Scientific Series

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.

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.

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.

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.

Hawking's discovery of black holes radiance along with Bekenstein's conjecture of the generalized second law of thermodynamics inspired a conceptually pleasing connection between gravity, thermodynamics and quantum theory. However, the discovery that the spectrum of the radiation is in fact thermal, together with the no-hair theorem, has brought along with it some undesirable consequences, most notably the information loss paradox. There have been many proposals to the resolution of this paradox, with the most natural resolution being that during the time of collapse the radiation given off is not completely thermal and can carry small amounts of information with it. In this talk, we will revisit the so-called pre-Hawking radiation given off during the scenario of gravitational collapse by utilizing the so-called functional Schroedinger equation (FSE) and quantum kinetic equation (QKE). Here we find that the spectrum never becomes thermal and discuss the reasons for this. Finally we will discuss the implications of this result, as well as previous results, toward the resolution of the information paradox.

We construct the q-deformed spinfoam vertex amplitude using Chern-Simons theory on the boundary 3-sphere of the 4-simplex. The rigorous definition involves the construction of Vassiliev-Kontsevich invariant for trivalent knot graph. Under the semiclassical asymptotics, the q-deformed spinfoam amplitude reproduce Regge gravity with cosmological constant at nondegenerate critical configurations.

In general relativity, the fields on a black hole horizon are obtained from those in the bulk by pullback and restriction. In quantum gravity, it would be natural to obtain them in the same manner. This is not fully realized in the quantum theory of isolated horizons in loop quantum gravity, in which a Chern-Simons phase space on the horizon is quantized separately from the bulk. I will outline an approach in which the quantum horizon degrees of freedom are simply components of the quantized bulk degrees of freedom. A condition is imposed on the quantum states to encode the existence of a horizon. I will present evidence that solutions to this condition have properties on the horizon that are remarkably similar to those of Chern-Simons theory. Instrumental in formulating the horizon condition are novel flux operators that use the Duflo isomorphism and seem to represent some type of quantum deformed SU(2). I will review their definition and summarize what I know about their properties.

It's usually assumed that youtube is just for kittens, babies, and music videos. However, youtube is also the highest-traffic site on the internet and it turns out it's actually a darn good place to teach people about physics! We'll start with the story and analysis of how my video series Minutephysics grew from a fun project to a youtube channel with 120,000 subscribers and 9 million views in just a few months, then discuss how media & technology (especially videos) can facilitate good (and bad) communication, and finally talk about how you can harness the power of the internet in your own physics outreach. And of course we'll watch a few cool videos along the way. As a primer, feel free to check out www.youtube.com/minutephysics

The experimental violation of Bell inequalities using spacelike separated measurements precludes the explanation of quantum correlations through causal influences propagating at subluminal speed. Yet, it is always possible, in principle, to explain such experimental violations through models based on hidden influences propagating at a finite speed v>c, provided v is large enough. Here, we show that for any finite speed v>c, such models predict correlations that can be exploited for faster-than-light communication. This superluminal communication does not require access to any hidden physical quantities, but only the manipulation of measurement devices at the level of our present-day description of quantum experiments. Hence, assuming the impossibility of using quantum non-locality for superluminal communication, we exclude any possible explanation of quantum correlations in term of finite-speed influences.

We consider the effect of an in-plane current on the magnetization dynamics of a quasi-two-dimensional spin-orbit coupled nanoscale itinerant ferromagnet. By solving the appropriate kinetic equation for an itinerant electron ferromagnet, we show that Rashba spin-orbit interaction provides transport currents with a switching action, as observed in a recent experiment (I. M. Miron et al., Nature 476, 189 (2011)). The dependence of the effective switching field on the magnitude and direction of an external magnetic field in our theory agrees well with experiment.

The partition function on the three-sphere of many supersymmetric Chern-Simons-matter theories reduces, by localization, to a matrix model. In this talk I will describe a new method to study these models in the M-theory limit, but at all orders in the 1/N expansion. The method is based on reformulating the matrix model as the partition function of a Fermi gas. This new approach leads to a completely elementary derivation of the N^{3/2} behavior for ABJM theory and other quiver Chern-Simons-matter theories. In addition, the full series of 1/N corrections to the original matrix integral can be simply determined by a next-to-leading calculation in the semiclassical expansion of the quantum gas.