Topological Quantum Phase Transitions and Quench Dynamics

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 ${Z}_{2}$ 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 ${F}_{i}$ 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.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 ${Z}_{2}$ 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 ${F}_{i}$ 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.

arXiv:1011.4667Physical Review AJun 17, 20118 citations

Topological Invariants for Quantum Quench Dynamics

Haiping Hu, Erhai Zhao

Bulletin of the American Physical SocietyMar 5, 20200 citations

A Critical Study of Quantum Phase Transition

Shyam Kishor Thakur

We study the dynamical quantum phase transition of a critical quantum quench, in which the pre-quenched Hamiltonian, or the post quenched Hamiltonian, or both of them are set to be the critical points of equilibrium quantum phase transitions. We find a half-quantized or unquantized dynamical topological order parameter and dynamical Chern number; these results and also the existence of dynamical quantum phase transition are all closely related to the singularity of the Bogoliubov angle at the gap-closing momentum. The effects of the singularity may also be canceled out if both the prequenched and postquenched Hamiltonians are critical; then the dynamical topological order parameter and dynamical Chern number restore to integer ones. Our findings show that the widely accepted definitions of the dynamical topological order parameter and dynamical Chern number are problematic for the critical quenches in the perspective of topology, which call for new definitions of them.We study the dynamical quantum phase transition of a critical quantum quench, in which the pre-quenched Hamiltonian, or the post quenched Hamiltonian, or both of them are set to be the critical points of equilibrium quantum phase transitions. We find a half-quantized or unquantized dynamical topological order parameter and dynamical Chern number; these results and also the existence of dynamical quantum phase transition are all closely related to the singularity of the Bogoliubov angle at the gap-closing momentum. The effects of the singularity may also be canceled out if both the prequenched and postquenched Hamiltonians are critical; then the dynamical topological order parameter and dynamical Chern number restore to integer ones. Our findings show that the widely accepted definitions of the dynamical topological order parameter and dynamical Chern number are problematic for the critical quenches in the perspective of topology, which call for new definitions of them.

International Journal of Scientific Research in Science and TechnologyOct 31, 20190 citations

Quantum Quenches in Topological Systems

Graham Kells, Diptiman Sen, Johannes K. Slingerland +1 more

Bulletin of the American Physical SocietyMar 6, 20140 citations

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

{Z}_{2}

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

{F}_{i}

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.