Measuring out quasi-local integrals of motion from entanglement

Abstract

Quasi-local integrals of motion are a key concept underpinning the modern understanding of many-body localisation, an intriguing phenomenon in which interactions and disorder come together. Despite the existence of several numerical ways to compute them - and astoundingly in the light of the observation that much of the phenomenology of many properties can be derived from them - it is not obvious how to directly measure aspects of them in real quantum simulations; in fact, the smoking gun of their experimental observation is arguably still missing. In this work, we propose a way to extract the real-space properties of such quasi-local integrals of motion based on a spatially-resolved entanglement probe able to distinguish Anderson from many-body localisation from non-equilibrium dynamics. We complement these findings with a new rigorous entanglement bound and compute the relevant quantities using tensor networks. We demonstrate that the entanglement gives rise to a well-defined length scale that can be measured in experiments.

6+12 pages, 13 figures, substantial detail added

References in corpus (17)

• The density-matrix renormalization group in the age of matrix product states
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• 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
• Integrals of motion in the Many-Body localized phase
• Constructing local integrals of motion in the many-body localized phase
• General entanglement scaling laws from time evolution
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Many-body localisation implies that eigenvectors are matrix-product states
• Quantum Mutual Information as a Probe for Many-Body Localization
• Thermalization of dilute impurities in one dimensional spin chains
• Entangling power and quantum circuit complexity
• Local Integrals of Motion in Quasiperiodic Many-Body Localized Systems
• Local integrals of motion and the logarithmic lightcone in many-body localized systems
• Quantum information spreading in random spin chains
• Disorder-induced spin-charge separation in the 1-D Hubbard model

Cited by in corpus (6)

• Many-Body Localization in the Age of Classical Computing
• Local integrals of motion and the stability of many-body localisation in Wannier-Stark potentials
• The dynamical $\alpha$-Rényi entropies of local Hamiltonians grow at most linearly in time
• Typical thermalization of low-entanglement states
• Operator Growth in Disordered Spin Chains: Indications for the Absence of Many-Body Localization
• 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?