Mean-field ansatz for topological phases with string tension

Abstract

We propose a simple mean-field ansatz to study phase transitions from a topological phase to a trivial phase. We probe the efficiency of this approach by considering the string-net model in the presence of a string tension for any anyon theory. Such a perturbation is known to be responsible for a deconfinement-confinement phase transition which is well described by the present variational setup. We argue that mean-field results become exact in the limit of large total quantum dimension.

12 pages, 4 figures, typos in Table I corrected

References in corpus (20)

• Non-Abelian Anyons and Topological Quantum Computation
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Robustness of a perturbed topological phase
• Explicit tensor network representation for the ground states of string-net models
• Generalizations and limitations of string-net models
• Adiabatic Preparation of Topological Order
• Entanglement renormalization and gauge symmetry
• Topological Phase Transitions in the Golden String-Net Model
• Topology driven quantum phase transitions in time-reversal invariant anyonic quantum liquids
• Microscopic models of interacting Yang-Lee anyons
• Simulation of anyons with tensor network algorithms
• Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization
• Ising anyons with a string tension
• The Kitaev-Ising model, Transition between topological and ferromagnetic order
• Quantum phase transition in the $Z_3$ Kitaev-Potts model
• A mean field approach for string condensed states
• Russian doll spectrum in a non-Abelian string-net ladder
• Tensor-product representations for string-net condensed states
• Environment tensor as order parameter for symmetry breaking and (symmetry-protected) topological orders

Cited by in corpus (15)

• Anyon condensation and its applications
• Quantum and classical spin network algorithms for $q$-deformed Kogut-Susskind gauge theories
• Partition function of the Levin-Wen model
• Bridging Perturbative Expansions with Tensor Networks
• Quantum robustness of fracton phases
• Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories
• Tensor-network approach to phase transitions in string-net models
• Tensor network approach to phase transitions of a non-Abelian topological phase
• Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters
• Quantum robustness and phase transitions of the 3D Toric Code in a field
• Boson condensation and instability in the tensor network representation of string-net states
• Wegner-Wilson loops in string nets
• Bound states in string nets
• Variational Tensor Network Operator
• Ising versus $SU(2{)}_2$ string-net ladder