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arXiv:1201.6133 · Physica Scripta

Fidelity and entanglement entropy in the one-dimensional transverse-field quantum compass model

Mostafa Motamedifar, S. Mahdavifar, Saber Farjami Shayesteh, Somayyeh Nemati

Published Jun 11, 2013• 10 citations
arXivHTMLPDF

Abstract

The one-dimensional extended quantum compass model in the presence of a transverse magnetic field is considered. Induced effects of the transverse magnetic field on the ground state of the system are studied from the viewpoint of fidelity. Using the numerical Lanczos method, the fidelity and susceptibility of fidelity are computed in finite chains. The critical exponent of the fidelity susceptibility is obtained in good agreement with the scaling behavior of the correlation length. In addition, the von Neumann entropy is calculated and its signature on the quantum phase transition is shown.

DOI
10.1088/0031-8949/88/01/015003

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The one-dimensional extended quantum compass model in the presence of a transverse magnetic field is considered. Induced effects of the transverse magnetic field on the ground state of the system are studied from the viewpoint of fidelity. Using the numerical Lanczos method, the fidelity and susceptibility of fidelity are computed in finite chains. The critical exponent of the fidelity susceptibility is obtained in good agreement with the scaling behavior of the correlation length. In addition, the von Neumann entropy is calculated and its signature on the quantum phase transition is shown.
The quantum phase transition (QPT) of the one-dimensional (1D) quantum compass model in a transverse magnetic field is studied in this paper. An exact solution is obtained by using an extended Jordan and Wigner transformation to the pseudo-spin operators. The fidelity susceptibility, the concurrence, the block-block entanglement entropy, and the pseudo-spin correlation functions are calculated with antiperiodic boundary conditions. The QPT driven by the transverse field only emerges at zero field and is of the second-order. Several critical exponents obtained by finite size scaling analysis are the same as those in the 1D transverse field Ising model, suggesting the same universality class. A logarithmic divergence of the entanglement entropy of a block at the quantum critical point is also observed. From the calculated coefficient connected to the central charge of the conformal field theory, it is suggested that the block entanglement depends crucially on the detailed topological structure of a system.
The quantum phase transition (QPT) of the one-dimensional (1D) quantum compass model in a transverse magnetic field is studied in this paper. An exact solution is obtained by using an extended Jordan and Wigner transformation to the pseudospin operators. The fidelity susceptibility, the concurrence, the block-block entanglement entropy, and the pseudospin correlation functions are calculated with antiperiodic boundary conditions. The QPT driven by the transverse-field only emerges at zero field and is of the second order. Several critical exponents obtained by finite-size scaling analysis are the same as those in the 1D transverse-field Ising model, suggesting the same universality class. A logarithmic divergence of the entanglement entropy of a block at the quantum critical point is also observed. From the calculated coefficient connected to the central charge of the conformal field theory, it is suggested that the block entanglement depends crucially on the detailed topological structure of a system.
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. We also derive scaling relations describing the singular behavior of the fidelity susceptibility in the quantum critical surfaces. Moreover, we study the time evolution of the system after a critical quantum quench using the Loschmidt echo (LE). We find that the revival times of LE are given by , where N is the size of the system and v max is the maximum of the 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.
The presence of a quantum critical point can significantly affect the thermodynamic properties of a material at finite temperatures. This is reflected, e.g., in the entropy landscape S(T, c) in the vicinity of a quantum critical point, yielding particularly strong variations for varying the tuning parameter c such as magnetic field. In this work we have studied the thermodynamic properties of the quantum compass model in the presence of a transverse field. The specific heat, entropy and cooling rate under an adiabatic demagnetization process have been calculated. During an adiabatic (de)magnetization process temperature drops in the vicinity of a field-induced zero-temperature quantum phase transitions. However close to field-induced quantum phase transitions we observe a large magnetocaloric effect. PACS numbers: 75.10.Pq; 75.30.Sg; 02.70.-c I.
The ground-state fidelity per lattice site is computed for the quantum three-state Potts model in a transverse magnetic field on an infinite-size lattice in one spatial dimension in terms of the infinite matrix product state algorithm. It is found that, on the one hand, a pinch point is identified on the fidelity surface around the critical point, and on the other hand, the ground-state fidelity per lattice site exhibits bifurcations at pseudo critical points for different values of the truncation dimension, which in turn approach the critical point as the truncation dimension becomes large. This implies that the ground-state fidelity per lattice site enables us to capture spontaneous symmetry breaking when the control parameter crosses the critical value. In addition, a finite-entanglement scaling of the von Neumann entropy is performed with respect to the truncation dimension, resulting in a precise determination of the central charge at the critical point. Finally, we compute the transverse magnetization, from which the critical exponent β is extracted from the numerical data.
In order to investigate the quantum phase transition in the one-dimensional quantum compass model, we numerically calculate non-local string correlations, entanglement entropy and fidelity per lattice site by using the infinite matrix product state representation with the infinite time evolving block decimation method. In the whole range of the interaction parameters, we find that four distinct string orders characterize the four different Haldane phases and the topological quantum phase transition occurs between the Haldane phases. The critical exponents of the string order parameters β = 1/8 and the cental charges c = 1/2 at the critical points show that the topological phase transitions between the phases belong to an Ising type of universality classes. In addition to the string order parameters, the singularities of the second derivative of the ground state energies per site, the continuous and singular behaviors of the Von Neumann entropy and the pinch points of the fidelity per lattice site manifest that the phase transitions between the phases are of the second-order, in contrast to the first-order transition suggested in previous studies.