Lattice Schwinger Model and Spacetime Supersymmetry

TL;DR

This paper investigates lattice gauge theories in (1+1)D, revealing a supersymmetric quantum critical point and phase transition changes, with implications for quantum simulation and understanding of universal features.

Contribution

It uncovers a supersymmetric critical point in lattice Schwinger and Abelian-Higgs models, and explores phase transition behaviors under Maxwell term sign reversal.

Findings

Reversal of Maxwell term sign changes the order of phase transitions.

Identifies a supersymmetric tricritical Ising point connecting different phase transition types.

Establishes the equivalence of truncated Abelian-Higgs model to the quantum Blume-Capel model.

Abstract

Gauge theories in (1+1)D have attracted renewed attention partially due to their experimental realizations in quantum simulation platforms. In this work, we revisit the lattice massive Schwinger model and the (1+1)D lattice Abelian-Higgs model, uncovering previously overlooked universal features, including the emergence of a supersymmetric quantum critical point when the Maxwell term's coefficient changes sign. To facilitate the quantum simulation of these theories, we adopt a strategy of truncating the electric field eigenvalues to a finite subset, preserving the exact gauge and global symmetries. Our primary focus is the truncated lattice Schwinger model at $\theta=0$, a model not equivalent to familiar spin models. We find that upon reversing the sign of the Maxwell term, the second-order deconfinement-confinement transition can become first-order, and the two types of transitions are connected by a supersymmetric critical point in the tricritical Ising universality class. In the case of truncated abelian-Higgs model at $\theta=0$, which turns out to be equivalent to the quantum Blume-Capel model, the very existence of a deconfined phase requires a negative-sign Maxwell term. Similarly, there is a tricritical Ising point separating first-order and second-order phase transitions.