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Physical review. B, Condensed matter

Effect of an interchain magnetic interaction on the dimerized state of a two-XY-quantum-spin-chain ladder

Laurent Hubert, A. Caillé

Published Jun 1, 1991• 5 citations
Publisher

Abstract

The model that we study is a two-XY-quantum-spin-chain system with Ising interchain magnetic interaction. This model, referred to as the spin-ladder model, is used as a first step to model the thermodynamic properties of low-dimensional spin system. Similarities between the spin-ladder model and the one-dimensional Hubbard model are used in our analysis. As a consequence we can qualitatively understand the heat capacity and spin susceptibilty and show that both measurements are necessary to analyze a spin-ladder system. We also show that the strong-interchain-coupling limit of the spin-ladder model is equivalent to a one-chain spin Heisenberg Hamiltonian. Furthermore, the spin-Peierls transition is investigated for small (\ensuremath{\Vert}I/2J\ensuremath{\Vert}\ensuremath{\ll}1) and large (\ensuremath{\Vert}I/2J\ensuremath{\Vert}\ensuremath{\gg}1) interchain coupling, and we show its occurrence at relatively small spin-phonon coupling (\ensuremath{\lambda}\ensuremath{\lesssim}0.6). From the results obtained for the small- and large-interchain-interaction limits, we propose the conjecture that the in-phase dimerization persists for all values of the interaction parameter at zero temperature.

DOI
10.1103/physrevb.43.13187

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The model that we study is a two-XY-quantum-spin-chain system with Ising interchain magnetic interaction. This model, referred to as the spin-ladder model, is used as a first step to model the thermodynamic properties of low-dimensional spin system. Similarities between the spin-ladder model and the one-dimensional Hubbard model are used in our analysis. As a consequence we can qualitatively understand the heat capacity and spin susceptibilty and show that both measurements are necessary to analyze a spin-ladder system. We also show that the strong-interchain-coupling limit of the spin-ladder model is equivalent to a one-chain spin Heisenberg Hamiltonian. Furthermore, the spin-Peierls transition is investigated for small (\ensuremath{\Vert}I/2J\ensuremath{\Vert}\ensuremath{\ll}1) and large (\ensuremath{\Vert}I/2J\ensuremath{\Vert}\ensuremath{\gg}1) interchain coupling, and we show its occurrence at relatively small spin-phonon coupling (\ensuremath{\lambda}\ensuremath{\lesssim}0.6). From the results obtained for the small- and large-interchain-interaction limits, we propose the conjecture that the in-phase dimerization persists for all values of the interaction parameter at zero temperature.
The zero and finite temperature spin-Peierls transitions in a quasi-one-dimensional spin-12\frac{1}{2}21​ Heisenberg model coupled to adiabatic bond phonons is investigated using the stochastic series expansion (SSE) quantum Monte Carlo (QMC) method. The quantum phase transition from a gapless N\'eel state to a spin-gapped Peierls state is studied in the parameter space spanned by spatial anisotropy, interchain coupling strength, and spin-lattice coupling strength. It is found that for any finite interchain coupling, the transition to a dimerized Peierls ground state only occurs when the spin-lattice coupling exceeds a finite, nonzero critical value. This is in contrast to the pure 1D model (zero interchain coupling), where adiabatic/classical phonons lead to a dimerized ground state for any nonzero spin-phonon interaction. The phase diagram in the parameter space shows that for a strong interchain coupling, the relation between the interchain coupling and the critical value of the spin-phonon interaction is linear whereas for weak interchain coupling, this behavior is found to have a natural logarithmlike relation. No region was found to have a long range magnetic order and dimerization occurring simultaneously. Instead, the N\'eel state order vanishes simultaneously with the setting in of the spin-Peierls state. For the thermal phase transition, a continuous heat capacity with a peak at the critical temperature Tc{T}_{c}Tc​ shows a second order phase transition. The variation of the equilibrium bond length distortion ${\ensuremath{\delta}}_{eq}$ with temperature showed a power law relation which decayed to zero as the temperature was increased to Tc{T}_{c}Tc​, indicating a continuous transition from the dimerized phase to a paramagnetic phase with uniform bond length and zero antiferromagnetic susceptibility.
The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-1/21/21/2 ladder, and a two-legged spin-1/21/21/2 ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an XXZ\mathrm{XXZ}XXZ spin-1/21/21/2 chain in a magnetic field; the second-order terms give corrections to the XXZ\mathrm{XXZ}XXZ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.
Using an extension of the Jordan - Wigner transformation (JWT) in two dimensions, the effects of weak interchain coupling on the spin - Peierls (SP) system is studied. The magnetic interaction is considered to be a quantum XY-interaction, and the spin - lattice distortion is treated quasiclassically. On the analogy of the stepped Peierls transition theory, we propose a stepped SP transition theory. We find that, when any finite transverse coupling is introduced between nearest chains, the usual SP transition will be modified, and the dimerization and the opening of the gap will no longer occur simultaneously. This leads to the appearance of a gapless SP phase over a certain temperature region.
The ground-state properties of spin-Peierls ladder model with interchain Heisenberg interaction and interchain Dzyaloshinskii-Moriya(DM)interaction are studied by Lanczos numerical method. We mainly concentrate on the influence of interchain Heisenberg interaction and interchain DM interaction on system dimerization. The results show that these two interchain interations always act against the dimerization of the system, and they can make system ground state dimerization diminishing, which means that increasing the system dimensions may reduce system dimerization, even destroy the dimerization phase.
We investigate the thermodynamic behavior of the Kitaev ladder model under varying interchain coupling [Formula: see text] and external magnetic fields using the finite temperature Lanczos method and machine-learning approach. At zero magnetic field, we find that the specific heat exhibits a double-peak structure for finite [Formula: see text]. The characteristic temperature [Formula: see text] of the low-temperature peak increases significantly with increasing [Formula: see text], whereas the high-temperature peak remains insensitive to [Formula: see text]. We argue that stronger interchain coupling elevates the characteristic temperature required for flux excitations. The further analysis of the specific-heat phase diagram under a magnetic field for different [Formula: see text] values indicates that when the external magnetic field continuously increases, the specific heat of the system undergoes a transition from well-defined two peaks to one peak, and the system finally enters a fully polarized phase. Concurrently, the low-temperature peak of the specific heat vanishes, which is corroborated in the thermodynamic limit predicted by the machine-learning approach. As [Formula: see text] decreases, weaker interchain coupling makes the system more susceptible to magnetization. These results demonstrate that the Kitaev ladder with finite [Formula: see text] exhibits qualitatively similar character to the two-dimensional honeycomb Kitaev model under a magnetic field, highlighting the crucial role of interchain coupling in regulating flux excitation properties and stabilizing the spin liquid phase.
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.