Non-equilibrium Quantum Spin Dynamics from 2PI Functional Integral Techniques in the Schwinger Boson Representation

TL;DR

This paper introduces a non-equilibrium quantum field theory method using 2PI functional integral techniques in the Schwinger boson representation to study complex spin dynamics in large, disordered, and long-range interacting systems.

Contribution

It develops a novel 2PI NLO approach for non-equilibrium spin dynamics applicable to large systems and higher dimensions, capturing diverse non-perturbative phenomena.

Findings

Successfully models relaxation in 3D long-range systems with disorder

Reproduces different relaxation behaviors near quantum phase transitions

Shows the crossover from relaxation to many-body localization

Abstract

We present a non-equilibrium quantum field theory approach to the initial-state dynamics of spin models based on two-particle irreducible (2PI) functional integral techniques. It employs a mapping of spins to Schwinger bosons for arbitrary spin interactions and spin lengths. At next-to-leading order (NLO) in an expansion in the number of field components, a wide range of non-perturbative dynamical phenomena are shown to be captured, including relaxation of magnetizations in a 3D long-range interacting system with quenched disorder, different relaxation behaviour on both sides of a quantum phase transition and the crossover from relaxation to arrest of dynamics in a disordered spin chain previously shown to exhibit many-body-localization. Where applicable, we employ alternative state-of-the-art techniques and find rather good agreement with our 2PI NLO results. As our method can handle large system sizes and converges relatively quickly to its thermodynamic limit, it opens the possibility to study those phenomena in higher dimensions in regimes in which no other efficient methods exist. Furthermore, the approach to classical dynamics can be investigated as the spin length is increased.