Quantum invariants of motion in a generic many-body system

TL;DR

This paper introduces a dynamical Lie-algebraic method to construct local quantum invariants in many-body systems, exploring transitions between integrable, intermediate, and ergodic regimes, and proposing a dynamical phase transition in the thermodynamic limit.

Contribution

It presents a novel Lie-algebraic approach to identify quantum invariants and analyzes phase transitions between different dynamical regimes in many-body systems.

Findings

Transition from integrable to ergodic regimes in parameter space.

Existence of local conservation laws correlates with non-ergodic regimes.

Time-correlation functions align with conservation law predictions.

Abstract

Dynamical Lie-algebraic method for the construction of local quantum invariants of motion in non-integrable many-body systems is proposed and applied to a simple but generic toy model, namely an infinite kicked $t-V$ chain of spinless fermions. Transition from integrable via {pseudo-integrable (\em intermediate}) to quantum ergodic (quantum mixing) regime in parameter space is investigated. Dynamical phase transition between ergodic and intermediate (neither ergodic nor completely integrable) regime in thermodynamic limit is proposed. Existence or non-existence of local conservation laws corresponds to intermediate or ergodic regime, respectively. The computation of time-correlation functions of typical observables by means of local conservation laws is found fully consistent with direct calculations on finite systems.