Z2 topological order and first-order quantum phase transitions in systems with combinatorial gauge symmetry

Abstract

We study a generalization of the two-dimensional transverse-field Ising model, combining both ferromagnetic and antiferromagnetic two-body interactions, that hosts exact global and local Z2 gauge symmetries. Using exact diagonalization and stochastic series expansion quantum Monte Carlo methods, we confirm the existence of the topological phase in line with previous theoretical predictions. Our simulation results show that the transition between the confined topological phase and the deconfined paramagnetic phase is of first-order, in contrast to the conventional Z2 lattice gauge model in which the transition maps onto that of the standard Ising model and is continuous. We further generalize the model by replacing the transverse field on the gauge spins with a ferromagnetic XX interaction while keeping the local gauge symmetry intact. We find that the Z2 topological phase remains stable, while the paramagnetic phase is replaced by a ferromagnetic phase. The topological-ferromagnetic quantum phase transition is also of first-order. For both models, we discuss the low-energy spinon and vison excitations of the topological phase and their avoided level crossings associated with the first-order quantum phase transitions.

References in corpus (23)

• Fault-tolerant quantum computation by anyons
• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• An RVB phase in the triangular lattice quantum dimer model
• Fidelity approach to quantum phase transitions
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Computational Studies of Quantum Spin Systems
• Fractionalization in an Easy-axis Kagome Antiferromagnet
• Quantum dimer model on the kagome lattice: solvable dimer liquid and Ising gauge theory
• Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Ground State and Finite Temperature Lanczos Methods
• Fidelity susceptibility made simple: A unified quantum Monte Carlo approach
• The critical behaviour of the 2D Ising model in Transverse Field; a Density Matrix Renormalization calculation
• Symmetry enhanced first-order phase transition in a two-dimensional quantum magnet
• Spin liquid phase in a $S=1/2$ quantum magnet on the kagome lattice
• Detecting signals of weakly first-order phase transitions in two-dimensional Potts models
• Example of a first-order Néel to Valence-Bond-Solid transition in two-dimensions
• Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry
• Quasi-adiabatic quantum Monte Carlo algorithm for quantum evolution in imaginary time
• Dynamic scaling of topological ordering in classical systems
• Exotic phase diagram of a cluster charging model of bosons on the kagome lattice
• Stochastic Series Expansion Methods
• Correlation holes and slow dynamics induced by fractional statistics in gapped quantum spin liquids

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