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arXiv:1302.0781

Floquet topological quantum phase transitions in the transverse Wen-plaquette model

V. M. Bastidas, Clive Emary, Gernot Schaller, Álvaro Gómez-León, Gloria Platero, Tobias Brandes

Published Feb 4, 2013• 1 citation
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Abstract

Our aim in this work is to study the nonequilibrium behavior of the topological quantum phase transition in the transverse Wen-plaquette model. We show that under the effect of a nonadiabatic driving the system exhibits a new topological phase and a rich phase diagram. We define generalized topological order parameters by considering cycle-averaged expectation values of string operators in a Floquet state

DOI
10.48550/arxiv.1302.0781

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Our aim in this work is to study the nonequilibrium behavior of the topological quantum phase transition in the transverse Wen-plaquette model. We show that under the effect of a nonadiabatic driving the system exhibits a new topological phase and a rich phase diagram. We define generalized topological order parameters by considering cycle-averaged expectation values of string operators in a Floquet state
In this paper we study the quantum phase transition between a quantum state with topological order and that without topological order (TQPT) in the transverse Wen-plaquette model. By mapping the transverse Wen-plaquette model onto the d =1 Ising model in a transverse field, some exact results of the TQPT are obtained. The transverse Wen-plaquette model undergoes a continuous TQPT which is characterized in terms of the expectation values of string operators. In particular, the duality relationship between open-string and closed-string is explored —the expectation value of closed-string operator and that of open-string operator play the role of "order parameter" and "disorder order parameter" of the topological order, respectively. At the critical point the "condensation" of both Z 2 vortex and Z 2 charge indicates that the TQPT is a new type of phase transition beyond the Landau-Ginzburg-Wilson paradigm.
We study the quench dynamics of the topological quantum phase transition in the two-dimensional transverse Wen-plaquette model, which has a phase transition from a Z2{Z}_{2}Z2​ topologically ordered to a spin-polarized state. By mapping the Wen-plaquette model onto a one-dimensional quantum Ising model, we calculate the expectation value of the plaquette operator Fi{F}_{i}Fi​ during a slowly quenching process from a topologically ordered state. A logarithmic scaling law of quench dynamics near the quantum phase transition is found, which is analogous to the well-known static critical behavior of the specific heat in the one-dimensional quantum Ising model.
In this paper a duality between the d=2 Wen-plaquette model in a transverse field and the d=1 Ising model in a transverse field is used to learn the nature of the quantum phase transition (QPT) between a spin-polarized phase and a topological ordered state with the string-net condensation. The QPT is not induced by spontaneous symmetry breaking and there are no conventional Landau-type local order parameters. Instead the string-like non-local order parameters are introduced to describe the QPT. In particular, the duality character between the open-string and closed string for the QPT are explored.
Dynamical quantum phase transitions (DQPTs) are characterized by nonanalytic behaviors of physical observables as functions of time. When a system is subject to time-periodic modulations, the nonanalytic signatures of its observables could recur periodically in time, leading to the phenomena of Floquet DQPTs. In this work, we systematically explore Floquet DQPTs in a class of periodically quenched one-dimensional system with chiral symmetry. By tuning the strength of quench, we find multiple Floquet DQPTs within a single driving period, with more DQPTs being observed when the system is initialized in Floquet states with larger topological invariants. Each Floquet DQPT is further accompanied by the quantized jump of a dynamical topological order parameter, whose values remain quantized in time if the underlying Floquet system is prepared in a gapped topological phase. The theory is demonstrated in a piecewise quenched lattice model, which possesses rich Floquet topological phases and is readily realizable in quantum simulators like the nitrogen-vacancy center in diamonds. Our discoveries thus open a new perspective for the Floquet engineering of DQPTs and the dynamical detection of topological phase transitions in Floquet systems.
The periodically driven quantum Ising chain has recently attracted a large attention in the context of Floquet engineering. In addition to the common paramagnet and ferromagnet, this driven model can give rise to new topological phases. In this work, we systematically explore its quantum phase diagram by examining the properties of its Floquet ground state. We specifically focus on driving protocols with time-reversal invariant points, and demonstrate the existence of an infinite number of distinct phases. These phases are separated by second-order quantum phase transitions, accompanied by continuous changes of local and string order parameters, as well as sudden changes of a topological winding number and of the number of protected edge states. When one of these phase transitions is adiabatically crossed, the correlator associated to the order parameter is nonvanishing over a length scale which shows a Kibble-Zurek scaling. In some phases, the Floquet ground state spontaneously breaks the discrete time-translation symmetry of the Hamiltonian. Our findings provide a better understanding of topological phases in periodically driven clean integrable models.
We investigate both pure and mixed states Floquet dynamical quantum phase transition (DQPT) in the periodically time-dependent extended XY model. We exactly show that the proposed Floquet Hamiltonian of interacting spins can be expressed as a sum of noninteracting quasispins imposed by an effective time dependent magnetic field (Schwinger-Rabi model). The calculated Chern number indicates that there is a topological transition from the nonadiabatic to adiabatic regime. In the adiabatic regime, the quasispins trace the time dependent effective magnetic field and then oscillate between spin up and down states. While in the nonadiabatic regime, the quasispins cannot follow the time dependent effective magnetic field and feel an average magnetic field. We find the range of driving frequency over which the quasispins experience adiabatic cyclic processes. Moreover, we obtain the exact expression of the Loschmidt amplitude and generalized Loschmidt amplitude of the proposed Floquet system. The results represent that both pure and mixed states dynamical phase transition occurs when the system evolves adiabatically. In other words, the minimum required driving frequency for the appearance of Floquet DQPT is equal to the threshold frequency needed for transition from the nonadiabatic to adiabatic regime.