How is a Red Giant formed and how long does it take for a star to reach the Red Giant stage?

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.

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.

Explanation of the experimentally observed dynamical layer decoupling in high temperature superconductors as a manifestation of a novel superconducting state, the pair density wave state. A key consequence of this result is the prediction of the existence of half vortices in this system and of charge 4e superconducting order.

A theory of topological insulators due to electron-electron interactions.

Theory of the universal behavior of the entanglement entropy at a class of non-trivial quantum critical points in two space dimensions.

Theory of metallic phases with spontaneous breaking of time reversal invariance.

Nematic and Ferro-Nematic phases in ultra-cold dipolar Fermi gases.

Theory of the nematic-smectic (stripe) quantum critical point.

- Cesar Milstein Fellowship, Ministry of Science, Technology and Productive Innovation, Argentina, July 2007, June 2011
- Fellow of the American Academy of Arts and Sciences (2009)
- Elected Member, National Academy of Sciences, April 30, 2013
- Fellow of the American Physical Society (1998)

**Fall 2000:**PHYS 498 (*outstanding*)

- E. H. Fradkin. Field Theories of Condensed Physics. 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).
- 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).
- 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 NaĆ³n, 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).
- 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).
- B. Fregoso and E. Fradkin. Unconventional magnetism in imbalanced Fermi systems with magnetic dipolar interactions. Phys. Rev. B 81, 214443 (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).
- D. S. Caplan, V. Orlyanchik, M. B. Weissman, D. J. Van Harlingen, E. H. Fradkin, M. J. Hinton, and T. R. Lemberger. Anomalous noise in the pseudogapregime of YBa_2Cu_3O_{7-delta}. Phys. Rev. Lett. 104, 177001 (2010).
- S. A. Kivelson and E. Fradkin. Fluctuation diamagnetism in high temperature superconductors. Viewpoint invited article. Phys. 3, 15 (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). - E. Fradkin and S. A. Kivelson. Electron nematics proliferate. "Perspectives" invited article, Science 327, 155 (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 Choice)
- 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).
- K. Sun and E. Fradkin. Time reversal symmetry breaking and spontaneous anomalous Hall effect in Fermi fluids. Phys. Rev. B 78, 245122 (2008).
- H. Barath, M. Kim, S. L. Cooper, P. Abbamonte, E. Fradkin, I. Mahns, M. Rubhausen, N. Aliouane, and D. N. Argyriou, Domain fluctuations near the field-induced incommensurate-commensurate phase transition of TbMnO3. Phys. Rev. B 78, 134407 (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).
- D. Schuricht, F. Essler, A. Jaefari, and E. Fradkin. Local density of states of 1D Mott insulators and CDW states with a boundary. Phys. Rev. Lett. 101, 086403 (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).
- M. Kim, H. Barath, S. L. Cooper, P. Abbamonte, E. Fradkin, M. Rubhausen, C. L. Zhang, and S.-W. Cheong. Raman scattering studies of temperature- and field-induced melting of charge order in (La,Pr,Ca)MnO3. Phys. Rev. B 77, 134411 (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), (2008).
- E. Fradkin. Quantum physics: Debut of the quarter electron (News & Views article in Nature). Nature 452, 822-823 (2008).
- H. Barath, M. Kim, J. F. Karpus, S. L. Cooper, P. Abbamonte, E. Fradkin, E. Morosan, and R. J. Cava, Quantum and classical mode softening near the charge-density-wave/superconductor transition of Cu_x Ti Se_2: Raman spectroscopic studies. Phys. Rev. Lett. 100, 106402 (2008).
- S. Papanikolaou, R. M. Fernandes, E. Fradkin, P. W. Phillips, J. Schmalian, and R. Sknepnek. Universality of liquid-gas Mott transitions at finite temperatures. Phys. Rev. Lett. 100, 026408 (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. Chamon, E. Fradkin, and A. Lopez. Fractional statistics and duality: strong coupling behavior of edge states of quantum Hall liquids in the Jain sequence. Phys. Rev. Lett. 98, 176801 (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).
- 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, 085101-1-19 (2006).
- E.-A. Kim, M. Lawler, S. Vishveshwara, and E. H. Fradkin. Signatures of fractional statistics in noise experiments in quantum Hall fluids. Phys. Rev. Lett. 95, 176402-1-4 (2005).
- P. Fendley and E. H. Fradkin. Realizing non-Abelian statistics in time-reversal-invariant systems. Phys. Rev. B 72, 024412-1-8 (2005).
- S. A. Kivelson, E. H. Fradkin, and T. H. Geballe. Quasi-one-dimensional dynamics and Nematic phases in the two-dimensional Emery model. Phys. Rev. B 69, 144505-1-7 (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).
- 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).
- V. Oganesyan, S. A. Kivelson, and E. H. Fradkin. Quantum theory of a nematic Fermi fluid. Phys. Rev. B 64, 195109-1-6 (2001).
- V. J. Emery, E. H. Fradkin, S. A. Kivelson, and T. C. Lubensky. Quantum theory of the smectic metal state in stripe phases. Phys. Rev. Lett. 85, 2160-2163 (2000).
- E. H. Fradkin, C. Nayak, and K. Schoutens. Landau-Ginzburg theories for non-Abelian quantum Hall states. Nucl. Phys. B 546, 711-730 (1999).
- 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).
- E. H. Fradkin, M. Srednicki, and L. Susskind. Fermion representation for the Z
_{2}lattice gauge theory in 2 + 1 dimensions. Phys. Rev. D 21, 2885-2891 (1980). - 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 S. Raby. Real space renormalization-group scheme for spin and gauge systems. Phys. Rev. D 20, 2566-2582 (1979).
- 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).
- E. H. Fradkin and T. P. Eggarter. Ising models with several phase transitions. Phys. Rev. A 14, 495-499 (1976).
- Eduardo Fradkin, "Electronic Liquid Crystal Phases in Strongly Correlated Systems", in Proceedings of the Les Houches Summer School on "Modern theories of correlated electron systems", Les Houches, Haute Savoie, France (May 2009), Daniel C. Cabra, Andreas Honecker, and Pierre Pujol, editors, Lecture Notes in Physics 843, Springer-Verlag Berlin Heidelberg (2012).

**Office**

2119 Engineering Sciences Building

**Phone**

217.333.4409

**Fax**

217.244.7704

**Email**

efradkin@illinois.edu

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