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arXiv:1710.08713 · Journal of Physics Condensed Matter

Phase transitions and thermal entanglement of the distorted Ising–Heisenberg spin chain: topology of multiple-spin exchange interactions in spin ladders

Hamid Arian Zad, N.S. Ananikian

Published Oct 19, 2017• 13 citations
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Abstract

We consider a symmetric spin-1/2 Ising-XXZ double sawtooth spin ladder obtained from distorting a spin chain, with the XXZ interaction between the interstitial Heisenberg dimers (which are connected to the spins based on the legs via an Ising-type interaction), the Ising coupling between nearest-neighbor spins of the legs and rungs spins, respectively, and additional cyclic four-spin exchange (ring exchange) in the square plaquette of each block. The presented analysis supplemented by results of the exact solution of the model with infinite periodic boundary implies a rich ground state phase diagram. As well as the quantum phase transitions, the characteristics of some of the thermodynamic parameters such as heat capacity, magnetization and magnetic susceptibility are investigated. We prove here that among the considered thermodynamic and thermal parameters, solely heat capacity is sensitive versus the changes of the cyclic four-spin exchange interaction. By using the heat capacity function, we obtain a singularity relation between the cyclic four-spin exchange interaction and the exchange coupling between pair spins on each rung of the spin ladder. All thermal and thermodynamic quantities under consideration should be investigated by regarding those points which satisfy the singularity relation. The thermal entanglement within the Heisenberg spin dimers is investigated by using the concurrence, which is calculated from a relevant reduced density operator in the thermodynamic limit.

DOI
10.1088/1361-648x/aa8dd0

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We consider a symmetric spin-1/2 Ising-XXZ double sawtooth spin ladder obtained from distorting a spin chain, with the XXZ interaction between the interstitial Heisenberg dimers (which are connected to the spins based on the legs via an Ising-type interaction), the Ising coupling between nearest-neighbor spins of the legs and rungs spins, respectively, and additional cyclic four-spin exchange (ring exchange) in the square plaquette of each block. The presented analysis supplemented by results of the exact solution of the model with infinite periodic boundary implies a rich ground state phase diagram. As well as the quantum phase transitions, the characteristics of some of the thermodynamic parameters such as heat capacity, magnetization and magnetic susceptibility are investigated. We prove here that among the considered thermodynamic and thermal parameters, solely heat capacity is sensitive versus the changes of the cyclic four-spin exchange interaction. By using the heat capacity function, we obtain a singularity relation between the cyclic four-spin exchange interaction and the exchange coupling between pair spins on each rung of the spin ladder. All thermal and thermodynamic quantities under consideration should be investigated by regarding those points which satisfy the singularity relation. The thermal entanglement within the Heisenberg spin dimers is investigated by using the concurrence, which is calculated from a relevant reduced density operator in the thermodynamic limit.
The ground state, entropy, and magnetic Grüneisen parameter of the antiferromagnetic spin-1/2 Ising-Heisenberg model on a double sawtooth ladder are rigorously investigated using the classical transfer-matrix technique. The model includes the XXZ interaction between the interstitial Heisenberg dimers, the Ising coupling between nearest-neighbor spins of the legs and rungs, and additional cyclic four-spin Ising term in each square plaquette. For a particular value of the cyclic four-spin exchange, we found in the ground-state phase diagram of the Ising-Heisenberg ladder a quadruple point, at which four different ground states coexist together. During an adiabatic demagnetization process, a fast cooling accompanied with an enhanced magnetocaloric effect can be detected near this quadruple point. The ground-state phase diagram of the Ising-Heisenberg ladder is confronted with the zero-temperature magnetization process of the purely quantum Heisenberg ladder, which is calculated by using exact diagonalization based on the Lanczos algorithm for a finite-size ladder of 24 spins and the density-matrix renormalization group simulations for a finite-size ladder with up to 96 spins. Some indications of the existence of intermediate magnetization plateaus in the magnetization process of the full Heisenberg model for a small but nonzero four-spin Ising coupling were found. The DMRG results reveal that the quantum Heisenberg double sawtooth ladder exhibits some quantum Luttinger spin-liquid phase regions that are absent in the Ising-Heisenberg counterpart model. Except this difference, the magnetic behavior of the full Heisenberg model is quite analogous to its simplified Ising-Heisenberg counterpart and, hence, may bring insight into the fully quantum Heisenberg model from rigorous results for the Ising-Heisenberg model.
The entropy and cooling rate of the both antiferromagnetic spin-1/2 double sawtooth IsingHeisenberg model and mixed-spin (1,1/2) double sawtooth Ising-Heisenberg model on the distorted ladders are rigorously investigated under an adiabatic demagnetization process using the quantum transfer-matrix technique. The models include the XXZ interaction between the interstitial Heisenberg dimers, the Ising coupling between nearest-neighbor spins of the legs and rungs, and additional cyclic four-spin exchange (ring exchange) in the square plaquette of each block. Close to field-induced quantum phase transitions, we compare both models together in the ability of cooling/heating near the quantum critical points. However, we observe a large magnetocaloric effect for both models, the mixed-spin double sawtooth ladder shows much more magneticaloric efficiency than the spin-1/2 double sawtooth ladder. During an adiabatic demagnetization process it can be seen a temperature dropping in the vicinity of the zero-temperature quantum phase transitions. Various fixed values of the Isotropic and anisotropic parameters explicitly alter the quality of the magnetocaloric effect. This properties suggest double sawtooth Ising-Heisenberg ladders as promising alternative refrigerant materials for low-temperature magnetic refrigeration.
The entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain were analyzed. Due to the separable nature of the Ising-type exchange interactions between neighboring Heisenberg dimers, calculation of the entanglement can be performed exactly for each individual dimer. Pairwise thermal entanglement was studied in terms of the isotropic Ising-Heisenberg model and analytical expressions for the concurrence (as a measure of bipartite entanglement) were obtained. The effects of external magnetic field H and next-nearest neighbor interaction J(m) between nodal Ising sites were considered. The ground state structure and entanglement properties of the system were studied in a wide range of coupling constant values. Various regimes with different values of ground state entanglement were revealed, depending on the relation between competing interaction strengths. Finally, some novel effects, such as the two-peak behavior of concurrence versus temperature and coexistence of phases with different values of magnetic entanglement, were observed.
The spin-1/2 transverse field two-leg Ising ladder with nearest-neighbor exchange and plaquette four-spin interaction J4{J}_{4}J4​ is studied analytically and numerically with the density matrix renormalization group approach. The quantum phase diagram in the transverse field BBB versus J4{J}_{4}J4​ plane has been obtained. There are three different phases: a paramagnetic (PM) phase for high values of the transverse field and, for low values of BBB, a ferromagnetic (FM) ordered phase for small J4{J}_{4}J4​, and a dimerized-rung (DR) phase for large negative values of J4{J}_{4}J4​. All phases are separated by quantum phase transition lines meeting at a multicritical point. The critical lines have been obtained by exploring the entanglement entropy. The results show that along the critical lines the central charge is c=1/2c=1/2c=1/2, while at the multicritical point one has c=1c=1c=1. The scaling dimension of the energy operator is ${X}_{\ensuremath{\epsilon}}=1$, in agreement with the universality class of the critical behavior of the quantum Ising chain. An effective field theory for the multicritical point is also discussed. The FM and the DR order parameters have also been computed and we found a region where the FM and the DR phases coexist.
Most quantum entanglement investigations are focused on two qubits or some finite (small) chain structure, since the infinite chain structure is a considerably cumbersome task. Therefore, the quantum entanglement properties involving an infinite chain structure is quite important, not only because the mathematical calculation is cumbersome but also because real materials are well represented by an infinite chain. Thus, in this paper we consider an entangled diamond chain with Ising and anisotropic Heisenberg (Ising-XXZ) coupling. Two interstitial particles are coupled through Heisenberg coupling or simply two-qubit Heisenberg, which could be responsible for the emergence of entanglement. These two-qubit Heisenberg operators are interacted with two nodal Ising spins. An infinite diamond chain is organized by interstitial-interstitial and nodal-interstitial (dimer-monomer) site couplings. We are able to get the thermal average of the two-qubit operator, called the reduced two-qubit density operator. Since these density operators are spatially separated, we could obtain the concurrence (entanglement) directly in the thermodynamic limit. The thermal entanglement (concurrence) is constructed for different values of the anisotropic Heisenberg parameter, magnetic field, and temperature. We also observed the threshold temperature via the parameter of anisotropy, Heisenberg and Ising interaction, external magnetic field, and temperature.
We present the phase diagram of the S=1/2S=1/2S=1/2 Heisenberg model on the two leg ladder with cyclic four-spin exchange, determined by a combination of exact diagonalization and density-matrix renormalization group techniques. We find six different phases and regimes: the rung singlet phase, a ferromagnetic phase, two symmetry broken phases with staggered dimers and staggered scalar chiralities, and a gapped region with dominant vector chirality, or collinear spin correlations. We localize the phase transitions and investigate their nature.