Talks

Searching for a proper set of order parameters which distinguishes different phases of matter sits in the heart of condensed matter physics. In this talk, I discuss topological invariants as (non-local) order parameters for symmetry protected topological (SPT) phases of fermions in the presence of time-reversal symmetry. It turns out that topological invariants provide a natural definition for the partial transpose of density matrices. The partial transpose can then be used to define an entanglement measure (analog of entanglement negativity) for mixed states of fermions. I will show that this quantity captures the mixed state entanglement in fermionic SPTs as well as in a system of free fermions with a Fermi surface.

Conventional equations of state suggest that in complete gravitational collapse a singular state of matter with infinite density could be reached finally to a black hole, the characteristic feature of which is its apparent horizon, where light rays are first trapped. The loss of information to the outside world this implies gives rise to serious difficulties with well-established principles of quantum mechanics and statistical physics.

The formation of a gravitational vacuum condensate star with a p=−ρ interior solves these problems and remarkably, actually follows from Schwarzschild's second paper over a century ago. The surface tension of the condensate star surface is the difference of equal and opposite surface gravities between the exterior and interior Schwarzschild solutions. The First Law is then recognized as a purely mechanical classical relation at zero temperature and zero entropy. The Schwarzschild time of such a non-singular gravitational condensate star is a global time, fully consistent with unitary time evolution in quantum theory.

The advent of BH imaging by the EHT and Gravitational Wave Astronomy with LIGO should allow for observational tests of the gravastar hypothesis, particularly in the discrete surface modes of oscillation and GW resonances or “echoes,” which may be observable by advanced LIGO and successor GW detectors.

Classical chaotic systems exhibit exponential divergence of initially infinitesimally close trajectories, which is characterized by the Lyapunov exponent. This sensitivity to initial conditions is popularly known as the  "butterfly effect." Of great recent interest has been to understand how/if the butterfly effect and Lyapunov exponents generalize to quantum mechanics, where the notion of a trajectory does not exist. In this talk, I will introduce the measure of quantum chaoticity  – a so-called out-of-time-ordered four-point correlator (whose semiclassical limit reproduces classical Lyapunov growth), and use it to describe quantum chaotic dynamics and its eventual disappearance in the standard models of classical and quantum chaos – Bunimovich stadium billiard and standard map or kicked rotor [1]. I will describe our recent results on the quantum Lyapunov exponent in these single-particle models as well as results in interacting many-body systems, such as disordered metals [2]. The latter many-body model exhibits an interaction-induced transition from quantum chaotic to non-chaotic dynamics, which may manifest itself in a sharp change of the distribution of energy levels from Wigner-Dyson to Poisson statistics. I will conclude by formulating a many-body analogue of the Bohigas-Giannoni-Schmit conjecture.
References:
[1] "Lyapunov exponent and out-of-time-ordered correlator's growth rate in a chaotic system,"  E. Rozenbaum, S. Ganeshan, and V. Galitski, Physical Review Letters 118, 086801 (2017)
[2] "Non-linear sigma model approach to many-body quantum chaos," Y. Liao and and V. Galitski, arXiv:1807.09799

Dr. Avery Broderick will provide a highly accessible and interesting lecture on the Event Horizon Telescope (EHT) and international efforts to interpret horizon-resolving images of numerous supermassive black holes. Black holes are among the most powerful and mysterious phenomena in the universe. Almost every galaxy has at its core a supermassive black hole, millions or even billions of times more massive than our sun. Despite composing a small fraction of the galactic mass budgets, they set the stage for astrophysical dramas that dictate the fates of their hosts. Though black holes are in theory the ultimate manifestation of strong gravity’s impact on the visible universe, placing these exotic phenomena on concrete empirical footing has been impossible - until now.

I will present a method for the implementation of a universal set of fault-tolerant logical gates using homological product codes. In particular, I will show how one can fault-tolerantly map between different encoded representations of a given logical state, enabling the application of different classes of transversal gates belonging to the underlying quantum codes. This allows for the circumvention of no-go results pertaining to universal sets of transversal gates and provides a general scheme for fault-tolerant computation while keeping the stabilizer generators of the code sparse.

Recently there have been several proposals of low-energy precision experiments that can search for new particles, new forces, and the Dark Matter of the Universe in a way that is complementary to collider searches. In this talk, I will present some examples involving atomic clocks, nuclear magnetic resonance, and astrophysical black holes accessible to LIGO.

Entanglement spectrum (ES) contains more information than the entanglement entropy, a single number. For highly excited states, this can be quantified by the ES statistics, i.e. the distribution of the ratio of adjacent gaps in the ES. I will first present examples in both random unitary circuits and Hamiltonian systems, where the ES signals whether a time-evolved state (even if maximally entangled) can be efficiently disentangled without precise knowledge of the time evolution operator. This allows us to define a notion of entanglement complexity that is not revealed by the entanglement entropy.

In the second part, I will discuss how quantum states are scrambled via braiding in systems of non-Abelian anyons through the lens of ES statistics. We define a distance between the entanglement level spacing distribution of a state evolved under random braids and that of a Haar-random state, using the Kullback-Leibler divergence $D_{\mathrm{KL}}$. We study $D_{\mathrm{KL}}$ numerically for random braids of Majorana fermions (supplemented with random local four-body interactions) and Fibonacci anyons. Our results reveal a hierarchy of scrambling among various models --- even for the same amount of entanglement entropy --- at intermediate times, whereas all models exhibit the same late-time behavior. In particular, we find that braiding of Fibonacci anyons scrambles more efficiently than the universal H+T+CNOT set. Our results promote $D_{\mathrm{KL}}$ as a quantifiable metric for scrambling and quantum chaos, which applies to generic quantum systems.

Most current dark matter detection strategies, including both direct and indirect efforts, are based on the assumption that the galactic dark matter number density is quite high, allowing for the detection of rare scattering events. Such a paradigm arises naturally if the dark matter self-interactions are weak. However, strong interactions within the dark sector can give rise to large composite objects, whose detection requires a different experimental paradigm. We call these object Dark Blobs. In such theories, the energy transfer due to a single collision with a Standard Model particle tends to be small, below the energy threshold of many nuclear recoil experiments. Fortunately, due to their exponentially large composite nature, the interactions between these objects and a terrestrial detector can be coherently enhanced. Therefore, while the effect on a single probe is small, the large collective effect can be quite dramatic and, importantly, above experimental thresholds. In this talk, I will briefly motivate the early Universe formation of certain types of Dark Blobs and then focus on multiple detection avenues for these objects.

This talk will explore the applications of the computing power of numerical relativity to gravitational theories beyond general relativity. Specifically, I will consider dynamical Chern-Simons gravity, which has roots in string theory and loop quantum gravity. I will discuss our  formalism and efforts to simulate binary black holes in this theory to generate waveforms LIGO and LISA. Additionally, I will discuss the generation of numerical black hole solutions in this theory, and applications to probing black hole shadows with the Event Horizon Telescope.