Probability transport on the Fock space of a disordered quantum spin chain

Abstract

Within the broad theme of understanding the dynamics of disordered quantum many-body systems, one of the simplest questions one can ask is: given an initial state, how does it evolve in time on the associated Fock-space graph, in terms of the distribution of probabilities thereon? A detailed quantitative description of the temporal evolution of out-of-equilibrium disordered quantum states and probability transport on the Fock space, is our central aim here. We investigate it in the context of a disordered quantum spin chain which hosts a disorder-driven many-body localisation transition. Real-time dynamics/probability transport is shown to exhibit a rich phenomenology, which is markedly different between the ergodic and many-body localised phases. The dynamics is for example found to be strongly inhomogeneous at intermediate times in both phases, but while it gives way to homogeneity at long times in the ergodic phase, the dynamics remain inhomogeneous and multifractal in nature for arbitrarily long times in the localised phase. Similarly, we show that an appropriately defined dynamical lengthscale on the Fock-space graph is directly related to the local spin-autocorrelation, and as such sheds light on the (anomalous) decay of the autocorrelation in the ergodic phase, and lack of it in the localised phase.

20 pages, 16 figures

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Cited by in corpus (13)

• Many-Body Localization in the Age of Classical Computing
• Role of Fock-space correlations in many-body localization
• Hilbert space delocalization under random unitary circuits
• Ergodicity-to-localization transition on random regular graphs with large connectivity and in many-body quantum dots
• The Fock-space landscape of many-body localisation
• Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems
• The connection between Hilbert-space return probability and real-space autocorrelations in quantum spin chains
• Finite-size prethermalization at the chaos-to-integrable crossover
• Characterizing dynamical criticality of many-body localization transitions from the Fock-space perspective
• Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space
• Anatomy of localisation protected quantum order on Hilbert space
• Krylov-space anatomy and spread complexity of a disordered quantum spin chain
• Orthogonal projections of hypercubes