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Advanced materials research

Thermal Entanglement Entropy Signature of Spin-Peierls Transition in Dimerized Isotropic XY Chain with Multi-Spin Interactions

Hai Lin Huang, Lin Jie Ding, Zhao‐Yu Sun

Published Aug 1, 2014• 0 citations
Publisher

Abstract

The finite-temperature entanglement entropy for an alternating spin-1/2 chain with multi-spin interactions is investigated by means of Green’s function theory combined with Jordan-Wigner transformation, to identify the spin-Peierls (SP) transition. It is found that the two-site thermal entanglement entropy is a useful tool to characterize theSPtransition. In addition, the competition between multi-spin interaction and Peierls-dimerization plays a central role in the critical phenomenon of the system.

DOI
10.4028/www.scientific.net/amr.1021.46

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The finite-temperature entanglement entropy for an alternating spin-1/2 chain with multi-spin interactions is investigated by means of Green’s function theory combined with Jordan-Wigner transformation, to identify the spin-Peierls (SP) transition. It is found that the two-site thermal entanglement entropy is a useful tool to characterize theSPtransition. In addition, the competition between multi-spin interaction and Peierls-dimerization plays a central role in the critical phenomenon of the system.
We study the spin-Peierls (SP) transition of one-dimensional chain polymeric complexes coupled to lattice by means of many-body Green's function theory. The chain effective elastic constant is an intrinsic factor that determines the order of SP transition. It is found that the SP transition temperature T(SP) and the susceptibility-maximum temperature T(max) are in agreement with the experimental results. When an external magnetic field is applied to the chain, it makes T(SP) and T(max) decrease, and drives the SP transition from the second order to the first order. Besides, we show that the two-site thermal entanglement entropy is a good indicator of SP transition. Further considering the effect of interchain coupling on SP transition, with weak coupling of double-chain, the theoretical values are closer to the experimental results. We also calculate the density of states and spectral functions, which show that the energy gap vanishes at a critical temperature lower than T(SP), indicating a gapless SP phase lies in the gapped dimerized phase. The interchain coupling can drive the SP transition from the second order to the first order, while the SP dimerization may collapse for large interchain couplings.
Through the Jordan—Wigner transformation, the entanglement entropy and ground state phase diagrams of exactly solvable spin model with alternating and multiple spin exchange interactions are investigated by means of Green's function theory. In the absence of four-spin interactions, the ground state presents plentiful quantum phases due to the multiple spin interactions and magnetic fields. It is shown that the two-site entanglement entropy is a good indicator of quantum phase transition (QPT). In addition, the alternating interactions can destroy the magnetization plateau and wash out the spin-gap of low-lying excitations. However, in the presence of four-spin interactions, apart from the second order QPTs, the system manifests the first order QPT at the tricritical point and an additional new phase called “spin waves”, which is due to the collapse of the continuous tower-like low-lying excitations modulated by the four-spin interactions for large three-spin couplings.
The quantum criticality and thermodynamics for the trimerized spin-1/2 isotropic XY chain with three-spin interactions in an external magnetic field are investigated by means of the Green's function theory combined with Jordan–Wigner transformation. The ground-state phase diagrams are explored, in which various phases are identified and described by typical M–h curves. Therein, two cusps emerge for strong three-spin interactions in two gapless phases at low and high fields, respectively. Moreover, the spin correlations and two-site entanglement entropy are calculated for a further understanding of quantum phase transition (QPT). It is also found that the magnetic-field-driven quantum criticality is closely related to the energy spectrum, in which an energy gap responsible for the appearance of 1/3 magnetization plateau can be opened up by three-spin interactions. The critical behavior disappears when the temperature becomes nonzero, yielding only a crossover behavior. In addition, the gapped low-lying excitations are responsible for the observed thermodynamic behaviors, wherein a structure with three peaks in the temperature dependence of specific heat is unveiled.
The two-dimensional Jordan-Wigner transformation is used to investigate the zero-temperature spin-Peierls transition for an anisotropic two-dimensional XY\mathrm{XY}XY model in the adiabatic limit. The phase diagram between the dimerized (D) state and uniform (U) state is shown in the parameter space of dimensionless interchain coupling $h{(=J}_{\ensuremath{\perp}}/J)$ and spin-lattice coupling \ensuremath{\eta}. It is found that the spin-lattice coupling $\ensuremath{\eta}$ must exceed some critical value ${\ensuremath{\eta}}_{c}$ in order to reach the D phase for any finite h. The dependence of ${\ensuremath{\eta}}_{c}$ on h is given by $\ensuremath{-}1/\mathrm{ln}h$ for $\stackrel{\ensuremath{\rightarrow}}{h}0$ and the transition between the U and D phases is of first order for at least $h>{10}^{\ensuremath{-}3}.$
In this paper we explore the entanglement in an orthogonal dimer-plaquette Ising-Heisenberg chain, assembled between plaquette edges, also known as orthogonal dimer plaquettes. The quantum entanglement properties involving an infinite chain structure are quite important, not only because the mathematical calculation is cumbersome but also because real materials are well represented by infinite chains. Using the local gauge symmetry of this model, we are able to map onto a simple spin-1 like Ising and spin-1/2 Heisenberg dimer model with single effective ion anisotropy. Thereafter this model can be solved using the decoration transformation and transfer matrix approach. First, we discuss the phase diagram at zero temperature of this model, where we find five ground states, one ferromagnetic, one antiferromagnetic, one triplet-triplet disordered and one triplet-singlet disordered phase, beside a dimer ferromagnetic-antiferromagnetic phase. In addition, we discuss the thermodynamic properties such as entropy, where we display the residual entropy. Furthermore, using the nearest site correlation function it is possible also to analyze the pairwise thermal entanglement for both orthogonal dimers. Additionally, we discuss the threshold temperature of the entangled region as a function of Hamiltonian parameters. We find a quite interesting thin reentrance threshold temperature for one of the dimers, and we also discuss the differences and similarities for both dimers.
We demonstrate that a Peierls dimerization can occur in ferromagnetic spin chains activated by thermal fluctuations. The dimer order parameter and entanglement measures are studied as functions of the modulation of the magnetic exchange interaction and temperature, using a spin-wave theory and the density-matrix renormalization group. We discuss the case where a periodic modulation is caused by spin-phonon coupling and the case where electronic states effectively induce such a modulation. The importance of the latter for a number of transition metal oxides is highlighted.