Journal Club for Condensed Matter Physics01 November 2020
Daniel Arovas (UC San Diego) was kind enough to recommend a recent paper by Anatoli Polkovnikov and me for the Journal Club for Condensed Matter Physics. The journal club presents A Monthly Selection of Interesting Papers by Distinguished Correspondents, and each recommendation is accompanied by a commentary. Read Daniel Arovas's commentary, titled A New Approach to the Classical-Quantum Correspondence, here — including some unpublished results!
I've been following this Journal Club for a while now and am always interested in their selection of papers, so I'm pretty proud of this!
Adiabatic Eigenstate Deformations in Phys. Rev. X23 October 2020
Our paper on Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos has just been published in Physical Review X! Including short blurb on the Physical Review X homepage. Find the article here.
Popular summary: Quantum chaos and ergodicity, which underlies all of statistical mechanics and thermodynamics, manifests itself in a vast range of phenomena. While researchers have developed powerful mathematical tools for understanding the emergence of chaos in quantum systems, the same cannot be said for probes that verify that the system is indeed chaotic. Although standard measures of quantum chaos exist, they are generally not very sensitive. We propose a sensitive probe for quantum chaos that is in line with both quantum and classical definitions of chaos.
To understand the emergence of chaos in quantum systems, researchers rely on the eigenstate thermalization hypothesis. Briefly, the hypothesis says that quantum chaos is encoded in the set of allowed energy states of a quantum system, as opposed to classical chaos which is expressed through exponential sensitivity of particle trajectories to initial conditions. Our proposed probe of quantum chaos blends both definitions by quantifying the sensitivity of allowed energy states to small perturbations. Using an appropriate measure, we can detect quantum chaos orders of magnitude before standard measures and extract information about nontrivial dynamics close to nonchaotic regimes. We use this probe to establish the existence of a regime separating nonchaotic and chaotic systems, characterized by a maximal sensitivity of allowed energy states and anomalously slow (exponentially long) relaxation times.
This work shows that there is a maximally susceptible regime separating chaotic and nonchaotic systems. Our measure can probe this regime, which is completely invisible to standard measures such as level-spacing statistics.
Constructing dual-unitary gates09 September 2020
Some follow-up work on dual-unitary circuits now on arXiv! Given a dual-unitary gate, we know exactly how to calculate its dynamical properties and we can classify all dynamics. However, so far it wasn't possible to systematically construct dual-unitary gates, such that most works were restricted to qubit systems or Hadamard gates. In the paper, titled Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension, we (perhaps not surprisingly) show how to construct dual-unitary gates for any dimension of the local Hilbert space with any desired level of ergodicity. We then also show how such systems relax to either an infinite-temperature Gibbs state or a generalized Gibbs ensemble, with an additional example on prethermalization. Joint work with Austen Lamacraft.
Dual-unitary quantum circuits can be used to construct 1+1 dimensional lattice models for which dynamical correlations of local observables can be explicitly calculated. We show how to analytically construct classes of dual-unitary circuits with any desired level of (non-)ergodicity for any dimension of the local Hilbert space, and present analytical results for thermalization to an infinite-temperature Gibbs state (ergodic) and a generalized Gibbs ensemble (non-ergodic). It is shown how a tunable ergodicity-inducing perturbation can be added to a non-ergodic circuit without breaking dual-unitarity, leading to the appearance of prethermalization plateaux for local observables.