Topological Quantum Glassiness

TL;DR

This paper introduces exactly solvable models of topological quantum glasses where quantum tunneling is exponentially suppressed with system size, leading to dynamically arrested low-temperature relaxation without local order parameters.

Contribution

It provides new examples of topological quantum glasses with slow dynamics, including models with fractal topological defects, expanding understanding of quantum glassiness.

Findings

Quantum tunneling is exponentially suppressed in these models.

Systems exhibit slow, glass-like relaxation dynamics.

Topological defects can be fractal objects with non-integer dimension.

Abstract

Quantum tunneling often allows pathways to relaxation past energy barriers which are otherwise hard to overcome classically at low temperatures. However, this is not always the case. In this paper we provide simple exactly solvable examples where the barriers each system encounters on its approach to lower and lower energy states become increasingly large and eventually scale with the system size. If the environment couples locally to the physical degrees of freedom in the system, tunnelling under large barriers requires processes whose order in perturbation theory is proportional to the width of the barrier. This results in quantum relaxation rates that are exponentially suppressed in system size: For these quantum systems, no physical bath can provide a mechanism for relaxation that is not dynamically arrested at low temperatures. The examples discussed here are drawn from three dimensional generalizations of Kitaev's toric code, originally devised in the context of topological quantum computing. They are devoid of any local order parameters or symmetry breaking and are thus examples of topological quantum glasses. We construct systems that have slow dynamics similar to either strong or fragile glasses. The example with fragile-like relaxation is interesting in that the topological defects are neither open strings or regular open membranes, but fractal objects with dimension $d^* = ln 3/ ln 2$.