Research

I am primarily a quantum condensed matter physicist with a focus on "strongly correlated" systems, although inevitably I also work on problems in classical statistical mechanics as do all members of my tribe. The term strongly correlated refers to materials in which the interactions among the electrons are important, even for a qualitative understanding of their behavior. This is in contrast to the textbook examples of metals, semiconductors and insulators, whose behavior is largely explicable in terms of independent electrons.

Currently, I am interested in the following problems:

Topological Phases: Phases of matter are defined by their boundaries which are loci of non-analyticity of the thermodynamic functions. The classical explanation of why there is more than one phase of a system with a given microscopics, due to Landau, is that the thermodynamic state of the system can break one or more symmetries. Via Landau's notion of an order parameter this leads to non-analyticities in the thermodynamics at a symmetry-breaking phase transition. A while back Wegner constructed the first spin models with phase transitions  but no breaking of symmetries. His models were, in subsequent parlance, lattice gauge theories with local symmetries. Starting with work on the fractional quantum Hall effect and on the cuprate superconductors there has been a growing recognition that condensed matter systems can give rise to an "emergent" gauge structure at low energies, i.e. unlike in Wegner's models it does not have to be built in at the ground level. With this insight it is clear that condensed matter systems can generally exhibit phases and phase transitions whose raison d'etre is not symmetry breaking. While the list of such "topological phases"  in experimental systems is currently small (fractional quantum Hall states, protons in ice obeying the Bernal-Fowler rules and superconductivity with electromagnetic interactions are examples) the list of models with such phases is growing rapidly. My own interest has centered around the "resonating valence bond" (RVB) state proposed by Anderson at about the same time as Wegner's work which turns out to be the simplest of the topological phases with an emergent Ising gauge field. In a series of papers my collaborators and I have demonstrated its existence in quantum dimer models and spin models and elucidated its description by a topological gauge theory.

High temperature Superconductivity: There is still no consensus on the microscopic origin of high temperature superconductivity in the cuprates and it remains an area of intense and active research. These are perhaps the most comprehensively studied materials in history and at issue is giving a coherent explanation of their entire phase diagram inclusive of antiferromagnetism, superconductivity,  the "pseudogap" region in between and a host of interesting temperature dependences. While my work on RVB theory bears on general theoretical questions in this area, my direct involvement has grown out of experiments carried out by my colleague Phuan Ong's group and is focused on understanding the effect of superconducting fluctuations on the physics of the cuprates outside the superconducting region. Specifically, my collaborators and I have provided a theoretical account of such fluctuations in the Nernst effect and in magnetization measurements.

Frustrated Magnetism: Classical frustrated magnets are primarily identified by large ground state degeneracies, the Ising antiferromagnet on a triangular lattice being the canonical example of this phenomenon and of the subclass of geometrically frustrated magnets. There is an increasing list of laboratory realizations of such systems, especially of the geometrically frustrated variety on lattices such as the kagome and pyrochlore. The challenge for theorists is to work out the statistical mechanics which is sensitive to the precise lattices and interactions at issue and can exhibit the phenomenon of "order by disorder" in which a non-trivial ordering is selected for entropic reasons. Further, interesting new physics can arise when quantum dynamics is introduced into these large ground state manifolds on account of the singular nature of the perturbation. Understanding quantum effects is important for laboratory realizations with small spins. My recent work in this area has covered the coupling between lattice and magnetic degrees of freedom in the pyrochlore system, the low temperature correlations of the same, the statistical mechanics of spin ice and the study of quantum Ising models on various frustrated lattices.

Quantum Phase Transitions: These are continuous phase transitions that take place at absolute zero, i.e., in the ground state of the system, when some parameter other than the temperature is varied. They are very interesting, for quantum effects are intrinsically important to them, most importantly in scrambling the dynamics with the thermodynamics. This leads to a host of new features, relative to their classical counterparts, which are an area of active research. I have worked on such transitions between quantum Hall states and most recently on the theory of non-linear transport in their proximity which ends up involving the Schwinger-Zener mechanism of vacuum breakdown .

Previously I have worked a fair amount on the fascinating physics of the quantum Hall effect and I retain an interest in that problem.

Quantum Hall Effect: Two-dimensional electron gases placed in high magnetic fields exhibit the quantum Hall Effect, which reflects an underlying intricate set of novel phases. The excitations in these phases have been of great interest for they are believed to carry fractional quantum numbers, i.e., charge and statistics. I've been interested in various aspects of these excitations--whether they carry a third fractional quantum number (an intrinsic spin), under what circumstances the various quantum numbers can be measured in the laboratory, and their internal structure in various limits.

For example, interesting variants of these excitations arise when the spin of the electrons can fluctuate. In some cases the excitations develop topologically nontrivial spin order ("skyrmions") as a consequence of geometric, or Berry, phases in the system. This led to questions about the role of these geometric phases near the edges of quantum Hall systems where yet another class of fascinating excitations lives ("edge states"), and other electronic systems where local spin order and conduction coexist.

As this page will not always be completely up-to-date, the best way to get a sense of my current research interests is to look up the recent ones among my papers posted on the cond-mat archive.

Some selected papers are listed here:

Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies (1993)

Off-Diagonal Long Range Order and Scaling in a Disordered Quantum Hall System (1994)

Evidence for Charge-Flux Duality near the Quantum Hall Liquid-to-Insulator Transition (1996)

Continuous quantum phase transitions (tutorial, 1997)

Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model (2001)

Phase structure of non-commutative scalar field theories (2001)

Gaussian Superconducting Fluctuations, Thermal Transport, and the Nernst Effect (2002)

Dipolar Spin Correlations in Classical Pyrochlore Magnets (2004)

SU (2)-invariant spin-1/2 Hamiltonians with RVB and other valence bond phases (2005)

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                                                             This site was last updated 01/24/08