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Chinese Physics B

Detection of multi-spin interaction of a quenched XY chain by the average work and the relative entropy*

Xiu-Xing Zhang, Fang-Jv Li, Kai Wang, Jing Xue, Guang-Wen Huo, Aiping Fang, Hongrong Li

Published Mar 16, 2021• 2 citations
Publisher

Abstract

We investigate the nonequilibrium thermodynamics of a quenched XY spin chain with multi-spin interaction in a transverse field. The analytical expressions of both the average work and the relative entropy are obtained under different quenching parameters. The influences of the system parameters on the nonequilibrium thermodynamics are investigated. We find that at finite temperature the critical phenomenon induced by the multi-spin interaction and the external field can be revealed by the properties of the system nonequilibrium thermodynamics. In addition, our results indicate that the average work and the relative entropy can be used to detect both the existence and strength of the multi-spin interaction in the nonequlibrium system.

DOI
10.1088/1674-1056/abeef5

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We investigate the nonequilibrium thermodynamics of a quenched XY spin chain with multi-spin interaction in a transverse field. The analytical expressions of both the average work and the relative entropy are obtained under different quenching parameters. The influences of the system parameters on the nonequilibrium thermodynamics are investigated. We find that at finite temperature the critical phenomenon induced by the multi-spin interaction and the external field can be revealed by the properties of the system nonequilibrium thermodynamics. In addition, our results indicate that the average work and the relative entropy can be used to detect both the existence and strength of the multi-spin interaction in the nonequlibrium system.
In recent years, the property of nonequilibrium thermodynamics in closed system, especially in spin chain system undergoing a quenching process, has become one of the hot topics in the quantum thermodynamics. The nonequilibrium thermodynamic properties of XY spin chain with XZX + YZY type of three-site interaction under a transverse field are studied by considering an exactly solvable model. First we review some basic concepts, i.e., the work distribution, the averaged work, the fluctuation of work, and the irreversible entropy in the nonequilibrium thermodynamics, and give the theoretical model and its solutions. Then, we concretely discuss the effects of the three-site interaction of XZX + YZY type on the average work, the fluctuation of work and the irreversible entropy in the extended XY chain undergoing a quench process. The theoretical calculation and numerical simulation show that the three-site interaction of XZX + YZY type may play a positive and negative role in the increase of the averaged work, which depends on the strength of initial external magnetic field. Moreover, we also find that work fluctuation can be effectively suppressed by adjusting the intensity of XZX + YZY three-site interaction. Finally, it is found that the irreversible entropy production presents a sharp peak characteristic near the critical magnetic field, and the value of the peak sharp decreases with the increase of XZX + YZY three-site interaction. Simultaneously, the corresponding physical explanations are also given. In a word, the results given in present paper may increasingly arouse one’s interest in the nonequilibrium quantum thermodynamics.
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.
We investigate geometric phase (GP) of a qubit symmetrically coupled to a XY spin chain with three-spin interaction in a transverse magnetic field. An analytical expression for the GP is found in the weak coupling limit. It is shown that the GP displays a sharp peak or dip around the quantum phase transition (QPT) point of the spin chain. Without the three-spin interaction, the GP has a peak or dip around the critical point λ=1λ=1λ=1. If the three-spin interaction exists, the peak or dip position is obviously shifted away from the original position. This result reveals that the GP may be taken as an observable to detect both the existence and strength of multi-spin interaction in a spin chain.
We consider global quenches in the quantum XY chain in a transverse field and study the nonequilibrium relaxation of the magnetization and the correlation function as well as the entanglement entropy in finite systems. For quenches in the ordered phase, the exact results are well described by a semiclassical theory (SCT) in terms of ballistically moving quasiparticles. In the thermodynamic limit the SCT is exact for the entanglement entropy and its modified version following the method of Calabrese, Essler and Fagotti: arXiv:1204.3911 is exact for the magnetization and the correlation function, too. The stationary correlation function is shown to be described by a generalized Gibbs ensemble.
In this paper, we extend the studies on the emergent thermodynamics in a quenched quantum Ising chain (QIC) [R. Dorner, J. Goold, C. Cormick, M. Paternostro, and V. Vedral, Phys. Rev. Lett. 109, 160601 (2012)] to a more general quantum spin chain with asymmetrical excitation spectra. We verify that the Jarzynski and Tasaki-Crooks relations are still tenable in this system. As an example, we discuss the behaviors of the work done and irreversible entropy production induced by a sudden quenching in the anisotropic XY chain in a transverse field with the XZY-YZX type of three-site interactions. Different from the QIC, this system has the phase transitions not only between two gapped phases, but also between gapped (or gapless) and gapless phases at zero temperature. We discuss the effects of quantum phase transitions on the work done and irreversible entropy production at low temperature.
In this paper, we investigate the nonequilibrium geometric phase (GP) of a spin chain system whose two end spins are respectively coupled to thermal reservoirs at different temperatures. In the spin chain, there exists the XX-type spin interaction and an external field is applied to each spin. An analytical expression for the GP is found in the weak coupling limit. The influences of various parameters on the deviation of GP from the unitary one are investigated. It is found that the GP is more stable against the decoherence when the external field is homogenously applied. In addition, the present result may provide a useful approach to the maintenance of GP in the nonequilibrium system.