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

Abstract

The presence and character of local integrals of motion -- quasi-local 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 thermalisation when there are extensively many such operators. In this work, we explicitly construct local conserved operators in $1$D spin chains by directly minimising their commutator with the Hamiltonian. We demonstrate the existence of an extensively large set of local integrals of motion in the many-body localised 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 localised operators, and confirm that in the many-body localised phase they are well-described by "dressed" spin operators.

12 pages, 8 figures

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Cited by in corpus (6)

• Recent progress in many-body localization
• Non-thermalized Dynamics of Flat-Band Many-Body Localization
• Catching thermal avalanches in the disordered XXZ model
• Explicit construction of quasi-conserved local operator of translationally invariant non-integrable quantum spin chain in prethermalization
• Edge mode locality in perturbed symmetry protected topological order
• Quench dynamics of quasi-periodic systems exhibiting Rabi oscillations of two-level integrals of motion