Characterizing entanglement at finite temperature: how does a "classical" paramagnet become a quantum spin liquid?

TL;DR

This paper investigates how quantum entanglement develops at finite temperatures in models of quantum spin liquids, revealing the temperature thresholds for entanglement onset and the emergence of their characteristic entanglement structures.

Contribution

It introduces a new method to characterize entanglement depth and structure at finite temperature, applied to the Kitaev honeycomb and Kagome lattice models.

Findings

Identified temperature at which spins first become entangled.

Determined temperature where structured multipartite entanglement emerges.

Provided insights into the formation of QSL states from high-temperature paramagnets.

Abstract

Quantum spin liquids (QSL) are phases of matter which are distinguished not by the symmetries they break, but rather by the patterns of entanglement within them. Although these entanglement properties have been widely discussed for ground states, the way in which QSL form at finite temperature remains an open question. Here we introduce a method of characterizing both the depth and spatial structure of entanglement, and use this to explore how patterns of entanglement form as temperature is reduced in two widely studied models of QSL, the Kitaev honeycomb model, and the spin-1/2 Heisenberg antiferromagnet on a Kagome lattice. These results enable us to evaluate both the temperature at which spins within the high-temperature paramagnet first become entangled, and the temperature at which the system first develops the structured, multipartite entanglement characteristic of its QSL ground state.