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 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.
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 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-1/2 ladder, and a two-legged spin-1/2 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 spin-1/2 chain in a magnetic field; the second-order terms give corrections to the XXZ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.
Abstract In this paper we consider ladders with two, three, and four coupled Ising spin chains, characterized by interchain and intrachain couplings, to study in detail their magnetic behaviour for different ratios of the interaction constants and different values of magnetic field, by using a transfer matrix method and a complex algorithm, realizing the diagonalization and the differentiation. We have proposed a combined algorithm to realize also the generation of the elements of the transfer matrix for more complicated ladder configurations. The problem of Ising ladders is straightforward with a crossover between a 2D high‐temperature region and a 1D low‐temperature region when the 2D correlation length equals the width. To emphasize the fact that there is no finite magnetization in absence of the magnetic field, we study also analytically this case for the ladder with two coupled Ising chains. In presence of the magnetic field, for very weak magnetic fields (of the order 10−8, in reduced units) the magnetization goes from the value one to the value zero in a narrow interval of nonzero temperatures, where also the susceptibility exhibits a very high peak. This narrow interval, increasing the number of chains, is displaced towards higher temperatures. Also, in the case of interchain antiferromagnetic couplings, the formation of interchain spin pairs becomes clear.
We investigate a bilayer Kitaev model in which two honeycomb layers are coupled by the Heisenberg interactions to discuss the effects of interlayer coupling on Kitaev quantum spin liquids (QSLs). In this model, there exists a local conserved quantity which results in no long-range spin correlations in the system. Using the exact diagonalization, bond-operator mean-field theory, and cluster expansion techniques, we study ground-state properties in the system. The obtained results suggest the existence of a first-order quantum phase transition between the Kitaev QSL and dimer-singlet states. We find that a one-triplet excitation from the dimer-singlet ground state is localized owing to the existence of the local conserved quantity. To examine finite-temperature properties, we make use of the thermal pure quantum state approach. We clarify that the double-peak structure in the specific heat inherent in the Kitaev QSL is maintained even above the quantum phase transition. The present results suggest that the Kitaev QSL is stable against the interlayer interference. Magnetic properties of multilayer Kitaev models are also addressed.
The linear-perturbation renormalization-group transformation is used to study s=21 spin chains with antiferromagnetic intrachain interactions J<0 coupled by weak ferromagnetic interchain interactions ${J}^{\ensuremath{'}}>0$ in the longitudinal external magnetic field H. The field dependence of the specific heat for several models (XY, anisotropic Heisenberg, and Ising) has been found. The specific heat of the one-dimensional models ${(J}^{\ensuremath{'}}=0)$ exhibits a maximum at H=Hmax which decreases and shifts to higher fields with increasing temperature, and a minimum which disappears for the temperature higher than some characteristic temperature Tg. For the antiferromagnetic XY and Ising models the specific-heat maximum is shifted linearly, whereas for the Heisenberg model the shift cannot be fitted to a single power law. For an arbitrary small ferromagnetic interchain interaction ${(J}^{\ensuremath{'}}>0)$ the specific heat as a function of temperature has a singularity characterizing the antiferromagnetic phase transition. From the flow diagram analysis the dependence of the transition temperature on the interchain interaction and the external field has been found.
We study the 3D Kitaev and Kitaev-Heisenberg models, respectively, on the hyperhoneycomb and hyperoctagon lattices, both at zero and finite-temperature, in the thermodynamic limit. Our analysis relies on advanced tensor network (TN) simulations based on graph projected entangled-pair states (gPEPS). We map out the TN phase diagrams of the models and characterize their underlying gapped and gapless phases both at zero and finite temperature. In particular, we demonstrate how cooling down the hyperhoneycomb system from high temperature leads to fractionalization of spins to Majorana fermions and gauge fields that occurs in two separate temperature regimes, leaving their fingerprint on specific heat as a double-peak feature as well as on other quantities such as the thermal entropy, spin-spin correlations, and bond entropy. Using the Majorana representation of the Kitaev model, we further show that the low-temperature thermal transition to the Kitaev quantum spin liquid (QSL) phase is associated with the nontrivial Majorana band topology and the presence of Weyl nodes, which manifests itself via nonvanishing Chern number and finite thermal Hall conductivity. Beyond the pure Kitaev limit, we study the 3D Kitaev-Heisenberg (KH) model on the hyperoctagon lattice and extract the full phase diagram for different Heisenberg couplings. We further explore the thermodynamic properties of the magnetically-ordered regions in the KH model and show that, in contrast to the QSL phase, here the thermal phase transition follows the standard Landau symmetry-breaking theory.