Local Integrals of Motion in Quasiperiodic Many-Body Localized Systems

Abstract

Local integrals of motion play a central role in the understanding of many-body localization in many-body quantum systems in one dimension subject to a random external potential, but the question of how these local integrals of motion change in a deterministic quasiperiodic potential is one that has received significantly less attention. Here we develop a powerful new implementation of the continuous unitary transform formalism and use this method to directly compute both the effective Hamiltonian and the local integrals of motion for many-body quantum systems subject to a quasiperiodic potential. We show that the effective interactions between local integrals of motion retain a strong fingerprint of the underlying quasiperiodic potential, exhibiting sharp features at distances associated with the incommensurate wavelength used to generate the potential. Furthermore, the local integrals of motion themselves may be expressed in terms of an operator expansion which allows us to estimate the critical strength of quasiperiodic potential required to lead to a localization/delocalization transition, by means of a finite size scaling analysis.

Destruction of localization by thermal inclusions: Anomalous transport and Griffiths effects in the Anderson and André-Aubry-Harper models

“…eding the localization transition, several numerical ies have found evidence of anomalous subdiffusive sport of particles [18][19][20][21]. The microscopic origin his subdiffusion is still uncertain.…”

“…The fate of quantum localization in presence of many-body interactions, and in regimes far from low temperature equilibrium, has been at the center of theoretical and experimental interest, both for its fundamental interest for our basic understanding of quantum statistical mechanics and for its practical implications in the search for mechanisms to protect quantum information [5][6][7][8][9][10][11][12][13]. The existence of a Many-Body Localized (MBL) phase has been discussed and established, both for quenched randomness and quasi-periodic disorder [14][15][16][17][18][19][20], yet many questions remain open. In particular the transport and thermalization properties on both sides of the MBL transition have attracted particular interest, triggered by the evidence for anomalous (sub) diffusion [21][22][23][24][25][26][27][28][29][30], a remarkably robust phenomenon which has been since then also observed experimentally with cold atoms, ultracold ions, and superconducting circuits [31][32][33][34][35].…”

Localisation and Sub-Diffusive Transport in Quantum Spin Chains With Dilute Disorder

“…The focus of this work is many-body localisation [4][5][6][7][8][9], the interacting variant of Anderson localisation [1,2] where an isolated many-body quantum system can become localised at all energy scales via the addition of a random on-site chemical potential or magnetic field [3]. Recent years have seen huge progress in understanding many-body localisation -particularly from the point of view of local integrals of motion [7,[20][21][22][23][24][25] -as well as in establishing under what conditions it can and can not exist. Remarkably, there is even a class of spin chains for which an analytical proof of many-body localisation exists [6], subject to the assumption of limited level attraction, which is widely considered to be a reasonable assumption.…”

Measuring out quasi-local integrals of motion from entanglement

“…From a theoretical standpoint, MBL is now fairly well understood in terms of the emergence of an extensive number of conserved quantities known as (quasi-)local integrals of motion (LIOMs, also known as localised bits or l-bits) which can prevent many-body systems from reaching thermal equilibrium [7,13]. While phenomenological models based around the concept of l-bits have seen great success [14,15], and there are several approaches that can map microscopic models onto effective l-bit models [16][17][18][19][20][21][22][23][24][25][26], the l-bits themselves remain a strictly theoretical construct, inaccessible to any experimental probes. This is in contrast with the case of Anderson localised systems, where the exponentially localised l-bits can be straightforwardly related to the real-space decay of the single-particle states, which has been experimentally observed [27].…”