Topology-driven phase transitions in the classical monomer-dimer-loop model

TL;DR

This paper explores phase transitions in a classical monomer-dimer-loop model on a square lattice, revealing a topological phase transition characterized by nonlocal order parameters and topological ergodicity breaking.

Contribution

It introduces a tensor network approach to analyze the model and identifies a topological phase transition with novel nonlocal order parameters.

Findings

Identifies a second-order phase transition between monomer-condensation and loop-condensation phases.

Discovers topological ergodicity breaking in the loop-condensation phase.

Proposes nonlocal string order parameter as a marker for the phase transition.

Abstract

In this work, we investigate the classical loop models doped with monomers and dimers on a square lattice, whose partition function can be expressed as a tensor network (TN). In the thermodynamic limit, we use the boundary matrix product state technique to contract the partition function TN, and determine the thermodynamic properties with high accuracy. In this monomer-dimer-loop model, we find a second-order phase transition between a trivial monomer-condensation and a loop-condensation (LC) phases, which can not be distinguished by any local order parameter, while nevertheless the two phases have distinct topological properties. In the LC phase, we find two degenerate dominating eigenvalues in the transfer-matrix spectrum, as well as a non-vanishing (nonlocal) string order parameter, both of which identify the \textit{topological ergodicity breaking} in the LC phase and can serve as the order parameter for detecting the phase transitions.