Three-site Interaction Research Articles

Anomalous spin frustration enforced by a magnetoelastic coupling in the mixed-spin Ising model on decorated planar lattices

The mixed spin-1/2 and spin-S Ising model on a decorated planar lattice accounting for lattice vibrations of decorating atoms is treated by making use of the canonical coordinate transformation, the decoration-iteration transformation, and the harmonic approximation. It is shown that the magnetoelastic coupling gives rise to an effective single-ion anisotropy and three-site four-spin interaction, which are responsible for the anomalous spin frustration of the decorating spins in virtue of a competition with the equilibrium nearest-neighbor exchange interaction between the nodal and decorating spins. The ground-state and finite-temperature phase diagrams are constructed for the particular case of the mixed spin-1/2 and spin-1 Ising model on a decorated square lattice for which thermal dependencies of the spontaneous magnetization and specific heat are also examined in detail. It is evidenced that a sufficiently strong magnetoelastic coupling leads to a peculiar coexistence of the antiferromagnetic long-range order of the nodal spins with the disorder of the decorating spins within the frustrated antiferromagnetic phase, which may also exhibit double reentrant phase transitions. The investigated model displays a variety of temperature dependencies of the total specific heat, which may involve in its magnetic part one or two logarithmic divergences apart from one or two additional round maxima superimposed on a standard thermal dependence of the lattice part of the specific heat.

Magnetic-field control of electric polarization in coupled spin chains with three-site interactions

Magnetic-field control of electric polarization in coupled spin chains with three-site interactions

Quantum Correlation in the XY Spin Model with Anisotropic Three-Site Interaction

We investigate pairwise entanglement and quantum discord (QD) in the XY spin model with anisotropic three-site interaction at zero and finite temperatures. For both the nearest-neighbor spins and the next nearest-neighbor spins, special attention is paid to the dependence of entanglement and QD on the anisotropic parameter $\delta $ induced by the next nearest-neighbor spins. We show that the behavior of QD differs in many ways from entanglement under the influences of the anisotropic three-site interaction at finite temperatures. More important, comparing the effects of $\delta $ on the entanglement and QD, we find the anisotropic three-site interaction plays an important role in the quantum correlations at zero and finite temperatures. It is found that $\delta $ can strengthen the quantum correlation for both the nearest-neighbor spins and the next nearest-neighbor spins, especially for the nearest-neighbor spins at low temperature.

Magnetic Ground State Stabilized by Three-Site Interactions: Fe/Rh(111).

We report the direct observation of a theoretically predicted magnetic ground state in a monolayer Fe on Rh(111), which is referred to as an up-up-down-down (↑↑↓↓) double-row-wise antiferromagnetic spin structure, using spin-polarized scanning tunneling microscopy. This exotic phase, which exists in three orientational domains, is revealed by experiments with magnetic probe tips performed in external magnetic fields. It is shown that a hitherto unconsidered four-spin-three-site beyond-Heisenberg interaction distinctly contributes to the spin coupling of atoms with S≥1 spins. The observation of the ↑↑↓↓ order substantiates the presence of higher-order, in particular, three-site interactions, in thin magnetic films of itinerant magnets.

Fidelity susceptibility and entanglement entropy in S=1 quantum spin chain with three-site interactions

In the present work, we study the fidelity susceptibility and the entanglement entropy in an antiferromagnetic spin-1 chain with additional next-nearest neighbor interactions and three-site interactions, which are given by H=(J1SiSi+1+ J2SiSi+2)+[J3(SiSi+1)(Si+1Si+2)+ h.c.]. By using the density matrix renormalization group method, the ground-state properties of the system are calculated with very high accuracy. We investigate the effect of the three-site interaction J3 on the fidelity susceptibility numerically, and then analyze its relation with the quantum phase transition (QPT). The fidelity measures the similarity between two states, and the fidelity susceptibility describes the associated changing rate. The QPT is intuitively accompanied by an abrupt change in the structure of the ground-state wave function, so generally a peak of the fidelity susceptibility indicates a QPT and the location of the peak denotes the critical point. For the case of J2=0, a peak of the fidelity susceptibility is found by varying J3, and the height of the peak grows as the system size increases. The location of the peak shifts to a slightly lower J3 up to a particular value as the system size increases. Through a finite size scaling, the critical point J3c=0.111 of the QPT from the Haldane spin liquid to the dimerized phase is identified. We also study the effect of the three-site interaction on the entanglement entropy between the right half part and the rest. It is noted that the peak of the entanglement entropy does not coincide with the critical point. Instead, the critical point is determined by the position at which the first-order derivative of the entanglement entropy takes its minimum, since a second-order QPT is signaled by the first derivative of density matrix element. Moreover, the entanglement entropy disappears when J3=1/6, which corresponds to the size-independent Majumdar-Ghosh point. The positions of quantum critical points extracted from these two quantum information observables agree well with those obtained by the string order parameters, which characterizes the topological order in the Haldane phase. Secondly, we also study the case of J20, and obtain the critical points by both the fidelity susceptibility and the entanglement entropy. Finally we provide a ground-state phase diagram of the system. To sum up, the quantum information observables are effective tools for detecting diverse QPTs in spin-1 models.

Tripartite and bipartite quantum correlations in the XXZ spin chain with three-site interaction

Tripartite and bipartite quantum correlations in the three-qubit XXZ Heisenberg spin chain with two types of three-site interactions and an external magnetic field are investigated. We show that the increase in XZY − YZX interaction can enhance the robustness of both tripartite and bipartite correlations, whereas the increase in XZX $$+$$ YZY interaction could improve the robustness of tripartite quantum correlations, but diminish the robustness of bipartite quantum correlations. Tripartite measurement-induced disturbance is the most robust against temperature, and bipartite entanglement is the most fragile. Tripartite entanglement is even more robust than bipartite quantum discord when XZX $$+$$ YZY or XZY − YZX interaction is relatively large. The cooperative effect of XZX $$+$$ YZY and XZY − YZX interaction could induce bipartite entanglement even at high temperature. The cooperative effect of XZX $$+$$ YZY and XZY − YZX interaction is the most optimal to improve the robustness of all quantum correlations when the magnetic field is negative. When the magnetic field is positive, the effective of XZY − YZX interaction alone is more ideal to preserve different quantum correlations.

Mixed spin-1/2 and 3/2 Ising model with multi-spin interactions on a decorated square lattice

A mixed spin-1/2 and spin-3/2 Ising model on a decorated square lattice with a nearest-neighbor interaction, next-nearest-neighbor bilinear interaction, three-site four-spin interaction and single-ion anisotropy is exactly investigated using a generalized decoration-iteration transformation, Callen-Suzuki identity and differential operator technique. The ground-state and finite-temperature phase boundaries are obtained by identifying all relevant phases corresponding to minimum internal or free energy of the system. The thermal dependencies of magnetization, correlation functions, entropy and specific heat are also calculated exactly and the most interesting cases are discussed in detail.

Emergent phases in a compass chain with multisite interactions

We study a dimerised spin chain with biaxial magnetic interacting ions in the presence of an externally induced three-site interactions out of equilibrium. In the general case, the three-site interactions play a role in renormalizing the effective uniform magnetic field. We find that the existence of zero-energy Majorana modes is intricately related to the sign of Pfaffian of the Bogoliubov-de Gennes Hamiltonian and the relevant $Z_2$ topological invariant. In contrast, we show that an exotic spin liquid phase can emerge in the compass limit through a Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition. Such a BKT transition is characterized by a large dynamic exponent $z=4$, and the spin-liquid phase is robust under a uniform magnetic field. We find the relative entropy and the quantum discord can signal the BKT transitions. We also uncover a few differences in deriving the correlation functions for the systems with broken reflection symmetry.

Quantum discord and quantum phase transition in the XXZ spin chain with three-site interaction

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.

Energy dynamics in a generalized compass chain

We investigate the energy dynamics in a generalized compass chain under an external magnetic field. We show that the energy current operators act on three contiguous sites in the absence of the magnetic field, and they are incorporated with inhomogenous Dzyaloshinskii-Moriya interactions in the presence of the magnetic field. Under these complex interactions the Hamiltonian remains an exactly solvable spin model. We study the effects of the three-site interactions and the Dzyaloshinskii–Moriya interactions on the energy spectra and phase diagram. The results have revealed that the energy current of the pristine quantum compass model is conserved due to the associated intermediate symmetries, and for other general cases such a characteristic does not exist.

Quantum phase transitions in a generalized compass chain with three-site interactions

We consider a class of one-dimensional compass models with XYZ$-$YZX-type of three-site exchange interaction in an external magnetic field. We present the exact solution derived by means of Jordan-Wigner transformation, and study the excitation gap, spin correlations, and establish the phase diagram. Besides the canted antiferromagnetic and polarized phases, the three-site interactions induce two distinct chiral phases, corresponding to gapless spinless-fermion systems having two or four Fermi points. We find that the $z$ component of scalar chirality operator can act as an order parameter for these chiral phases. We also find that the thermodynamic quantities including the Wilson ratio can characterize the liquid phases. Finally, a nontrivial magnetoelectric effect is explored, and we show that the polarization can be manipulated by the magnetic field in the absence of electric field.

Frustration in an exactly solvable mixed-spin Ising model with bilinear and three-site four-spin interactions on a decorated square lattice

Competitive effects of so-called three-site four-spin interactions, single ion anisotropy and bilinear interactions is studied in the mixed spin-1/2 and spin-1 Ising model on a decorated square lattice. Exploring the decoration–iteration transformation, we have obtained exact closed-form expressions for the partition function and other thermodynamic quantities of the model. From these relations, we have numerically determined ground-state and finite-temperature phase diagrams of the system. We have also investigated temperature variations of the correlation functions, internal energy, entropy, specific heat and Helmholtz free energy of the system. From the physical point of view, the most interesting result represents our observation of a partially ordered ferromagnetic or phase in the system with zero bilinear interactions. It is remarkable, that due to strong frustrations disordered spins survive in the system even at zero temperature, so that the ground state of the system becomes macroscopically degenerate with non-zero entropy. Introduction of arbitrarily small bilinear interaction completely removes degeneracy and the entropy always goes to zero at the ground state.

SU(3) quantum critical model emerging from a spin-1 topological phase

Different from the spin-1 Haldane gapped phase, we propose a novel SO(3) spin-1 matrix product state (MPS), whose parent Hamiltonian includes three-site spin interactions. From the entanglement spectrum of a single block with $l$ sites, an enlarged SU(3) symmetry is identified in the edge states, which are conjugate to each other for the $l=even$ block but identical for the $l=odd$ block. By blocking this novel state, the blocked MPS explicitly displays the SU(3) symmetry with two distinct structures. Under a symmetric bulk bipartition with a sufficient large block length $% l=even$, the entanglement Hamiltonian (EH) of the reduced system characterizes a spontaneous dimerized phase with two-fold degeneracy. However, for the block length $l=odd$, the corresponding EH represents an SU(3) quantum critical point with delocalized edge quasiparticles, and the critical field theory is described by the SU(3) level-1 Wess-Zumino-Witten conformal field theory.

One-dimensional quantum spin heterojunction as a thermal switch

We study the thermal transport through a quantum spin-[Formula: see text] heterojunction, which consists of a finite-size chain with two-site anisotropic XY interaction and three-site XZX+YZY interaction coupled at its ends to two semi-infinite isotropic XY chains. By performing the Jordan–Wigner transformation, the original spin Hamiltonian is mapped onto a fermionic Hamiltonian. Then, the fermionic structure is discussed, and the heat current as a function of structural parameters is evaluated. It is found that the magnetic fields applied at respective chains play different roles in adjusting the heat current in this heterojunction. Moreover, the interplay between the anisotropy of the XY interaction and the three-site spin interaction assists to further control the thermal transport. In view of the numerical results, we propose this heterojunction to be an alternate candidate for manipulating the heat current in one-dimensional (1D) systems.

Optimal quantum communication transfer through two XXZ spin chains with three-site and Dzyaloshinsky–Moriya interactions

We investigate quantum entanglement transfer through two independent spin chains with three site and Dzyaloshinsky–Moriya interactions and the effect of phase shift. The initial target state |01+|10/2 or its mixed state is shown to be more suitable for quantum correlation transfer in this system. Although the three-site or Dzyaloshinsky–Moriya interaction can partially improve the transmission quality of quantum entanglement, it mainly enhances the amplitude rather than prolongs the survival time of entanglement. We find that strengthening the three-site interaction enhances the amplitude of quantum entanglement more significantly, and that of Dzyaloshinsky–Moriya interaction accelerates the entanglement vibration as time evolution more obviously.

Entanglement and quantum teleportation in a three-qubit Heisenberg chain with three-site interactions

The thermal entanglement of a three-qubit XXZ Heisenberg model with three-site interactions in an external magnetic field, and the quantum teleportation via this model in thermal equilibrium state are investigated. It is found that entanglement and average fidelity depend on temperature, magnetic field, and anisotropy parameter $$J_Z$$JZ. Only ferromagnetic system is suitable for quantum teleportation. $$\hbox {XZX}+\hbox {YZY}$$XZX+YZY interaction is in favor of entanglement, average fidelity, and critical temperatures, while $$\text{ XZY }- \hbox {YZX}$$XZY-YZX interaction against all of them. Moreover, we also find entanglement does not fully reflect average fidelity in virtue of study the relation between entanglement and average fidelity.

Global quantum discord in matrix product states and the application

Global quantum discord (GQD) is a measure of quantum correlation for multi-site quantum states. In this paper, we propose an efficient procedure to calculate global quantum discord (Gn) for consecutive n-site subsystems in infinite-size matrix product states (MPSs). We apply the method to study the scaling behavior of Gn in several one-dimensional infinite quantum spin chains, i.e., (1) a three-site interaction model whose ground state can be exactly expressed as MPSs, and (2) a spin-12 XXZ chain whose ground state is approximately expressed as MPSs with the help of infinite time-evolving block decimation (iTEBD) algorithm. In both models, as the increase of n, Gn shows an approximately linear growth. Unambiguous clue for the convergence of the incremental ΔGn=Gn−Gn−1 is observed when n is large enough. Moreover, in non-critical (gapped) regions ΔGn converges very fast, while in critical (gapless) regions it converges relatively slow. The behaviors are explained in a model-independent physical picture with finite-range correlations. Based on these results, we propose to use “discord per site” (Gnn) to describe the global correlations in infinite-size spin chains. Moreover, we find that the global discord shows a size-independent maximum at the infinite-order quantum phase transition point of the XXZ model.

One-norm geometric quantum discord of two-qubit state in spin chain environment at finite temperature

We study the dynamics of quantum correlations measured by quantum discord (QD) and one-norm geometric quantum discord (GQD) in a two-qubit system coupled to an XY spin chain with finite temperature. It is shown that one-norm GQD is more robust than QD against the decoherence induced by the spin chain with finite temperature, and one-norm GQD is superior to QD in detecting the critical point of quantum phase transition (QPT) of the spin chain. Considering the effects of the state parameters, the temperature of the spin chain and the asymmetric coupling parameter, we analyze the phenomenons of sudden transition and double sudden transitions occurred in the evolutions of QD and one-norm GQD. Besides, the influences of the Dzyaloshinsky–Moriya (DM) interaction and the three-site interaction in the spin chain are also taken into account.

Work done and irreversible entropy production in a suddenly quenched quantum spin chain with asymmetrical excitation spectra.

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.

Examining quantum correlations in the XY spin chain by local quantum uncertainty

We study the thermal quantum correlations in terms of entanglement, quantum discord (QD) and local quantum uncertainty (LQU) in the XY spin chain, and analyze their capability in detecting the critical points of quantum phase transition. By considering the effects of the three-site interaction, site distance, system size and anisotropy parameter, we show that LQU is superior to QD in detecting the critical points. The advantages of LQU are not to be restricted to zero temperature, and it is possible to estimate the critical points at high temperature. Furthermore, the properties of LQU are very interesting and exhibit different quantum correlations which cannot be shown by entanglement and QD.