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Physical Review A

Fidelity susceptibility approach to quantum phase transitions in the XY spin chain with multisite interactions

W. W. Cheng, Jun‐Ming Liu

Published Jul 12, 2010• 38 citations
Publisher

Abstract

We study the quantum critical behavior of the $\mathit{XY}$ spin chain with multisite interaction by means of a fidelity susceptibility (FS) calculation. The key ingredients (e.g., finite-size scaling behavior, universality principle) of the quantum criticality near the critical point are investigated carefully. The results show that the FS calculation is reliable to characterize the quantum critical behavior and that the multisite interaction can induce the redistribution of the criticality region.

DOI
10.1103/physreva.82.012308

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We study the quantum critical behavior of the XY\mathit{XY}XY spin chain with multisite interaction by means of a fidelity susceptibility (FS) calculation. The key ingredients (e.g., finite-size scaling behavior, universality principle) of the quantum criticality near the critical point are investigated carefully. The results show that the FS calculation is reliable to characterize the quantum critical behavior and that the multisite interaction can induce the redistribution of the criticality region.
By means of the density matrix renormalization group technique, the scaling relation of the fidelity susceptibility proposed recently is verified for the spin-one XXZXXZXXZ spin chain with an on-site anisotropic term. Moreover, from the results of both the fidelity susceptibility and the entanglement entropy, the critical points and some of the corresponding critical exponents are determined through a proper finite-size scaling analysis, and these values agree with the findings in the literature. Thus our work provides a numerical support of the use of the fidelity in detecting quantum phase transitions.
The phase diagram of a quantum XYXYXY spin chain with Gaussian-distributed random anisotropies and transverse fields is investigated, with focus on the fidelity susceptibility, a recently introduced quantum information theoretical measure. Monitoring the finite-size scaling of the probability distribution of this quantity as well as its average and typical values, we detect a disorder-induced disappearance of criticality and the emergence of Griffiths phases in this model. It is found that the fidelity susceptibility is not self-averaging near the disorder-free quantum-critical lines. At the Ising critical point the fidelity susceptibility scales as a disorder-strength independent stretched exponential of the system size, in contrast with the quadratic scaling at the corresponding point in the disorder-free XYXYXY chain. Along the line where the average anisotropy vanishes the fidelity susceptibility appears to scale extensively, whereas in the disorder-free case this point is quantum critical with quadratic finite-size scaling.
Abstract We investigate the quantum coherence of an XY spin chain with Dzyaloshinskii–Moriya interaction using a quantum renormalization group-based method, and show that the relative entropy of coherence increases with Dzyaloshinskii–Moriya interaction strength at zero temperature, as well as at finite temperature. We also study the quantum criticality of the system by making use of the relative entropy of coherence and violation of Bell inequality, and find that the first derivatives of the renormalized quantum coherence exhibit singularity near the critical point of the quantum phase transition. Finally, we explore the finite-size scaling behaviors of the derivatives of the quantum coherence at the critical point of the quantum phase transition, and obtain several universal finite-size scaling laws.
We derive several closed-form expressions for the fidelity susceptibility (FS) of the anisotropic XY model in the transverse field. The basic idea lies in a partial fraction expansion of the expression so that all the terms are related to a simple fraction or its derivative. The critical points of the model are reiterated by the FS, demonstrating its validity for characterizing the phase transitions. Moreover, the critical exponents ν associated with the correlation length in both critical regions are successfully extracted by the standard finite-size scaling analysis.
The deconfined quantum critical point was proposed as a second-order quantum phase transition between two broken-symmetry phases beyond the Landau-Ginzburg-Wilson paradigm. However, numerical studies cannot completely rule out a weakly-first-order transition because of strong violations of finite-size scaling. We demonstrate that the fidelity is a simple probe to study the deconfined quantum critical point. We study the ground-state fidelity susceptibility close to the deconfined quantum critical point in a spin chain using the large-scale finite-size density-matrix renormalization-group method. We find that the finite-size scaling of the fidelity susceptibility obeys the conventional scaling behavior for continuous phase transitions, supporting the idea that the deconfined quantum phase transition is continuous. We numerically determine the deconfined quantum critical point and the associated correlation length critical exponent from the finite-size-scaling theory of the fidelity susceptibility. Our results are consistent with recent results obtained directly from the matrix product states for infinite-size lattices using others observables. Our work provides a useful probe to study critical behaviors at the deconfined quantum critical point from the concept of quantum information.