Truncating loopy tensor networks by zero-mode gauge fixing: the $Z_2$ lattice gauge theory at finite temperature

TL;DR

This paper introduces a method for truncating loopy tensor networks using zero-mode gauge fixing, improving efficiency in representing thermal states of 2D $Z_2$ lattice gauge theories.

Contribution

The authors develop a bond truncation technique leveraging zero modes without prior gauge fixing, applied to finite-temperature $Z_2$ lattice gauge theory using iPEPS.

Findings

Effective bond truncation improves tensor network compression.

Method captures relevant loop correlations more efficiently.

Applied successfully to 2D $Z_2$ lattice gauge theory at finite temperature.

Abstract

Loopy tensor networks exhibit internal correlations that often render their compression inefficient. We show that even local bond optimization can more effectively exploit locally available information about relevant loop correlations. By cutting a bond, we define a set of states whose linear dependence can be identified through a zero mode of the states' metric tensor and used to truncate the bond dimension. In the absence of an exact zero mode, a linear combination of a small number of the lowest modes can instead be optimized to provide the optimal approximation to a zero mode. The truncation does not require prior gauge fixing. The method is applied to the two-dimensional finite-temperature $Z_2$ lattice gauge theory, whose thermal-state purification is represented by an infinite projected entangled-pair state (iPEPS).