From the Quantum Breakdown Model to the Lattice Gauge Theory

TL;DR

This paper explores the minimal quantum breakdown model, revealing its connection to lattice gauge theories and quantum link models, and uncovers conserved charges and scar states that explain its complex dynamical phases.

Contribution

It introduces a mapping from the minimal quantum breakdown model to U(1) lattice gauge theory and quantum link models, highlighting conserved charges and scar states.

Findings

Mapping to U(1) lattice gauge theory

Identification of local conserved charges

Connection to quantum many-body scars

Abstract

The one-dimensional quantum breakdown model, which features spatially asymmetric fermionic interactions simulating the electrical breakdown phenomenon, exhibits an exponential U(1) symmetry and a variety of dynamical phases including many-body localization and quantum chaos with quantum scar states. We investigate the minimal quantum breakdown model with the minimal number of on-site fermion orbitals required for the interaction, and identify a large number of local conserved charges in the model. We then reveal a mapping between the minimal quantum breakdown model in certain charge sectors and a quantum link model which simulates the U(1) lattice gauge theory, and show that the local conserved charges map to the gauge symmetry generators. A special charge sector of the model further maps to the PXP model, which shows quantum many-body scars. This mapping unveils the rich dynamics in different Krylov subspaces characterized by different gauge configurations in the quantum breakdown model.