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Acta Physica Sinica

Effects of multisite interaction on nonequilibrium thermodynamics of XY spin chain in a transverse filed

Zhi He, Min Yu, Qiong Wang

Published Jan 1, 2019• 1 citation

Abstract

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.

DOI: 10.7498/aps.68.20190525

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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 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 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.

We consider a spin-

\frac{1}{2}

XY

chain in a transverse

(z)

field with multisite interactions. The additional terms introduced into the Hamiltonian involve products of spin components related to three adjacent sites. A Jordan--Wigner transformation leads to a simple bilinear Fermi form for the resulting Hamiltonian and, hence, the spin model admits a rigorous analysis. We point out the close relationships between several variants of the model, which were discussed separately in previous studies. The ground-state phases (ferromagnet and two kinds of spin liquid) of the model are reflected in the dynamic structure factors of the spin chains, which are the main focus in this study. First, we consider the

zz

dynamic structure factor, reporting for this quantity a closed-form expression and analyzing the properties of the two-fermion (particle-hole) excitation continuum, which governs the dynamics of transverse spin component fluctuations and of some other local operator fluctuations. Then we examine the

xx

dynamic structure factor, which is governed by many-fermion excitations, reporting both analytical and numerical results. We discuss some easily recognized features of the dynamic structure factors, which are signatures of the presence of the three-site interactions.

Pairwise quantum discord (QD) and entanglement of the three-qubit XXZ Heisenberg spin chain with two types of three-site interactions and an external magnetic field are investigated. Our study found that both entanglement and quantum discord could detect the quantum critical phenomena of this model. We were able to obtain a nonzero value of quantum discord even at high temperature with the increase of XZX[Formula: see text]YZY or XZY[Formula: see text]YZX three-site interaction, however, the cooperative effect of XZX[Formula: see text]YZY and XZY[Formula: see text]YZX interactions is more ideal. Furthermore, in contrast to XZY[Formula: see text]YZX and XZX[Formula: see text]YZY interactions, the cooperative effect of XZX[Formula: see text]YZY and XZY[Formula: see text]YZX three-site interactions is more efficient to enhance the maximum value of quantum discord. Likewise, the cooperative effect of XZX[Formula: see text]YZY and XZY[Formula: see text]YZX interactions is the most optimal to increase the range of magnetic field or anisotropy parameter where quantum discord maintains the maximum value.

Abstract An exactly solvable cluster spin model with three-spin interaction couplings Jx(for XZX spin components) and J y (for YZY spin components) in the presence of a transverse magnetic field h for a spin chain is investigated. For h = 0, and with only one non-zero interaction strength, the ground state is the cluster state. Through the Jordan–Wigner fermion mapping, the odd sites and the even sites form two separate transverse-XY chains, connected only through the boundary terms. Consequently, all measures of quantum correlations for nearest neighbour spins, the concurrence, the quantum mutual information and the quantum discord are all zero in the ground state. The dynamics is spin conserving for J y = J x , exhibiting a line of critical points for | h / J x | ⩽ 2 , with an uncorrelated direct product ground state for | h / J x | > 2 . There are several quantum critical points in the parameter space, with multi-fold degenerate ground states. The magnetisation and the global entanglement measure exhibit strong singular features for the spin conserving case. The next-neighbour quantum correlation measures are investigated analytically, which exhibit singular features in the vicinity of degeneracy critical points. The Jy - and h- derivatives of the concurrence exhibit singular peak behaviour near the degeneracy critical points, except in the spin conserving case where the derivatives are zero.