Weak-ergodicity-breaking via lattice supersymmetry

Federica Maria Surace, Giuliano Giudici, and Marcello Dalmonte

The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy, and SISSA, via Bonomea 265, 34136 Trieste, Italy

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Abstract

We study the spectral properties of $D$-dimensional $N=2$ supersymmetric lattice models. We find systematic departures from the eigenstate thermalization hypothesis (ETH) in the form of a degenerate set of ETH-violating supersymmetric (SUSY) doublets, also referred to as many-body scars, that we construct analytically. These states are stable against arbitrary SUSY-preserving perturbations, including inhomogeneous couplings. For the specific case of two-leg ladders, we provide extensive numerical evidence that shows how those states are the only ones violating the ETH, and discuss their robustness to SUSY-violating perturbations. Our work suggests a generic mechanism to stabilize quantum many-body scars in lattice models in arbitrary dimensions.

In quantum field theory, supersymmetry has been studied for decades: it has a number of useful properties that make it essentially different from any internal symmetry. What happens when we endow a statistical mechanics lattice model with such exotic symmetry? While this question has attracted recent attention in relation to the physics of ground states and low-lying excitations, the consequences of supersymmetry on out-of-equilibrium properties have been largely unexplored. In this work, we show that a class of lattice models with exact supersymmetry displays very unusual spectral properties, in the form of non-thermal eigenstates (the so-called quantum many-body scars) that are at odds with conventional thermodynamics arguments. The presence of these eigenstates in any dimension implies that, for an appropriate choice of initial states, local observables do not relax to the values predicted by the thermal ensemble, providing a remarkable, observable consequence of the presence of an underlying exact supersymmetry.

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Cited by

[1] Sanjay Moudgalya, Nicolas Regnault, and B. Andrei Bernevig, "η -pairing in Hubbard models: From spectrum generating algebras to quantum many-body scars", Physical Review B 102 8, 085140 (2020).

[2] Jiří Minář, Bart van Voorden, and Kareljan Schoutens, "Kink dynamics and quantum simulation of supersymmetric lattice Hamiltonians", arXiv:2005.00607.

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