Eduardo H Fradkin

Professor

Ph.D. - Physics, Stanford University, 1979

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.

Other Activities

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.

Additional Information

During the 2008-2009 Academic Year Professor Fradkin and his group obtained a number of important results:

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.

For more information:

Eduardo Fradkin's personal website

Honors and awards:

• Fellow of the American Academy of Arts and Letters (2009)
• Arnold O. Beckmann Award of the research Board of the University of Illinois
• Simon Guggenheim Memorial Foundation Fellowship Award (1998)
• Fellow of the American Physical Society (1998)

Selected Publications:

• Benjamin Hsu, Michael Mulligan, Eduardo Fradkin and Eun-Ah Kim. Universal behavior of the entanglement entropy in 2D conformal quantum critical points. Phys. Rev. B 79, 115421 (2009).
• Erez Berg, Eduardo Fradkin and Steven A. Kivelson. Theory of the striped superconductor. Phys. Rev. B 79, 064515 (2009).
• Kai Sun and Eduardo Fradkin, Time reversal symmetry breaking and spontaneous anomalous Hall effect in Fermi fluids. Phys. Rev. B 78, 245122 (2008).
• Kai Sun, Benjamin M. Fregoso and Eduardo Fradkin. Fluctuating stripes in strongly correlated electron systems and the nematic-smectic quantum phase transition. Phys. Rev. B. 78, 085124 (2008).
• Erez Berg, Eduardo Fradkin, Eun-Ah Kim, Steven Kivelson, Vadim Oganesyan, John M. Tranquada, and Shoucheng Zhang. Dynamical layer decoupling in a stripe-ordered high $T_c$ superconductor. Phys. Rev. Lett. 99, 127003 (2007).
• Eduardo Fradkin and Joel 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. Fernández, 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).
• Eun-Ah 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).
• Steven A. Kivelson, Ian P. Bindloss, Eduardo Fradkin, Vadim Oganesyan, John Tranquada, Aharon Kapitulnik and Craig 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 (2002).
• 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, 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).