Scaling properties of a spatial one-particle density-matrix entropy in many-body localized systems

Abstract

We investigate a spatial subsystem entropy extracted from the one-particle density matrix (OPDM) in one-dimensional disordered interacting fermions that host a many-body localized (MBL) phase. Deep in the putative MBL regime, this OPDM entropy exhibits the salient features of localization, despite not being a proper entanglement measure. We numerically show that the OPDM entropy of the eigenstates obeys an area law. Similar to the von-Neumann entropy, the OPDM entropy grows logarithmically with time after a quantum quench, albeit with a different prefactor. Both these features survive at moderately large interactions and well towards the transition into the ergodic phase. The computational cost to calculate the OPDM entropy scales only polynomially with the system size, suggesting that the OPDM provides a promising starting point for developing diagnostic tools for MBL in simulations and experiments.

11 pages, 8 figures. Published version. Data shown in the manuscript is partially available as ancillary files

References in corpus (16)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Many-body localization edge in the random-field Heisenberg chain
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• Spectral signatures of many-body localization with interacting photons
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Can we study the many-body localisation transition?
• Many-body localisation implies that eigenvectors are matrix-product states
• Quantum Mutual Information as a Probe for Many-Body Localization
• Percolation in Fock space as a proxy for many-body localisation
• Many-body localization of spinless fermions with attractive interactions in one dimension
• Extensive entropy from unitary evolution

Cited by in corpus (11)

• Many-Body Localization in the Age of Classical Computing
• Unbounded entanglement production via a dissipative impurity
• Measurement-induced transitions beyond Gaussianity: a single particle description
• Scaling of Fock-space propagator and multifractality across the many-body localization transition
• Scrambling and Many-Body Localization in the XXZ-Chain
• Multifractality and Fock-space localization in many-body localized states: one-particle density matrix perspective
• Time periodicity from randomness in quantum systems
• Interacting Local Topological Markers: A one-particle density matrix approach for characterizing the topology of interacting and disordered states
• One-particle entanglement for one dimensional spinless fermions after an interaction quantum quench
• Fock-space geometry and strong correlations in many-body localized systems
• Gaussian state approximation of quantum many-body scars