Condensed Matter

Recent years have seen a renewed interest, both theoretically and experimentally, in the search for topological states of matter. On the theoretical side, while much progress has been achieved in providing a general classification of non-interacting topological states, the fate of these phases in the presence of strong interactions remains an open question. The purpose of this talk is to describe recent developments on this front. In the first part of the talk, we will consider, in a scenario with time-reversal symmetry breaking, dispersionless electronic Bloch bands (flatbands) with non-zero Chern number and show results of exact diagonalization in a small system at 1/3 filling that support the existence of a fractional quantum Hall state in the absence of an external magnetic field. In the second part of the talk, we will discuss strongly interacting electronic phases with time-reversal symmetry in two dimensions and propose a candidate topological field theory with fractionalized excitations that describes the low energy properties of a class of time-reversal symmetric states.

The description of non-Fermi liquid metals is one of the central problems in the theory of correlated electron systems. I present a holographic theory which builds on general features of the thermal entropy density and the entanglement entropy. Remarkable connections emerge between the holographic approach, and the postulated strong-coupling behavior of the field-theoretic approach.

Although the typical physical system achieves an ordered state at low temperatures, spin liquids stay disordered even in their ground state. In addition to an increasing number of experimental candidates for spin liquids, recent numerical work from Meng, et. al and Yan, et. al. has supplied strong numerical evidence for natural Hamiltonians having spin liquid ground states. Their featureless nature, though, makes  learning about these states particularly difficult. In this talk, we explore what variational ansatz can teach us about them. Additionally, we examine whether the canonical theoretical framework makes sense in the context of the best wave-functions. Finally, we look at what other tools we have to make sense of spin liquids.

The entanglement spectrum denotes the eigenvalues of the reduced density matrix of a region in the ground state of a many-body system. Given these eigenvalues, one can compute the entanglement entropy of the region, but the full spectrum contains much more information. I will review geometric methods to extract this spectrum for special subregions in lorentz and conformally invariant field theories (and any theory whose universal low energy physics is captured by such a field theory). Using this technology, I give a new proof that the entanglement spectrum in quantum hall states is the same as that of a physical edge. I will discuss a number of other applications of the formalism, including, if there is time, a more complicated calculation of universal terms in the entanglement entropy at certain deconfined quantum critical points. The ultimate messages are that geometry is intimately bound up with entanglement and that the entanglement cut should be viewed as a physical cut.