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arXiv:1007.2045 · Physical Review B

Quantum phase transitions in an exactly solvable quantum-spin biaxial model with multiple spin interactions

Andrei A. Zvyagin

Published Jul 10, 2009• 22 citations
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Abstract

A distinct integrable quantum-spin model is proposed. The model has a biaxial magnetic anisotropy of alternating coupling between spins together with multiple spin interactions. Our model gives the possibility to exactly find thermodynamic characteristics of the considered spin chain. The ground state of the model can reveal spontaneous values of the total magnetic and antiferromagnetic moments caused by multiple spin couplings. Also, in the ground state, depending on the strength of multiple spin couplings, our model manifests several quantum critical points, some of which are governed by the external magnetic field.

DOI
10.1103/physrevb.80.014414

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A distinct integrable quantum-spin model is proposed. The model has a biaxial magnetic anisotropy of alternating coupling between spins together with multiple spin interactions. Our model gives the possibility to exactly find thermodynamic characteristics of the considered spin chain. The ground state of the model can reveal spontaneous values of the total magnetic and antiferromagnetic moments caused by multiple spin couplings. Also, in the ground state, depending on the strength of multiple spin couplings, our model manifests several quantum critical points, some of which are governed by the external magnetic field.
We propose an exactly solvable quantum spin model, in which the alternation of the exchange interactions between neighboring spins is accompanied by the multiple spin exchange. The model permits us to obtain exactly thermodynamic characteristics of the considered quantum spin chain. In the ground state, depending on the strength of the three-spin coupling, the model manifests either the spin-gapped behavior of low-lying excitations at low magnetic fields, or the ferrimagnetic ordering with the spontaneous magnetization and with gapless low-lying excitations. The system undergoes second order or first order quantum phase transitions, governed by an external magnetic field and the multiple spin exchange coupling strength. Our exactly solvable quantum spin model demonstrates that multispin interactions in a dimerized quantum spin chain can produce a spontaneous magnetization. On the other hand, for quantum spin chains with a spontaneous magnetization, caused by multispin couplings, the alternation of nearest neighbor exchange interactions can be the reason for destroying of that magnetization and the onset of a spin gap for low-lying excitations.
Several exactly solvable quantum spin models with incommensurate magnetic structures, which manifest quantum phase transitions between incommensurate and commensurate phases, are proposed. The ground-state and thermodynamic characteristics of these quantum spin antiferromagnetic models with the Dzyaloshinsky-Moriya antisymmetric exchange interaction and spin-frustrating next-nearest-neighbor, three-spin, and four-spin (ring exchange) interactions are exactly studied. We investigated the ground state phases of the considered models, as function of the magnetic anisotropy, Dzyaloshinsky-Moriya interaction, next-nearest-neighbor coupling constants, and external magnetic field. Several quantum phase transitions between magnetically incommensurate phases and between incommensurate and ferromagnetic phases are predicted, and the behavior of thermodynamic characteristics of those models at phase transitions is studied. We have shown that for models with chiral three-spin interactions the Dzyaloshinsky-Moriya coupling yields the onset of the weak ferromagnetism, similar to three-dimensional ordered antiferromagnets, but not present in other quantum spin chains with the antisymmetric exchange. Considered models appeared to be important for several quasi-one-dimensional spin systems, studied in recent experiments.
Results for the characteristics of the macroscopic thermal entanglement for integrable spin-1/2 antiferromagnetic chain models with multispin interactions in the thermodynamic limit are presented. Such interactions cause quantum-phase transitions to incommensurate phases with partial spontaneous magnetization. We have derived exact equations, which determine the thermal and magnetic field behavior of the concurrence of spin chains. The analysis of these equations shows that there exists a critical temperature, below which the thermal entanglement of considered spin chains is nonzero. We have shown that at those quantum-phase transitions, caused by multispin interactions, the thermal entanglement is reduced. Also, we have shown that the thermal entanglement is reduced due to nonzero magnetization of spin chains in the ground state, caused by multispin interactions.
We present a class of exactly solvable quantum spin models which consist of two Heisenberg subsystems coupled via a long-range Lieb-Mattis interaction. The total system is exactly solvable whenever the individual subsystems are solvable and allows to study the effects of frustration. We consider i) the antiferromagnetic linear chain and ii) the Lieb-Mattis antiferromagnet for the subsystem Hamiltonians and present i) the complete ground-state phase diagram and ii) the full thermodynamic phase diagram. We find a novel phase which exhibits order-from-disorder phenomena.
The behavior in an external magnetic field is studied exactly for a wide class of multichain quantum spin models. It is shown that the magnetic field together with the interchain couplings cause commensurate–incommensurate phase transitions between the gapless phases in the ground state. The conformal limit of these models is studied and it is shown that the low-lying excitations for the incommensurate phases are not independent, because they are governed by the same magnetic field (chemical potential for excitations). A scenario for the transition from one to two space dimensions for the exactly integrable multichain quantum spin models is proposed, and it is shown that the incommensurate phases in an external magnetic field disappear in the limit of an infinite number of coupled spin chains. The similarities in the external field behavior for the quantum multichain spin models and a wide class of quantum field theories are discussed. The scaling exponents for the appearance of the gap in the spectrum of low-lying excitations of the quantum multichain models due to the relevant perturbations of the integrable theories are calculated.
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.