In recent decades, one of the central goals of condensed matter physics has been the classification and characterization of quantum phases of matter at zero temperature. This has led to the discovery of many exotic phases, notable those exhibiting topological order, characterized by long-range quantum entanglement and a ground state degeneracy that depends on the underlying topology. Much less is known about the situation at finite, non-zero temperatures; for example no examples of finite temperature topological order exist in spatial dimensions below 4. 

 

In this talk, I will discuss a series of results [1-3] relevant to the problem of quantum phases at nonzero temperatures. First, I will discuss a theorem that provides a "dynamical" perspective on finite temperature phases, relating them to open system dynamics. As an application of this perspective, I will discuss a family of spatially non-local models that exhibit a new kind of "topological quantum spin glass", combining quantum topological order, with features of classical mean-field spin glasses. Finally, I will discuss a model that realizes quantum topological order in 3 spatial dimensions for the first time. 

 

References:

[1]: Bottlenecks in quantum channels and finite temperature phases of matter, 

https://arxiv.org/abs/2412.09598

[2]: Topological Quantum Spin Glass Order and its realization in qLDPC codes, 

https://arxiv.org/abs/2412.13248

[3]: Finite-temperature quantum topological order in three dimensions, 

https://arxiv.org/abs/2503.02928