Weak Ergodicity Breaking in the Schwinger Model

Abstract

As a paradigm of weak ergodicity breaking in disorder-free nonintegrable models, quantum manybody scars (QMBS) can offer deep insights into the thermalization dynamics of gauge theories. Having been first discovered in a spin-1/2 quantum link formulation of the Schwinger model, it is a fundamental question as to whether QMBS persist for S > 1/2 since such theories converge to the lattice Schwinger model in the large-S limit, which is the appropriate version of lattice QED in one spatial dimension. In this work, we address this question by exploring QMBS in spin-S U(1) quantum link models (QLMs) with staggered fermions. We find that QMBS persist at S > 1/2, with the resonant scarring regime, which occurs for a zero-mass quench, arising from simple high-energy gauge-invariant initial states. We furthermore find evidence of detuned scarring regimes, which occur for finite-mass quenches starting in the physical vacua and the charge-proliferated state. Our results conclusively show that QMBS exist in a wide class of lattice gauge theories in one spatial dimension represented by spin-S QLMs coupled to dynamical fermions.

Prominent quantum many-body scars in a truncated Schwinger model

“…We have demonstrated this for the spin-S U(1) QLM in Ref. [71] for the extreme vacua. However, this can be seen even more clearly for the TSM, as shown in Fig.…”

“…This, along with other works proving the existence of quantum many-body scars in various discrete lattice gauge theories [67][68][69] and the necessity of gauge-symmetry stability for their robustness [70], has led to the natural question of whether scars are an inherent feature of "standard" lattice gauge theories with a continuous configuration space. In a recent work by us [71], we have shown that quantum many-body scars persist at larger link spin lengths S > 1/2 in the spin-S U (1) QLM in the form of resonant scarring when the initial state is an extreme vacuum, defined as the most highly excited vacuum state. We have additionally presented evidence of detuned scarring, recently demonstrated experimentally for S = 1/2 [64], also for S > 1/2 when starting in the physical vacuum or the charge-proliferated state.…”

“…In that case the presence of fermions is energetically favorable, and so the ground state is the In the spin-1/2 QLM, the scarred states are the two vacua |0 − = |0 + and 0 − = 0 + for the quench Hamiltonian with µ = g = 0 (resonant scarring). Numerical simulations show that for any S > 1/2 only the extreme vacua |0 − and 0 − exhibit scarring [71] (see Appendix A for results on the physical vacuum |0 + ). A typical signature of scarring is a strong overlap of the scarred state with a small set of eigenstates that are approximately equally spaced in energy.…”

Tuning the Topological $θ$-Angle in Cold-Atom Quantum Simulators of Gauge Theories

“…Scarring also occurs for massive quenches starting in the charge-proliferated state |−1/2, +1, −1/2, +1 , which is the nondegenerate Z 2 -symmetric ground state of Eq. (3) at µ → ∞ and θ = π [63,65,66]. In Sec.…”

Driving quantum many-body scars

“…Theoretical studies continue to identify large classes of models that exhibit various aspects of QMBS phenomena. Some notable examples include various nonintegrable lattice models [18][19][20][21][22][23][24][25] , models of correlated fermions and bosons [26][27][28][29][30][31][32][33] , frustrated magnets 34,35 , topological phases of matter 36,37 , lattice gauge theories [38][39][40][41][42] , and periodically-driven systems [43][44][45][46][47][48] .…”