Construction of exact constants of motion and effective models for many-body localized systems

Abstract

One of the defining features of many-body localization is the presence of extensively many quasi-local conserved quantities. These constants of motion constitute a corner-stone to an intuitive understanding of much of the phenomenology of many-body localized systems arising from effective Hamiltonians. They may be seen as local magnetization operators smeared out by a quasi-local unitary. However, accurately identifying such constants of motion remains a challenging problem. Current numerical constructions often capture the conserved operators only approximately restricting a conclusive understanding of many-body localization. In this work, we use methods from the theory of quantum many-body systems out of equilibrium to establish a new approach for finding a complete set of exact constants of motion which are in addition guaranteed to represent Pauli-$z$ operators. By this we are able to construct and investigate the proposed effective Hamiltonian using exact diagonalization. Hence, our work provides an important tool expected to further boost inquiries into the breakdown of transport due to quenched disorder.

8 pages, 8 figures, replaced with published version

References in corpus (11)

• Localization of interacting fermions at high temperature
• 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
• Constructing local integrals of motion in the many-body localized phase
• How a small quantum bath can thermalize long localized chains
• Many-body localisation implies that eigenvectors are matrix-product states
• Time Evolution of Many-Body Localized Systems with the Flow Equation Approach
• Local and Quasilocal Conserved Quantities in Integrable Systems
• Explicit construction of local conserved operators in disordered many-body systems
• Counting local integrals of motion in disordered spinless-fermion and Hubbard chains

Cited by in corpus (33)

• Many-body localization: an introduction and selected topics
• Measurement-induced entanglement transitions in many-body localized systems
• Time evolution of many-body localized systems in two spatial dimensions
• Are many-body localized systems stable in the presence of a small bath?
• Spin subdiffusion in disordered Hubbard chain
• Behavior of l-bits near the many-body localization transition
• Activating many-body localization in solids by driving with light
• Numerical evidence for many-body localization in two and three dimensions
• Level statistics of real eigenvalues in non-Hermitian systems
• Local integrals of motion detection of localization-protected topological order
• Local Integrals of Motion for Topologically Ordered Many-Body Localized Systems
• Comparing many-body localization lengths via non-perturbative construction of local integrals of motion
• Transient and persistent particle subdiffusion in a disordered chain coupled to bosons
• Approximating observables on eigenstates of large many-body localized systems
• Exact projector Hamiltonian, local integrals of motion, and many-body localization with topological order
• Simulation of many body localization and time crystals in two dimensions with the neighborhood tensor update
• Loschmidt echo singularities as dynamical signatures of strongly localized phases
• Charge and spin-specific local integrals of motion in a disordered Hubbard model
• Tensor networks demonstrate the robustness of localization and symmetry protected topological phases
• Classification of symmetry-protected topological many-body localized phases in one dimension
• Structural properties of local integrals of motion across the many-body localization transition via a fast and efficient method for their construction
• Local integrals of motion and the stability of many-body localisation in Wannier-Stark potentials
• Harnessing symmetry-protected topological order for quantum memories
• Many-body-localization protection of eigenstate topological order in two dimensions
• Measuring out quasi-local integrals of motion from entanglement
• Disorder-induced spin-charge separation in the 1-D Hubbard model
• Edge mode locality in perturbed symmetry protected topological order
• Renormalization view on resonance proliferation between many-body localized phases
• Finding local integrals of motion in quantum lattice models in the thermodynamic limit
• Quantum Circuits Reproduce Experimental Two-dimensional Many-body Localization Transition Point
• Multibody expansion of the local integrals of motion: How many pairs of particle-hole do we really need to describe the quasiparticles in the many-body localized phase?
• Quench dynamics of quasi-periodic systems exhibiting Rabi oscillations of two-level integrals of motion
• Two-dimensional many-body localized systems coupled to a heat bath