title: Topology-driven phase transitions in the classical monomer-dimer-loop model.
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) phase, which cannot 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 nonvanishing (nonlocal) string order parameter, both of which identify the topological ergodicity breaking in the LC phase and can serve as the order parameter for detecting the phase transitions.
authors.affiliation: Department of Physics, Beihang University, Beijing 100191, China.
authors.forename: Sazi
authors.initials: S
authors.lastname: Li
authors.affiliation: Department of Physics, Beihang University, Beijing 100191, China.|Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität, 80333 Munich, Germany.
authors.forename: Wei
authors.initials: W
authors.lastname: Li
authors.affiliation: Department of Physics, Beihang University, Beijing 100191, China.|Key Laboratory of Micro-nano Measurement-Manipulation and Physics (Ministry of Education), Beihang University, Beijing 100191, China.
authors.forename: Ziyu
authors.initials: Z
authors.lastname: Chen