Search Talks

Quantum Hall phases are the most exotic experimentally established quantum phases of matter.Recently they have been discovered at zero external magnetic field in two dimensional moire materials. I will describe recent work (with Xue-Yang Song and Ya-Hui Zhang) on their proximate phases and associated phase transitions that is motivated by the high tunability of thede moire systems. These phase transitions (and some of the proximate phases) are exotic as well, and realize novel ‘beyond Landau’ criticality that have been explored theoretically for many years. I will show that these moiré platforms provide a great experimental opportunity to study these unconventional phase transitions and related unconventional phases, thereby opening a new direction for research in quantum matter.

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Zoom link : https://pitp.zoom.us/j/97483204701?pwd=S2x4ck9tNHFjM0RiTDNWNFhaMk9SUT09

The interplay between topology, strong correlations, and kinetic energy presents a new challenge for the theory of quantum matter. In this talk I will describe some recent progress on understanding a simple class of problems where these effects can all be analytically handled. I will first present results on a microscopic lowest Landau theory of the composite fermi liquid state of bosons at filling 1.  Building on work from the 1990s I will derive an effective field theory for this system that takes the form of a non-commutative field theory. I will show that an approximate mapping of this theory to a commutative field theory yield the familiar Halperin-Lee-Read action but with parameters correctly described by the interaction strength. I will describe the effect of a finite bandwidth  introduced to the Landau Level and describe the evolution between the composite Fermi liquid and a boson superfluid. Time permitting, I will describe some generalizations that will include the evolution between a Quantum Anomalous Hall state and a Landau Fermi liquid that may be experimentally accessible in moire graphene systems.

The study of strongly  interacting quantum matter has been at the forefront of condensed matter research in the last several decades. An independent development is the discovery of topological band insulators.  In this talk I will  describe phenomena that occur at the confluence of topology and strong interactions. I will first discuss  how insights from the study of the relatively simple topological insulators are revolutionizing our theoretical understanding of more complex quantum many body systems.  Next I will describe some experimental situations in which both band topology and strong correlations are present, the resulting novel phenomena, and the theoretical challenges they present.

I will present recent results (with Zhen Bi) on novel quantum criticality and a possible field theory duality in 3+1 spacetime dimensions. We describe several examples of Deconfined Quantum Critical Points (DQCP) between Symmetry Protected Topological phases in 3 + 1-D.   We present situations in which the same phase transition allows for multiple universality classes controlled by distinct fixed points. We exhibit the possibility - which we dub “unnecessary quantum critical points” - of stable generic continuous phase transitions within the same phase. We present examples of interaction driven band-theory- forbidden continuous phase transitions between two distinct band insulators. The understanding we develop leads us to suggest an interesting possible 3 + 1-D field theory duality between SU(2) gauge theory coupled to one massless adjoint Dirac fermion and the theory of a single massless Dirac fermion augmented by a decoupled topological field theory.