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Physical Review A

Effect of the Dzyaloshinskii-Moriya interaction on quantum speed limit and orthogonality catastrophe

Zheng-Rong Zhu, Qing Wang, Bin Shao, Jian Zou, Lian-Ao Wu

Published Apr 24, 2023• 6 citations
Publisher

Abstract

We study the effect of the Dzyaloshinskii-Moriya (DM) interaction on the quantum speed limit (QSL) and orthogonality catastrophe (OC) in XY spin chains. With an initial sudden quench, the general expressions of fidelity and QSL time are derived in terms of the antisymmetric quasiparticle excitation spectra. The numerical and analytical studies show that depending on the system parameters, the DM interaction has various influences on QSL and fidelity. In general, the OC is witnessed and QSL time vanishes in the thermodynamic limit as the variance of the quenched Hamiltonian in ground states scales with the system size, and the conclusion is independent of the DM interaction strength. However, it is interesting to note that the QSL can uniquely detect the critical points and lines induced by the DM interaction. We further analyze the actual evolution speed, a measure of the criticality, and find its direct correspondence with the OC. We also study an interesting phenomenon arising from the magnetic field and DM interaction in the presence of classical noise. Notably, we find that the system dynamic is fault tolerant when the system is subject to a uniform classical noise in the DM interaction strength.

DOI
10.1103/physreva.107.042427

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We study the effect of the Dzyaloshinskii-Moriya (DM) interaction on the quantum speed limit (QSL) and orthogonality catastrophe (OC) in XY spin chains. With an initial sudden quench, the general expressions of fidelity and QSL time are derived in terms of the antisymmetric quasiparticle excitation spectra. The numerical and analytical studies show that depending on the system parameters, the DM interaction has various influences on QSL and fidelity. In general, the OC is witnessed and QSL time vanishes in the thermodynamic limit as the variance of the quenched Hamiltonian in ground states scales with the system size, and the conclusion is independent of the DM interaction strength. However, it is interesting to note that the QSL can uniquely detect the critical points and lines induced by the DM interaction. We further analyze the actual evolution speed, a measure of the criticality, and find its direct correspondence with the OC. We also study an interesting phenomenon arising from the magnetic field and DM interaction in the presence of classical noise. Notably, we find that the system dynamic is fault tolerant when the system is subject to a uniform classical noise in the DM interaction strength.
We present an interesting relationship between the orthogonality catastrophe (OC) and the quantum speed limit (QSL) for a spin chain with uniform nearest neighbour couplings perturbed by an impurity spin. We thoroughly study the catastrophic QSL that specifies a bound on the evolution time between the initial and final states and in this respect, link it to the emerging OC effect. It is found that the speed of state evolution subtle but fundamental, and the bound characterized by QSL shows the same behaviours as the OC effect in the thermodynamic limit. It allows us to reveal some universal properties, in particular finite temperature effects. Significantly, the threshold of temperature and system size is clearly demonstrated for the QSL under finite temperature.
We examine the effects of the Dzyaloshinsky-Moriya (DM) interaction on the nonequilibrium thermodynamics in an anisotropic XY spin chain, which is driven out of equilibrium by a sudden quench of the control parameter of the Hamiltonian. By analytically evaluating the statistical properties of the work distribution and the irreversible entropy production, we investigate the influences of the DM interaction on the nonequilibrium thermodynamics of the system with different parameters at various temperatures. We find that depending on the anisotropy of the system and the temperature, the DM interaction may have different impacts on the nonequilibrium thermodynamics. Interestingly, the critical line induced by the DM interaction can be revealed via the properties of the nonequilibrium thermodynamics. In addition, our results suggest that the strength of the DM interaction can be detected experimentally by studying the nonequilibrium thermodynamics.
Jordan-Wigner transformation and Bogolyubov transformation are the main steps of the diagonalization of Hamiltonian and paly an important role in the statistical mechanics calculations for one-dimensional Heisenberg spin chain model. Many methods can be exploited as a tool to detect quantum phase transition, regions of criticality and scaling behavior in the vicinity of a quantum phase transition, such as geometric phase, fidelity susceptibility, order parameter, and entanglement entropy, which have direct relation with Bogolyubov transformation. We diagonalized the Hamiltonian in XY spin-chain systems with Dzyaloshinskii-Moriya interactions, the results shows that only the energy spectrum but not the coefficients of the Bogolyubov transformation depends on DM interaction. Therefore, the DM interaction may not influence the critical magnetic field of quantum phase transitions and not induce new critical regions in the XY spin model. Moreover, we further prove the ideas by the methods of geometric phases in this model.
We study the effect of Dzyaloshinskii-Moriya (DM) interaction on pairwise quantum discord, entanglement, and classical correlation in the anisotropic XY\mathrm{XY}XY spin-half chain. Analytical expressions for both quantum and classical correlations are obtained from the spin-spin correlation functions. These pairwise quantities exhibit interesting behaviors in relation to the relative strengths of the physical parameters. For the infinite chain, we show that the quantum discord can be useful to highlight the quantum phase transition, especially for the long-distance spins, where entanglement decays rapidly. We observe nonanalyticities of the derivatives of both quantum and classical correlations with respect to the magnetic intensity at the critical point; interestingly, the DM interaction weakens the critical behavior in the derivatives of these correlations. While the DM interaction suppresses the standard behaviors of the XY\mathrm{XY}XY model, it enhances surprisingly the pairwise entanglement for the third nearest neighbor spins.
We study the effects of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the ground-state properties of the Heisenberg XY spin chain by means of the fidelity susceptibility, order parameter, and entanglement entropy. Our results show that the DM interaction could influence the distribution of the regions of quantum phase transitions and cause different critical regions in the XY spin model. Meanwhile, the DM interaction has effective influence on the degree of entanglement of the system and could be used to increase the entanglement of the spin system.
Abstract The orthogonality catastrophe (OC) of quantum many-body systems is an important phenomenon in condensed matter physics. Recently, an interesting relationship between the OC and the quantum speed limit (QSL) was shown (Fogarty 2020 Phys. Rev. Lett. 124 110601). Inspired by the remarkable feature, we provide a quantitative version of the quantum average speed as another different method to investigate the measure of how it is close to the OC dynamics. We analyze the properties of an impurity qubit embedded into an isotropic Lipkin-Meshkov-Glick spin model, and show that the OC dynamics can also be characterized by the average speed of the evolution state. Furthermore, a similar behavior of the actual speed of quantum evolution and the theoretical maximal rate is shown which can provide an alternative speed-up protocol allowing us to understand some universal properties characterized by the QSL.