Reduced-basis approach to many-body localization

Abstract

Within the standard model of many-body localization, i.e., the disordered chain of spinless fermions, we investigate how the interaction affects the many-body states in the basis of noninteracting localized Anderson states. From this starting point we follow the approach that uses a reduced basis of many-body states. Together with an extrapolation to the full basis, it proves to be efficient for the evaluation of the stiffnesses of local observables, which remain finite within the non-ergodic regime and represent the hallmark of the many-body localization (MBL). The method enables a larger span of system sizes and, within the MBL regime, allows for a more careful analysis of the size scaling of calculated quantities. On the other hand, the survival stiffness as the representative of non--local quantities, reveals limitations of the reduced-basis approach.

11 pages, 11 figures

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• Phenomenology of fully many-body-localized systems
• Integrals of motion in the Many-Body localized phase
• Anomalous diffusion and Griffiths effects near the many-body localization transition
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• Constructing local integrals of motion in the many-body localized phase
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• Counting local integrals of motion in disordered spinless-fermion and Hubbard chains
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• Relaxation at different length-scales in models of many-body localization
• Many-body localization as a percolation phenomenon
• The Fock-space landscape of many-body localisation
• Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems
• Dynamics of the one-dimensional Anderson insulator coupled to various bosonic baths
• Diffusion in the Anderson model in higher dimensions
• Breaking the chains: extreme value statistics and localization in random spin chains
• Local integrals of motion in dipole-conserving models with Hilbert space fragmentation
• Localization crossover and subdiffusive transport in a classical facilitated network model of a disordered, interacting quantum spin chain
• Dynamical decoherence of a qubit coupled to a quantum dot or the SYK black hole
• Critical quantum dynamics of observables at eigenstate transitions
• Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models
• Large deviations in the many-body localization transition: The case of the random-field XXZ chain