Spacetime supersymmetry in the truncated lattice Schwinger model

Gauge theories in (1+1) dimension $[(1+1)\mathrm{D}]$ have attracted renewed attention partially due to their experimental realizations in quantum simulation platforms. In this work, we revisit the truncated lattice massive Schwinger model and the truncated lattice Abelian-Higgs model in $(1+1)\mathrm{D}$, where to facilitate quantum simulation, the electric field eigenvalues are truncated to a finite subset while preserving the exact gauge and global symmetries. We uncover previously overlooked universal features in these models, including the emergence of a supersymmetric quantum critical point when the Maxwell term's coefficient changes sign. Our primary focus is the truncated lattice Schwinger model at $\ensuremath{\theta}=0$, a model not equivalent to familiar spin models. We find that upon reversing the sign of the Maxwell term, the second-order charge conjugation symmetry breaking transition (or confinement-deconfinement transition in a sense) can become first-order. Furthermore, 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 $\ensuremath{\theta}=0$, which we find to be equivalent to the quantum Blume-Capel model, the very existence of a symmetry-breaking phase requires a negative-sign Maxwell term. Similarly, there is a tricritical Ising point separating first-order and second-order phase transitions.