivelson. Topological insulators and nematic phases from spontaneous symmetry breaking in 2D Fermi systems with a quadratic band vrossing. Phys. Rev. Lett. 103, 046811 (2009).
- B. Hsu, M.l Mulligan, E. Fradkin, and E.-A. Kim. Universal entanglement entropy in two-dimensional conformal quantum critical points. Phys. Rev. B 79, 115421 (2009).
- E. Berg, E. Fradkin, and S. A. Kivelson. Theory of the striped superconductor. Phys. Rev. B 79, 064515 (2009). (Editor's Suggestion)
- K. Sun and E. Fradkin. Time reversal symmetry breaking and spontaneous anomalous Hall effect in Fermi fluids. Phys. Rev. B 78, 245122 (2008).
- K. Sun, B. M. Fregoso and E. Fradkin. Fluctuating stripes in strongly correlated electron systems and the nematic-smectic quantum phase transition. Phys. Rev. B. 78, 085124 (2008).
- E.-A. Kim, M. J. Lawler, P. Oreto, S. Sachdev, E. Fradkin, and S. A. Kivelson. Theory of the nodal nematic quantum phase transition in superconductors. Phys. Rev. B 77, 184514 (2008).
- S. Dong, E. Fradkin, R. G. Leigh, and S. Nowling, Topological entanglement entropy in Chern-Simons theories and quantum Hall fluids. J. of High Energy Phys. 2008 (5),016 (2008).
- S. Papanikolaou, K. S. Raman, and E. Fradkin. Topological phases and topological entropy of two-dimensional systems with finite correlation length. Phys. Rev. B 76, 224421(2007).
- E. Berg, E. Fradkin, E.-A. Kim, S. Kivelson, V. Oganesyan, J. M. Tranquada, and S. Zhang. Dynamical layer decoupling in a stripe-ordered high T
_{c}superconductor. Phys. Rev. Lett. 99, 127003 (2007). - S. Papanikolaou, E. Luijten, and E. Fradkin. Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models}. Phys. Rev. B 76, 134514 (2007).
- C. Wu, K. Sun, E. Fradkin, and S. Zhang. Fermi liquid instabilities in the spin channel. Phys. Rev. B 75, 115103 (2007).
- M. Lawler and E. Fradkin. Local quantum criticality in the nematic quantum phase transition of a Fermi fluid. Phys. Rev. B 75, 033304 (2007).
- E. Fradkin and J. E. Moore. Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum. Phys. Rev. Lett. 97, 050404-1-4 (2006).
- E.-A. Kim, M. Lawler, S. Vishveshwara, and Eduardo Fradkin. Measuring fractional charge and statistics in fractional quantum Hall fluids through noise experiments. Phys. Rev. B 74, 155324-1-23 (2006).
- M. Lawler, D. Barci, V. Fernandez, E. H. Fradkin, and L. Oxman. Non-perturbative behavior of the quantum phase transition to a nematic Fermi fluid. Phys. Rev. B 73, 085101(2006).
- P. Fendley and E. H. Fradkin. Realizing non-Abelian statistics in time-reversal-invariant systems. Phys. Rev. B 72, 024412-1-8 (2005).
- M. J. Lawler and E. H. Fradkin. Quantum Hall smectics, sliding symmetry, and the renormalization group. Phys. Rev. B 70, 165310-1-7 (2004).
- E. H. Fradkin, D. A. Huse, R. Moessner, V. Oganesyan, and S. L. Sondhi. Bipartite Rokhsar-Kivelson points and cantor deconfinement. Phys. Rev. B 69, 224415-1-8 (2004).
- E. Ardonne, P. Fendley, and E. H. Fradkin. Topological order and conformal quantum critical points. Ann. of Phys. 310, 493-551 (2004).
- S. A. Kivelson, I. P. Bindloss, E. Fradkin, V. Oganesyan, J. Tranquada, A. Kapitulnik, and C. Howald. How to detect fluctuating stripes in the high-temperature superconductors. Rev. Mod. Phys. 75, 1201-1241 (2003).
- S. A. Kivelson, D. H. Lee, E. H. Fradkin, and V. Oganesyan. Competing order in the mixed state of high-temperature superconductors. Phys. Rev. B 66, 144516-1-8 (2002).
- D. G. Barci and E. H. Fradkin. Theory of the quantum Hall smectic phase. II. Microscopic theory. Phys. Rev. B 65, 245320-1-19 (2002).
- R. Moessner, S. L. Sondhi, and E. H. Fradkin. Short-ranged resonating valence bond physics, quantum dimer models, and Ising gauge theories. Phys. Rev. B 65, 024504-1-16 (2001).
- E. H. Fradkin, V. Jejjala, and R. G. Leigh. Non-commutative Chern-Simons for the quantum Hall system and duality. Nucl. Phys. B 642, 483-500 (2002).
- V. Oganesyan, S. A. Kivelson, and E. H. Fradkin. Quantum theory of a nematic Fermi fluid. Phys. Rev. B 64, 195109-1-6 (2001).
- E. H. Fradkin, S. A. Kivelson, E. Manousakis, and K. Nho. Nematic phase of the two-dimensional electron gas in a magnetic field. Phys. Rev. Lett. 84, 1982-1985 (2000).
- E. H. Fradkin and S. A. Kivelson. Liquid-crystal phases of quantum Hall systems. Phys. Rev. B 59, 8065-8072 (1999).
- A. Lopez and E. H. Fradkin. Universal structure of the edge states of the fractional quantum Hall states. Phys. Rev. B 59, 15323-15331 (1999).
- E. H. Fradkin, C. Nayak, and K. Schoutens. Landau-Ginzburg theories for non-Abelian quantum Hall states. Nucl. Phys. B 546, 711-730 (1999).
- N. P. Sandler, C. C. C. Chamon, and E. H. Fradkin. Andreev reflection in the fractional quantum Hall effect. Phys. Rev. B 57, 12324-12332 (1998).
- E. H. Fradkin, C. Nayak, A. Tsvelik, and F. Wilczek. A Chern-Simons effective field theory for the Pfaffian quantum Hall State. Nucl. Phys. B 516, 704-718 (1998).
- S. A. Kivelson, E. H. Fradkin, and V. J. Emery. Electronic liquid-crystal phases of a doped Mott insulator. Nature 393, 550-553 (1998).
- H. E. Castillo, C. Chamon, E. H. Fradkin, P. M. Goldbart, and C. Mudry. Exact calculation of multifractal exponents of the critical wave function of Dirac fermions in a random magnetic field. Phys. Rev. B 56, 10668-10677 (1997).
- E. H. Fradkin and S. Kivelson. Modular invariance, self-duality and the phase transition between quantum Hall plateaus. Nucl. Phys. B 474, 543-574 (1996).
- A. H. Castro Neto and E. H. Fradkin. Bosonization of the low energy excitations of Fermi liquids. Phys. Rev. Lett. 72, 1393-1397 (1994).
- A. H. Castro Neto and E. H. Fradkin. Bosonization of Fermi liquids. Phys. Rev. B 49, 10877-10892 (1994).
- E. H. Fradkin and F. A. Schaposnik. The fermion-boson mapping in three-dimensional quantum field theory. Phys. Lett. B 338, 253-258 (1994).
- A. Lopez and E. H. Fradkin. Response functions and spectrum of collective excitations of fractional-quantum-Hall effect systems. Phys. Rev. B 47, 7080-7094 (1993).
- A. H. Castro Neto and E. H. Fradkin. The thermodynamics of quantum systems and generalizations of Zamolodchikov's C-theorem. Nucl. Phys. B 400, 525-546 (1993).
- E. H. Fradkin, E. F. Moreno, and F. A. Schaposnik. Ground-state wave functionals for (1 + 1)-dimensional fermion field theories. Nucl. Phys. B 392, 667-699 (1993).
- A. Lopez and E. H. Fradkin. Universal properties of the wave functions of fractional quantum Hall systems. Phys. Rev. Lett. 69, 2126-2129 (1992).
- E. H. Fradkin and F. A. Schaposnik. Chern-Simons gauge theories, confinement and the chiral spin liquid. Phys. Rev. Lett. 66, 276-279 (1991).
- A. Lopez and E. Fradkin. The fractional quantum Hall effect and Chern-Simons gauge theories. Phys. Rev. B 44, 5246 (1991).
- D. Withoff and E. H. Fradkin. Phase transitions in gapless Fermi systems with magnetic impurities. Phys. Rev. Lett. 64, 1835-1838 (1990).
- E. H. Fradkin and S. Kivelson. Short range resonating valence bond theories and superconductivity. Mod. Phys. Lett B [Rapid Commun. in High T
_{c}Superconductivity] 4, 225-232 (1990). - E. H. Fradkin. Jordan-Wigner transformation for quantum-spin systems in two dimensions and fractional statistics. Phys. Rev. Lett. 63, 322-325 (1989).
- E. Dagotto, E. H. Fradkin, and A. Moreo. SU(2) gauge invariance and order parameters in strongly coupled electronic systems. Phys. Rev B [Rapid Comm.] 38, 2926-2929 (1988).
- E. H. Fradkin and M. Stone. Topological terms in one and two-dimensional quantum Heisenberg antiferromagnets. Phys. Rev. B 38, 7215-7218 (1988).
- E. H. Fradkin, C. M. Naón, and F. A. Schaposnik. The complete bosonization of two-dimensional QCD in the path-integral framework. Phys. Rev. D 36, 3809-3812 (1987).
- F. Nori, Q. Niu, E. H. Fradkin, and S.-J. Chang. Superconducting-normal phase boundary of quasicrystalline arrays in a magnetic field. Phys. Rev. B 36, 8338-8342 (1987).
- E. H. Fradkin, E. Dagotto, and D. Boyanovsky. Physical realization of the parity anomaly in condensed matter physics. Phys. Rev. Lett. 57, 2967-2970 (1986).
- E. H. Fradkin. Critical behavior of disordered degenerate semiconductors. II: Spectrum and transport properties in mean field theory. Phys. Rev. B 33, 3263-3268 (1986).
- E. H. Fradkin. Critical behavior of disordered degenerate semiconductors. I: Models, symmetries and formalism. Phys. Rev. B 33, 3257-3262 (1986).
- M. P. A. Fisher and E. H. Fradkin. Localization in a magnetic field: Tight binding model with one-half of a flux quantum per plaquette. Nucl. Phys. B 251, 457-471 (1985).
- E. H. Fradkin. The roughening transition in quantum interfaces. Phys. Rev. B 28, 5338-5341 (1983).
- E. H. Fradkin and J. E. Hirsch. Phase diagram of one-dimensional electron-phonon systems I: The Su-Schrieffer-Heeger model. Phys. Rev. B 27, 1680-1697 (1983).
- J. E. Hirsch and E. H. Fradkin. Effects of quantum fluctuations on the Peierls instability: A Monte Carlo study. Phys. Rev. Lett. 49, 402-405 (1982).
- E. H. Fradkin and L. P. Kadanoff. Disorder variables and para-fermions in two-dimensional statistical mechanics. Nucl. Phys. B 170, 1-15 (1980).
- E. H. Fradkin and S. Shenker. Phase diagram of Lattice gauge theories with Higgs fields. Lattice Gauge Theories, 1979 (The Physical Society of Japan)) Phys. Rev. D 19, 3682-3697 (1980).
- E. H. Fradkin and L. Susskind. Order and disorder in gauge systems and magnets. Phys. Rev. D 17, 2637-2658 (1978).
- E. H. Fradkin, B. A. Huberman, and S. H. Shenker. Gauge symmetries in random magnetic systems. Phys. Rev. B 18, 4789-4812 (1978).

### Articles in Conference Proceedings

### Pending Articles

### Invited Lectures

- Invited speaker at the 2017 March Meeting of the American Physical Society, March 14, 2017. Title: "Nematic Order in Two-Dimensional Electronic Fluids in magnetic Fields''.
- Invited participant and speaker at the workshop "The Quantum Hall Effect: Past, Present and Future", Princeton Center for Theoretical Science, Princeton University, March 10, 2017. Title: "Nematic order in quantum Hall systems''.
- Invited participant and speaker at the workshop "Applied Newton-Cartan geometry", Simons Center for Geometry and Physics, Stony Brook, NY, March 6-10, 2017. Declined.
- Colloquium at the Department of Physics of the University of Illinois at Chicago, March 1, 2017. Title:"Intertwined orders in high temperature superconductors''.
- Invited speaker at the Max Planck Society-Argentina workshop "Frontiers in Physical Sciences", Buenos Aires (Argentina), November 16, 2016. Title: "Nematic Order in 2D Electronic Fluids.''
- Seminar at the Department of Physics of the University of Buenos Aires (Buenos Aires, Argentina), July 12, 2016. Title: ``Nematic order and geometry in fractional quantum Hall fluids''.
- Seminar at the Department pf Physics of the University of La Plata (La Plata, Argentina), July 11, 2016. Title: ``Chiral phases and magnetization plateaus in the frustrated spin-1/2 quantum Heisenberg antiferromagnet on the kagome lattice''.
- Seminar at the International Center for Advanced Study (ICAS), Universidad Nacional de San Martin (Argentina), July 6, 2016. Title:"Nematic order and the geometry of the quantum Hall liquids" (in Spanish).
- Seminar at Instituto de Fisica Balseiro, San Carlos de Bariloche (Rio Negro, Argentina), July 1, 2016. Title: ``Fractionalized Topological Insulators in 3D'' (in Spanish).
- Invited talk and Distinguished speaker at the workshop on Quantum Matter, Spacetime and Information, Yukawa Institute for Theoretical Physics, University of Kyoto, Japan, June 13-17, 2016. Title: "Finite universal terms in the entanglement entropy: new results for the quantum Lifshitz model".
- Invited talk at the Program on Geometry of Quantum Hall States at the Simons Center for Geometry and Physics of Stony Brook University, Stony Brook, NY, May 16, 2016. Title: ``The Nematic Fractional Quantum Hall State and the interplay of Geometry and Topology''.
- Co-organizer and speaker at the workshop on Intertwined Orders in Strongly Correlated Systems, Laguna Beach, California, January 29-31, 2016. Title: ``The case of the intertwined orders."
- Talk at the Joint Condensed Matter Theory Symposium of the Kadanoff Center for Theoretical Physics of the University of Chicago and the Institute for Condensed Matter Theory of the University of Illinois, Urbana, IL, April 2, 2016. Title: ``Nematic Order and geometry in the Fractional Quantum Hall Fluids".
- Condensed Matter Seminar, Department of Physics of the University of Illinois, Urbana, IL, February 12, 2016. Title: ``Pair-density-waves solve all your problems."
- Invited talk at the 2015 Emergent Phenomena in Quantum Systems (EPiQS) Initiative Investigator Symposium, August 4-7, Sausalito (CA). Title: "Pair-Density wave order in High Temperature Superconductors".
- Seminar at Instituto de Física Balseiro, San Carlos de Bariloche (RN, Argentina), July 3, 2015. Title: "Theory of the Nematic Fractional Quantum Hall State."
- Seminar at Instituto de Física Balseiro, San Carlos de Bariloche (RN, Argentina), July 2, 2015. Title: "Scaling behavior of the Entanglement Entropy in 2+1 Dimensions"
- Invited talk at the Condensed Matter Theory Meeting, University of La Plata (La Plata, Argentina), June 22, 2015. Title: "Theory of the Nematic Fractional Quantum Hall State".
- Invited Lecturer at the Canadian Institute for Fundamental and Applied Research (CIFAR) 2015 on Quantum Materials. May 4, 2015. Vancouver, British Columbia, Canada. Title: "Intertwined Orders in High Temperature Superconductors".
- Invited talk at the Program "Entanglement in Strongly-Correlated Quantum Matter", Kavli Institute for Theoretical Physics, University of California Santa Barbara. April 22, 2015. Title: "Scaling of Entanglement in 2+1 dimensional scale-invariant field theories".
- Seminar at the Department of Physics of Stanford University, Stanford, California. February 11, 2015. Title: "The Geometry of Fractional Quantum Hall Fluids".
- Colloquium at the Department of Physics of the University of Cincinnati, Cincinnati, Ohio. November 7, 2014. Title: "Intertwined Orders in High Temperature Superconductors".
- Seminar at the Department of Physics of the Massachusetts Institute of Technology, Cambridge, Massachusetts. November 17, 2014. Title: "Intertwined Orders in High Temperature Superconductors".
- Invited talk at the Program "Magnetism, Bad Metals and Superconductivity: Iron Pnictides and Beyond", Kavli Institute for Theoretical Physics, University of California Santa Barbara. September 4, 2014. Title: Intertwined Orders in High Temperature Superconductors.
- Invited talk at the Workshop "Correlations, Criticality and Coherence in Quantum Systems", Evora (Portugal) (October 6-10, 2014). Declined
- Invited talk at the Workshop "Geometric Aspects of Quantum States in Condensed Matter", held at the International Institute of Physics of the Universidad Federal de Rio Grande do Norte (Natal, Brazil), August 18-29, 2014. Declined.
- Seminar at the Departamento de Fisica, Universidad de Buenos Aires (Buenos Aires, Argentina) (August 15, 2014). Title: "Intertwined Orders in High temperature Superconductors"
- Seminar at the Departamento de Fisica of Universidad de La Plata (La Plata, Argentina) (August 14, 2014). Title: "The Geometry of the Quantum Hall Fluids"
- Member of the International Advisory Board of the International Conference in Low Temperature Physics LT27 (Buenos Aires, Argentina, August 6-13, 2014)
- Invited speaker and participant at the 2014 Summer Forum on Topology and Strong Correlation Physics, Institute for Advanced Study, Tsinghua University (Beijing, China) (June 23-July 18, 2014)
- Invited speaker at the Kivelson Fest Symposium on Strongly Correlated Electron Fluids, Stanford University, June 18-20, 2014.
- Invited talk at the workshop "Field Theoretic Computer Simulations for Particle Physics and Condensed Matter", Boston University (May 8-10, 2014). Title: "Effective Field Theory of Topological Insulators".
- Invited talk at the Stanford Workshop on Non-Fermi Liquids, Stanford CA (April 17-18, 2014). Title:"Nematic Quantum Criticality: A Bosonization Pespective"
- Invited talk at the 2014 March Meeting of the American Physical Society, Denver CO (March 3-7, 2014). Title:"High Temperature Superconductivity: Ineluctable Complexity."

### Conferences Organized or Chaired

- Co-organizer of the workshop on Intertwined Orders in Strongly Correlated Systems (Laguna Beach, CA), January 29-31, 2016.
- Co-organizer of the workshop on Geometrical Degrees of Freedom in Topological Phases at the Banff International Research Station (Banff, Alberta, Canada), August 21-26 (2016).
- Co-organizer of the Nobel Symposium 156, "New forms of matter: topological insulators and superconductors", Stockholm, Sweden (June 13-15, 2014).
- Co-organizer of the Workshop on Field Theoretic Computer Simulations for Particle Physics and Condensed Matter (8—10 May 2014), held at Boston University (Boston MA)
- Chair of the External Review Committee for the University of Kentucky Department of Physics. February 2014.
- Co-organizer of the Program "The Physics of Higher Temperature Superconductivity" at the Kavli Institute for Theoretical Physics, University of California, Santa Barbara. June 15-September 15, 2009.
- Co-organizer of the Conference "Critical Issues Related to Higher Temperature Superconductors", Kavli Insititute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, California, June 22-26, 2009
- Co-organizer of the Program on The Physics of Higher Temperature Superconductivity, Kavli Insititute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, California, Jun 15, 2009 - Sep 11, 2009
- Chair of the Invited panel (which I proposed) on the Current Status of the Theory of High Temperature Superconductors at the 2008 March Meeting of the American Physical Society.
- Organizer of the Workshop on Topological Phases in Condensed Matter, Institute of Condensed Matter Theory, University of Illinois, Urbana IL October 24-26, 2008
- Chair of the Invited panel (which I proposed) on Non-Abelian Fractional Statistics, the Fractional Quantum Hall Effect and Topological Quantum Computing at the 2006 March Meeting of the American Physical Society.
- Chair of the Invited Panel (which I proposed) on Entanglement and Quantum Criticality at the 2007 March Meeting of the American Physical Society.

### Honors

- Simons Distinguished Vising Scholar, Kavli Institute for Theoretical Physics (Santa Barbara, CA) (September 2014 and April 2015)
- Associate of the Center for Advanced Study (UIUC) (Spring 2015)
- Donald Biggar Willett Professor of Physics, department of Physics, University of Illinois at Urbana-Champaign (since 2014)
- Cesar Milstein Fellowship, Ministry of Science, Technology and Productive Innovation, Argentina, July 2007, June 2011 (July 2007, June 2011)
- Arnold O. Beckmann Award of the research Board of the University of Illinois (Academic Year 2006-2007)
- Fellow of the American Academy of Arts and Sciences (2009) (2009)
- Member, National Academy of Sciences, April 30, 2013 (2013)
- Simon Guggenheim Memorial Foundation Fellowship Award (1998) (1998)
- Fellow of the American Physical Society (1998) (1998)

### Teaching Honors

- Incomplete List of Teachers Ranked as Excellent by Their Students; Spring Semester 1996.