Talks

Entanglement in quantum many-body systems is typically fragile to interactions with the environment. Generic unital quantum channels, for example, have the maximally mixed state with no entanglement as their unique steady state. However, we find that for a unital quantum channel that is `strongly symmetric', i.e. it preserves a global on-site symmetry, the maximally mixed steady state in certain symmetry sectors can be highly entangled. For a given symmetry, we analyze the entanglement and correlations of the maximally mixed state in the invariant sector (MMIS), and show that the entanglement of formation and distillation are exactly computable and equal for any bipartition. For all Abelian symmetries, the MMIS is separable, and for all non-Abelian symmetries, the MMIS is entangled. Remarkably, for non-Abelian continuous symmetries described by compact semisimple Lie groups (e.g. SU(2)), the bipartite entanglement of formation for the MMIS scales logarithmically ∼logN with the number of qudits N.

The description of a quantum many-body system lacking quasiparticles is a longstanding challenge at the forefront of physics. A solvable example is provided by the Sachdve-Ye-Kitaev (SYK) model, which has attracted much attention due to its intriguing connections to black holes and intertwined questions on non-Fermi liquid metals, thermalization, and many-body quantum chaos. After a brief review of the phenomenology of Fermi (FL) and non-Fermi (NFL) liquids, I will give a pedagogical introduction to the large-N saddle-point method, spectral and thermodynamics properties, and the computation of the out-of-time-ordered correlation and Lyapunov exponent in the SYK model. I will then discuss a few generalizations/extensions of the SYK model with NFL-FL and other dynamical transitions. I will conclude with a discussion of an experimental realization of the SYK model in condensed matter systems. 

In this talk, I will discuss the current effort of creating emulators for the non-linear power spectrum in beyond-LCDM models. I will present a pipeline that has been developed to model the matter power spectrum from large to small scales, with a focus on stage-IV photometric galaxy surveys. I will delve into the fundamental components of this pipeline, the consistency checks performed to validate it, and how effectively this new tool performs when conducting a full Bayesian parameter estimation analysis with a survey similar to LSST.

Fermi's Golden Rule (FGR) applies in the limit where an initial quantum state is weakly coupled to a continuum of other final states overlapping its energy. In this seminar I will discuss what happens away from this limit, where the set of final states is discrete, with a nonzero mean level spacing. This question arises, for example, in the context of thermalization of closed many-body quantum systems when the many body localized phase becomes unstable to avalanches. After a brief motivation, I will discuss for different symmetry classes, the universal crossovers in the average decay of the initial state as the level spacing is varied, with the Golden Rule emerging in the limit of a continuum. Among the corrections to the exponential decay of the initial state given by FGR is the appearance of the spectral form factor in the long-time regime for small but nonzero level spacing. 

We will discuss connections between quantum relative entropy and other distance measures between probability distributions and quantum states. We will discuss the connection to hypothesis testing. If there is time, we will present applications of classical and quantum information theory to problems in combinatorics and computer science.