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. arXiv:1707.05181v3 [cond-mat.stat-mech]

Edge mode locality in perturbed symmetry protected topological order

“…(40) supp (m 2 , S L,j ) ∼ J − j 3(41) from which we infer that the support measure should have decending plateaus of width 3, all of which fall within an exponential envelope, which is precisely what is observed inFigure 1. The analysis for the right edge modes is identical, and we expect these to also show a plateau structure, which is also seen.…”

Almost conserved operators in nearly many-body localized systems

“…27,28 This approach explains, for instance, the dephasing [29][30][31] and entanglement dynamics 6,32 in the localized phase. Moreover, LIOMs have been constructed explicitly for some models using analytical techniques, 33 exact diagonalization [34][35][36][37][38][39] , stochastic methods, 40 and tensor networks. [41][42][43][44] Upon reducing the disorder, LIOMs become more and more extended in space and eventually cease to exist at the MBL transition.…”

Spin Subdiffusion in the Disordered Hubbard Chain

“…It has also been found that MBL prevents a driven system from heating [9,[36][37][38][39][40][41]. These unusual properties can be explained via the existence of a macroscopic number of local integrals of motion [12,25,26,[42][43][44][45][46][47].…”

“…It has also been found that MBL prevents a driven system from heating [9,[36][37][38][39][40][41]. These unusual properties can be explained via the existence of a macroscopic number of local integrals of motion [12,25,26,[42][43][44][45][46][47].While most of theoretical studies so far concentrated on the one-dimensional (1D) disordered model of interacting spinless fermions, the experiments on MBL are performed on cold-fermion lattices [14,[48][49][50] where the relevant model is the Hubbard model with spin-1/2 fermions, whereby the disorder enters only via a random (or quasi-periodic) charge potential. Recent numerical studies of such a model [47,[51][52][53] reveal that even at strong disorder, localization and nonergodicity occurs only in the charge subsystem, implying a partial MBL.…”