Explicit construction of local conserved operators in disordered many-body systems

T. E. O'Brien, Dmitry A. Abanin, Guifre Vidal, Z. Papić

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41 Scopus citations

Abstract

The presence and character of local integrals of motion - quasilocal operators that commute with the Hamiltonian - encode valuable information about the dynamics of a quantum system. In particular, strongly disordered many-body systems can generically avoid thermalization when there are extensively many such operators. In this work, we explicitly construct local conserved operators in one-dimensional spin chains by directly minimizing their commutator with the Hamiltonian. We demonstrate the existence of an extensively large set of local integrals of motion in the many-body localized phase of the disordered XXZ spin chain. These operators are shown to have exponentially decaying tails, in contrast to the ergodic phase where the decay is (at best) polynomial in the size of the subsystem. We study the algebraic properties of localized operators and confirm that in the many-body localized phase, they are well described by "dressed" spin operators.

Original languageEnglish (US)
Article number144208
JournalPhysical Review B
Volume94
Issue number14
DOIs
StatePublished - Oct 24 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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