Extended string-net model with all anyons at finite temperature

Andrea Velenich, Claudio Chamon, Xiao-Gang Wen

Chris N. Self, James R. Wootton, S. Iblisdir +1 more

André Soares, Anna Ritz-Zwilling, Jean-Noël Fuchs

The string-net model describes a vast family of topological orders in two spatial dimensions. Here, we consider the effect of thermal fluctuations on these topological phases. In the original string-net model, the description of charge (vertex) excitations can be problematic. Therefore, in order to describe all anyon excitations, we study an extended model [Y. Hu et al., Phys. Rev. B 97, 195154 (2018)]. Building on recent methods, we compute the spectral degeneracies of excited states and obtain the exact partition function. In the thermodynamic limit, the latter is dominated by the trivial (vacuum) anyon, so that topological order is destroyed at any nonzero temperature. In contrast, in a finite-size system, order survives up to a finite temperature, revealing a nontrivial scaling between temperature and size similar to that of the one-dimensional classical Ising model. We confirm this scaling by computing the thermal average of several observables such as Wegner-Wilson loops and topological mutual information.

Yu Zhao, Yidun Wan

A bstract We develop a comprehensive framework for realizing anyon condensation of topological orders within the string-net model by constructing a Hamiltonian that bridges the parent string-net model before and the child string-net model after anyon condensation. Our approach classifies all possible types of bosonic anyon condensation in any parent string-net model and identifies the basic degrees of freedom in the corresponding child models. The Kogut-Susskind lattice gauge theory model is a special case of our model if the full degrees of freedom of the model are truncated from SU(2) representations to quantum group SU(2) k . Compared with the traditional UMTC perspective of topological orders, our method offers a finer categorical description of anyon condensation at the microscopic level. We also explicitly represent relevant UMTC categorical entities characterizing anyon condensation through our model-based physical quantities, providing practical algorithms for calculating these categorical data.

Stefan V. Mashkevich, G.M. Zinov'ev

Nico Kirchner, Frank Pollmann, Technische Universität München