Talks

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 scaling of entanglement entropy, and more recently the full entanglement spectrum, have become useful tools for characterizing certain universal features of quantum many-body systems. Although entanglement entropy is difficult to measure experimentally, we show that for systems that can be mapped to non-interacting fermions both the von Neumann entanglement entropy and generalized Renyi entropies can be related exactly to the cumulants of number fluctuations, which are accessible experimentally. Such systems include free fermions in all dimensions, the integer quantum Hall states and topological insulators in two dimensions, strongly repulsive bosons in one-dimensional optical lattices, and the spin-1/2 XX chain, both pure and strongly disordered. The same formalism can be used for analyzing entanglement entropy generation in quantum point contacts with non-interacting electron reservoirs. Beyond the non-interacting case, we show that the scaling of fluctuations in one-dimensional critical systems behaves quite similarly to the entanglement entropy, and in analogy to the full counting statistics used in mesoscopic transport, give important information about the system. The behavior of fluctuations, which are the essential feature of quantum systems, are explained in a general framework and analyzed in a variety of specific situations.

Entanglement is a paradigmatic example of quantum correlations, a presumed reason for the superior performance of quantum computation and an obvious divider of states and processes into classical and quantum. In the last decade all these notions were challenged. Entanglement does not capture the totality of non-classical behavior. Quantum discord (in its different versions) is a more general measure of quantum correlations. It can be related to the advantage in some tasks like the extraction of work from a Szilrad heat engine using Maxwell's demons with various resources. The discord turns out to be the difference between the work extracted from a given bipartite system using a a global and a local strategy. Different strategies relate to different definitions of discord, but all definitions agree on zero, so "classical" systems are universal to all heat engines. One way of identifying a task as quantum or classical is by examining the quantum resources required to implement it. This can be done by examining the entanglement required for a LOCC implementation of the task. Creation (or non-creation) of entanglement as a result of its implementation is not enough to identify these resources. An example is a bi-local implementation of an entangling quantum gate (C-NOT) by LOCC with unentagled input and output states. This lack of entanglement does not guarantee the LOCC implementability. A method to determine if entanglement resources are required is to track the change in quantum discord during the process.

The multiscale entanglement renormalization ansatz can be reformulated in terms of a causality constraint on discrete quantum dynamics. This causal structure is that of de Sitter space with a flat spacelike boundary, where the volume of a spacetime region corresponds to the number of variational parameters it contains.

Violation of unitarity in black hole evaporation has been puzzling physicist since the seminal work of Hawking in the seventies. Although there are hopes for a resolution of the problem in a full theory of quantum gravity, it has eluded us so far. Even less ambitious efforts considering only quantum corrections beyond the external field approximation have proven hard to attack in 4 dimensions. All these obstacles directed researchers to investigate the black hole evaporation problem in simpler 2-dimensional models. In this talk, we will present results on a new investigation of one of these models, the 2-dimensional Callan-Giddings-Harvey-Strominger (CGHS) model. Using a combination of analytical and high precision numerical tools, we are able to resolve CGHS black hole evaporation within the mean field approximation all the way to the point where the black hole area vanishes. Our results confirm some of the assumptions of the standard paradigm, and strongly suggest the recovery of unitarity within the full quantum theory. On the other hand, there are several surprising new results, in particular remarkable universal behavior in the evaporation of initially macroscopic black holes. This suggests that information about the collapsing matter that formed the black hole can not be recovered from the evaporation radiation. Though this separation of the questions of information loss and unitarity is peculiar to the 2-dimensional model, insights into the higher dimensional case can still be garnered. Details of the numerical methods used will also be discussed.