Diagnosing Deconfinement and Topological Order

TL;DR

This paper introduces a new diagnostic tool for identifying deconfined topological phases in condensed matter systems, addressing limitations of traditional methods by leveraging insights from lattice gauge theory and applying them to higher-dimensional and multi-phase contexts.

Contribution

It constructs a line tension-based diagnostic for deconfinement, connecting lattice gauge theory concepts with condensed matter applications, and demonstrates its effectiveness in various complex systems.

Findings

Established the diagnostic's interpretation as a line tension.

Proved the diagnostic's utility in finite temperature topological phases in 3+ dimensions.

Reduced the toric code partition function to a well-studied problem.

Abstract

Topological or deconfined phases are characterized by emergent, weakly fluctuating, gauge fields. In condensed matter settings they inevitably come coupled to excitations that carry the corresponding gauge charges which invalidate the standard diagnostic of deconfinement---the Wilson loop. Inspired by a mapping between symmetric sponges and the deconfined phase of the $Z_2$ gauge theory, we construct a diagnostic for deconfinement that has the interpretation of a line tension. One operator version of this diagnostic turns out to be the Fredenhagen-Marcu order parameter known to lattice gauge theorists and we show that a different version is best suited to condensed matter systems. We discuss generalizations of the diagnostic, use it to establish the existence of finite temperature topological phases in $d \ge 3$ dimensions and show that multiplets of the diagnostic are useful in settings with multiple phases such as $U(1)$ gauge theories with charge $q$ matter. [Additionally we present an exact reduction of the partition function of the toric code in general dimensions to a well studied problem.]