Disorder-Free Localization in a Two-Dimensional Lattice Gauge theory- Transition and Spectral Response

There has been great recent interest in realizing lattice gauge theories in the lab in various quantum simulator platforms. We show that there exists a disorder-free localization transition in two dimensions in a model of a lattice gauge theory with discrete degrees of freedom , namely the U(1) quantum link model, one of the target models for such quantum simulator experiments and also relevant for frustrated magents. We study the nature of localization transition using a percolation model and we show that in a certain regime of the Hamiltonian, the disorder-free localization transition is a continuous transition whose universality class we determine by calculating exact critical exponents [1]. We also calculate spectral features of such a localized system deep in the localized phase using a cluster expansion approach [2]. We show that such a localized system has sharp peaks in spatially averaged high temperature spectral functions combined with a vanishing response in the zero frequency limit, even in the infinite size limit. Our results highlight unique features of such disorder-free localization in lattice gauge theories which distinguish it from conventional many body localization in disordered systems as well as otherwise expected high temperature paramagnetic response in frustrated magnets.

[1] N. Chakraborty, M. Heyl, P. Karpov, R. Moessner: PRB 106 (6), L060308

[2] N. Chakraborty, M. Heyl, P. Karpov, R. Moessner: In prep