Quench dynamics and ground state fidelity of the one-dimensional extended quantum compass model in a transverse field

Abstract

We study the ground state fidelity, fidelity susceptibility and quench dynamics of the extended quantum compass model in a transverse field. This model reveals a rich phase diagram which includes several critical surfaces depending on exchange couplings. We present a characterization of quantum phase transitions in terms of the ground state fidelity between two ground states obtained for two different values of external parameters. However, we derive scaling relations describing the singular behavior of fidelity susceptibility in the quantum critical surfaces. Moreover, we study the time evolution of the system after a critical quantum quench using the Loschmidt. We find that the revival times of Loschmidt echo are given by Trev = N/2vmax, where N is the size of the system and vmax is the maximum of lower bound group velocity of quasi-particles. Although the fidelity susceptibility shows the same exponent in all critical surfaces, the structure of the revivals after critical quantum quenches displays two different regimes reflecting different equilibration dynamics.

Exact Solutions and Degenerate Properties of Spin Chains with Reducible Hamiltonians

“…At present, the compass model is known to own various symmetries [18]; hence, we naturally search a case in the compass model. Indeed, the 1D compass model [14,19] (for one's interest in recent progress, see [20][21][22]), which is also referred to as the reduced Kitaev model [23], is found to be a case of our proposition. The 1D compass model has the following Hamiltonian:…”

Decoherence from spin environments: Loschmidt echo and quasiparticle excitations

“…, where |0 is the Bogoliubov vacuum annihilated by the γ k :s 36 . While excited states can be similarly obtained, their construction becomes quite cumbersome within the Bogoliubov-de Gennes formalism.…”

Decoherence and relaxation of topological states in extended quantum Ising models

“…More recently, the quantum Ising model was studied in the non-equilibrium regime to investigate the dynamical behavior of quantum phase transitions, e.g. the quenching in a driven Ising chain [13][14][15][16][17][18], the Kibble-Zurek mechanism [19,20], the Loschmidt echo of a single impurity coupled to the Ising chain [21], the engineered quantum transfer [22], the quantum superposition of topological defects [23], the decoherence dynamics in the strong coupling regime [24] as well as the role of quantum correlations in quantum phase transitions [25][26][27]. Importantly, the generalized class of Ising models can be characterized by a topological number [28][29][30][31][32] and, in the topologically nontrivial phase, localized states can occur at the end of an open chain [1,4] or at the interface separating regions with different topological number [33].…”