Dynamical heterogeneity and large deviations in the open quantum East glass model from tensor networks

TL;DR

This paper investigates the non-equilibrium dynamics of the dissipative quantum East model using tensor networks, revealing dynamical heterogeneity, enhanced glassiness with quantum fluctuations, and a first-order dynamical phase transition.

Contribution

It introduces tensor network methods to study large-scale quantum glass models, demonstrating dynamical heterogeneity and phase transitions beyond classical approaches.

Findings

Dynamical heterogeneity accompanies slow relaxation in the quantum East model.

Quantum fluctuations enhance glassiness compared to the classical case.

Evidence of a first-order active-inactive dynamical phase transition.

Abstract

We study the non-equilibrium dynamics of the dissipative quantum East model via numerical tensor networks. We use matrix product states to represent evolution under quantum-jump unravellings for sizes beyond those accessible to exact diagonalisation. This allows us to demonstrate that dynamical heterogeneity accompanies slow relaxation, in analogy with what is seen in classical glassy systems. Furthermore, using variational matrix product operators we: (i) compute the spectral gap of the Lindbladian, and show that glassiness is enhanced in the presence of weak quantum fluctuations compared to the pure classical case, and (ii) obtain the dynamical large deviations by calculating the leading eigenvector of the tilted Lindbladian, and find clear evidence for a first-order active-inactive dynamical phase transition. We also show how to directly sample the rare quantum trajectories associated to the large deviations.