Bounding the resources for thermalizing many-body localized systems
arXiv:1912.04920 · doi:10.1038/s42005-020-00503-1
Abstract
Understanding under which conditions physical systems thermalize is a long-standing question in many-body physics. While generic quantum systems thermalize, there are known instances where thermalization is hindered, for example in many-body localized (MBL) systems. Here we introduce a class of stochastic collision models coupling a many-body system out of thermal equilibrium to an external heat bath. We derive upper and lower bounds on the size of the bath required to thermalize the system via such models, under certain assumptions on the Hamiltonian. We use these bounds, expressed in terms of the max-relative entropy, to characterize the robustness of MBL systems against externally-induced thermalization. Our bounds are derived within the framework of resource theories using the convex split lemma, a recent tool developed in quantum information. We apply our results to the disordered Heisenberg chain, and numerically study the robustness of its MBL phase in terms of the required bath size.
arXiv comment8+13 pages, comments welcomed
References in corpus (50)
- Chaos and Quantum Thermalization
- Area laws for the entanglement entropy - a review
- Nonequilibrium dynamics of closed interacting quantum systems
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Localization of interacting fermions at high temperature
- Many-body localization, thermalization, and entanglement
- Observation of many-body localization of interacting fermions in a quasi-random optical lattice
- Rényi Divergence and Kullback-Leibler Divergence
- Quantum many-body systems out of equilibrium
- Many-body localization edge in the random-field Heisenberg chain
- Unbounded growth of entanglement in models of many-body localization
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Many body localization in Heisenberg XXZ magnet in a random field
- Phenomenology of fully many-body-localized systems
- A phenomenology of certain many-body-localized systems
- Local conservation laws and the structure of the many-body localized states
- Fundamental limitations for quantum and nano thermodynamics
- The second laws of quantum thermodynamics
- The operational meaning of min- and max-entropy
- The Resource Theory of Quantum States Out of Thermal Equilibrium
- Quantum mechanical evolution towards thermal equilibrium
- Area laws in a many-body localized state and its implications for topological order
- Min- and Max- Relative Entropies and a New Entanglement Monotone
- Coupling Identical 1D Many-Body Localized Systems
- Quantum Information Processing with Finite Resources -- Mathematical Foundations
- Thermalizing Quantum Machines: Dissipation and Entanglement
- Max- relative entropy of coherence: an operational coherence measure
- A derivation (and quantification) of the third law of thermodynamics
- How a small quantum bath can thermalize long localized chains
- Spectral features of a many-body localized system weakly coupled to a heat bath
- Robustness of many-body localization in the presence of dissipation
- Dynamics of a Many-Body-Localized System Coupled to a Bath
- Finding matrix product state representations of highly-excited eigenstates of many-body localized Hamiltonians
- Many-body localisation implies that eigenvectors are matrix-product states
- On Random Unitary Channels
- MBL-mobile: Quantum engine based on many-body localization
- Quantum message compression with applications
- Signatures of the Many-body Localized Regime in Two Dimensions
- Elementary Thermal Operations
- Many-body Localization Transition: Schmidt Gap, Entanglement Length & Scaling
- Quantifying resource in catalytic resource theory
- Time evolution of many-body localized systems in two spatial dimensions
- Thermal inclusions: how one spin can destroy a many-body localized phase
- Are many-body localized systems stable in the presence of a small bath?
- Revivals imply quantum many-body scars
- Incoherent transport induced by a single static impurity in a Heisenberg chain
- The maximum efficiency of nano heat engines depends on more than temperature
- Non-interacting central site model: localization and logarithmic entanglement growth
- A limit relation for entropy and channel capacity per unit cost