Chinese Physics Letters

Quantum Fidelity and Thermal Phase Transitions in a Two-Dimensional Spin System

Bo Wang, Hailin Huang, Zhao‐Yu Sun, Su-Peng Kou

Published Dec 1, 2012• 11 citations

Abstract

We investigate the ability of quantum fidelity in detecting the classical phase transitions (CPTs) in a two-dimensional Heisenberg—Ising mixed spin model, which has a very rich phase diagram and is exactly soluble. For a two-site subsystem of the model, the reduced fidelity (including the operator fidelity and the fidelity susceptibility) at finite temperatures is calculated, and it is found that an extreme value presents at the critical temperature, thus shows a signal for the CPTs. In some parameter region, the signal becomes blurred. We propose to use the "normalized fidelity susceptibility" to solve this problem.

DOI: 10.1088/0256-307x/29/12/120301

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Chinese Physics Letters

Quantum Fidelity and Thermal Phase Transitions in a Two-Dimensional Spin System

Bo Wang, Hailin Huang, Zhao‐Yu Sun, Su-Peng Kou

Published Dec 1, 2012• 11 citations

Publisher

Abstract

DOI: 10.1088/0256-307x/29/12/120301

Related papers

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1/2

{J}_{1}

{J}_{2}

antiferromagnetic Heisenberg chain. For this model, we study three fidelity susceptibilities, ${\ensuremath{\chi}}_{\ensuremath{\rho}}$, ${\ensuremath{\chi}}_{D}$, and ${\ensuremath{\chi}}_{\mathrm{AF}}$, which are related to the spin stiffness, the dimer order, and antiferromagnetic order, respectively. All these ground-state fidelity susceptibilities are sensitive to the phase diagram of the

{J}_{1}

{J}_{2}

model. We show that they all can accurately identify a quantum critical point in this model occurring at ${J}_{2}^{c}\ensuremath{\sim}0.241{J}_{1}$ between a gapless Heisenberg phase for

{J}_{2}<{J}_{2}^{c}

and a dimerized phase for

{J}_{2}>{J}_{2}^{c}

. This phase transition, in the Berezinskii-Kosterlitz-Thouless universality class, is controlled by a marginal operator and is therefore particularly difficult to observe.

T=0

quantum phase transition with that of its classical limit, in order to single out the genuinely quantum effects. To this aim, we consider the one-dimensional Ising model in a transverse field: while the quantum

S=1∕2

Ising chain is exactly solvable and extensively studied, results for the classical limit $(S\ensuremath{\rightarrow}\ensuremath{\infty})$ of such model are lacking, and we supply them here. They are obtained numerically, via the transfer-matrix method, and their asymptotic low-temperature behavior is also derived analytically by self-consistent spin-wave theory. We draw the classical phase diagram according to the same procedure followed in the quantum analysis, and the two phase diagrams are found unexpectedly similar: Three regimes are detected also in the classical case, each characterized by a functional dependence of the correlation length on temperature and field analogous to that of the quantum model. What discriminates the classical from the quantum case are the different values of the exponents entering such dependencies, a consequence of the different nature of zero-temperature quantum fluctuations with respect to the thermal ones.