My research seeks to develop a theoretical framework for describing the physics of novel quantum many particle systems by combining phenomenological modeling of experiments with abstract theoretical ideas and methods.

Much of conventional condensed matter physics is based on two crucial ideas which can both be traced to Landau. The first is the concept of an electron quasiparticle to characterize the low energy excitations of a quantum many electron system. The second is the concept of broken symmetry and the associated order parameter as an organizing principle to describe phases and phase transitions of macroscopic matter. In the last 30 years discoveries such as high temperature superconductivity and the fractional quantum Hall effect in condensed matter physics have shown the general inadequacy of these two basic concepts. Many fundamental questions have been raised and some answered. The primary focus of my research is in developing new paradigms capable of describing ‘exotic’ phases and phase transitions of quantum matter that violate one or both of Landau’s two celebrated ideas.

Some specific topics (and a brief description) that in recent years I have been interested in within this broad area are below.

**1. Non-fermi liquid metals**

A growing number of metals (most famously in the cuprate materials) do not fit the Landau fermi liquid paradigm. Though many basic questions about such non-Fermi liquid metals are open, there has been slow but steady progress over the years. My most recent contributions (primarily with Dominic Else) focus on clean non-fermi liquid metals whose ground states preserve the microscopic (lattice) translation symmetry. We described a number of general constraints on the low energy theory of such non-fermi liquid ground states that generalize the famiiliar Luttinger theorem satisfied by fermi liquids. My current explorations in this area are to develop a theory of non-fermi liquid fixed points with a sharp `critical Fermi surface’ without Landau quasiparticles.

In the past I described a number of concrete models of non-fermi liquid metals either at quantum critical points or as stable phases of matter. For instance, I (together with my collaborators M. Vojta and S. Sachdev) introduced the concept of a fractionalized Fermi liquid, and showed that its phase transition to an ordinary fermi liquid is an interesting non-fermi liquid critical point.

**2. Graphene moire structures**

A remarkable recent development in condensed matter physics is the observation (by my colleague Pablo Jarillo-Herrero, and by others) of strong correlation phenomena in graphene moire superlattices. These systems offer a highly tunable platform in which phenomena like interaction-driven insulators and superconductivity are seen. With several students and collaborators I have been studying diverse aspects of these systems. Early on our work established (see, eg, here, here, and here) that many of these moire materials bring together the themes of strong correlation and band topology. Our prediction that moire graphene is a good platform to obeerve ferromagnetism and the quantum anomalous Hall effect (i.e one that occurs at zero external magnetic field) have since received experimental confirmation. The general challenge of dealing with correlation effects in a partially filled topological band posed by these systems is a situation for which there is currently no really good conceptual framework.

**3. Non-Landau quantum criticality**

In the conventional theory of continuous phase transitions, critical properties are described by long wavelength, long time fluctuations of the Landau order parameter field. Over the years it has become clear that this paradigm fails for a number of quantum phase transitions. The simplest situation is if one of the phases is not captured correctly within the Landau order parameter framework (for instance it is topologically ordered or has other long range quantum entanglement). A more dramatic possibility is that of a Landau-forbidden quantum critical point separating two Landau-allowed phases. My collaborators and I initiated the theory of such phase transitions which show critical `deconfinement’ of fractionalized degrees of freedom. These `deconfined quantum critical points’ in bosonic systems provide (I hope!) guidance in my current attempts to describe metallic non-fermi liquid critical fixed points in electronic systems.

**4. Dualities in field theories of quantum many body systems**

Interacting systems with many degrees of freedom often admit two (or more) distinct - dual - descriptions of the same physics. Classic examples are the duality of the 2d Ising model, or the electric-magnetic duality of free Maxwell theory in 3 space dimensions. When available duality provides a powerful conceptual tool in thinking about the many body system/field theory. In quantum condensed matter physics, a famous example is the charge-vortex duality - discovered in the late 70s/early 80s - of interacting bosons in two space dimensions which has lead to many useful insights into correlated boson systems. In 2015, in two independent but simultaneous papers, Chong Wang and I as well as Max Metlitski and Ashvin Vishwanath, , found a version of this duality which applies to fermionic systems (with inspiration from a proposal by Son on a new description of composite fermions in the quantum Hall effect). In a subsequent paper, we (together with Seiberg and Witten) refined this original fermion-fermion duality, and showed that it was part of a large web of dualities of quantum field theories in 2+1-dimensions. In condensed matter physics, several applications of these developments have already been found (to the quantum hall effect, to quantum spin liquids, and to deconfined quantum critical points). See here for a review. I am actively further exploring duality phenomena and their applications to various other condensed matter problems.

**5. Interacting topological insulators**

A minimal generalization of the concept of topological insulators to interacting many particle systems is to states of matter known as Symmetry Protected Topological (SPT) phases. In common with the topological band insulators these states have a bulk gap and no exotic excitations but have non-trivial surface states that are protected by symmetry. A highlight of my work (with students Chong Wang and Andrew Potter) is a classification and description of spin-orbit coupled interacting electronic topological insulators in 3d. This built on my earlier work (with Ashvin Vishwanath) on the physics of interacting 3d bosonic topological insulators which, among other things, showed that the surface of many 3d SPT phases could be gapped while preserving the symmetries if it has topological order. My current interests are in identifying physical realizations of such phases.

**6. Quantum spin liquid insulators**

In electronic Mott insulators (in spatial dimension > 1), the electron spins often freeze into a magnetically ordered state at low temperature. An alternate possibility - a quantum spin liquid - was conceived and explored theoretically for more than two decades. The theoretical work shows that such a state is characterized by many novel properties such as the presence of fractional quantum numbers and the emergence of gauge forces. It is thus exciting to see the emergence in recent years of a number of candidate materials that are possibly in quantum spin liquid phases. My current research in this area has been in the direction of bringing the theory in contact with the ongoing experiments. I am specifically interested in describing effects in experiments that can serve to unambiguously identify the particular kind of spin liquid that may be realized in any given material. An example is a proposal (by student D. Mross and myself) of an experiment to identify a ‘ghost Fermi surface’ of electrically neutral particles that is hypothesized to exist in some of the candidate materials. An older example is my proposal of experiments to directly detect the topological order predicted to occur in some quantum spin liquid states. For a high level review I and some colleagues wrote on spin liquids, see here.

**7. Continuous Mott transitions**

The vicinity of the electronic Mott transition, where neither particle nor wave-like descriptions of the electron, are superior is a platform for some of the most striking phenomena in quantum many body physics. Despite this and despite decades of study the zero temperature electronic Mott transition remains poorly understood. A number of fundamental questions can be posed. Can they be continuous? What is the fate of the electronic Fermi surface as the Mott transition is approached? What is the spin physics in the Mott insulating side? The possibility of quantum spin liquid phases that have no magnetic ordering or other broken symmetries provides a great new opportunity for progress on these old and difficult problems. It enables focusing on the metal-insulator transition without the more usual complicated interplay with magnetism. Furthermore several of the experimental candidate spin liquid materials are close to pressure tuned Mott transitions to metallic phases. In 2008 I developed a concrete theory of a continuous zero temperature Mott transition in two dimensions from a Fermi liquid to a certain ‘gapless spin liquid’ Mott insulator. I continue to learn from this example and to search for other examples of continuous Mott transitions. Recent experiments on moire transition metal dichalcogenides seem to have observed continuous Mott transitions.

**8. Phenomenology of cuprate and related materials**

An ongoing effort is to synthesize theoretically diverse experiments on the cuprate and other novel materials, and decipher what they tell us about the underlying physics. Thinking about the phenomenology has proven to be a rich source of interesting conceptual questions, and is a driver of many of my other projects.

Click here for a full list of my publications (from the Los Alamos archives).

Slides of my recent conference talks can be found here.

Click here for slides of some lectures by Patrick Lee and me on the phenomenology of high Tc superconducting materials.