We address a detailed analysis of the dynamical spin conductivity of an anisotropic spin ladder in the direction of the legs by means of a quantum many-particle approach. Bond operator transformation has been employed in order to map the original spin model Hamiltonian to a bosonic one. This bosonic Hamiltonian should include an infinite hard-core repulsion to preserve the SU(2) algebra of the original model. Using a Green's function approach, the energy spectrum of quasiparticle excitation has been obtained. Linear response theory has been implemented to obtain spin conductivity via calculation of time-ordered energy current correlation. The results show the spin conductivity possessing a nonzero value in a finite frequency interval. Increasing the rung-coupling exchange constant moved this frequency interval to higher frequencies. Also, the spin conductivity presents a small nonzero value at very low frequency for low rung-coupling constants. Furthermore, the effects of spin anisotropies on both leg and rung couplings are investigated. A tiny dependence of the spin transport on the anisotropy in the leg direction is observed in contrast to the strong one on the anisotropy along the rung direction, due to the direct effect of the triplet density. Additionally, the frequency behavior of the spin conductivity of the isotropic case has been studied due to the temperature effects. The temperature dependence of static spin conductivity has been found for various rung-coupling exchange constants and anisotropies in both coupling strengths.
We address a detailed analysis of the dynamical spin conductivity of an anisotropic spin ladder in the direction of the legs by means of a quantum many-particle approach. Bond operator transformation has been employed in order to map the original spin model Hamiltonian to a bosonic one. This bosonic Hamiltonian should include an infinite hard-core repulsion to preserve the SU(2) algebra of the original model. Using a Green's function approach, the energy spectrum of quasiparticle excitation has been obtained. Linear response theory has been implemented to obtain spin conductivity via calculation of time-ordered energy current correlation. The results show the spin conductivity possessing a nonzero value in a finite frequency interval. Increasing the rung-coupling exchange constant moved this frequency interval to higher frequencies. Also, the spin conductivity presents a small nonzero value at very low frequency for low rung-coupling constants. Furthermore, the effects of spin anisotropies on both leg and rung couplings are investigated. A tiny dependence of the spin transport on the anisotropy in the leg direction is observed in contrast to the strong one on the anisotropy along the rung direction, due to the direct effect of the triplet density. Additionally, the frequency behavior of the spin conductivity of the isotropic case has been studied due to the temperature effects. The temperature dependence of static spin conductivity has been found for various rung-coupling exchange constants and anisotropies in both coupling strengths.
We investigate here the impact of an out-of-plane magnetic field and spin-orbit interaction on the spin conductivity of the two-dimensional Heisenberg model on a Lieb lattice. In this study, the Hamiltonian of the spin model has been transformed into a strongly interacting bosonic gas using a hard boson transformation. In this transformation, the occupation of a boson at each site is restricted by adding a hard core repulsion. To determine the excitation spectrum of the mapped model, the Green's function method has been employed. Based on the spectrum of the bosonic gas, the two-particle Green's function related to the spin conductivity of the two-dimensional Heisenberg model has been calculated. Computational results indicate that with an increase in the strength of the Dzyaloshinskii-Moriya interaction, the peak position in the dynamic spin conductivity shifts to higher frequencies under a constant magnetic field. However, the magnetic field does not affect the peak position of the dynamic spin conductivity. On the other hand, the intensity of dynamic spin conductivity increases with the strength of the Dzyaloshinskii-Moriya interaction. Our findings suggest that for a range of values of Dzyaloshinskii-Moriya interaction strength, the static transverse structure factor continuously decreases with the magnetic field. Additionally, for each value of the magnetic field, the temperature dependence of the static spin conductivity of localized electrons on the lattice exhibits a limited temperature peak.
We study the spin and thermal conductivity of spin-21 ladders and chains at finite temperature, relevant for experiments with quantum magnets. Using a state-of-the-art density matrix renormalization group algorithm, we compute the current autocorrelation functions on the real-time axis and then carry out a Fourier integral to extract the frequency dependence of the corresponding conductivities. The finite-time error is analyzed carefully. We first investigate the limiting case of spin-21XXZ chains, for which our analysis suggests nonzero dc conductivities in all interacting cases irrespective of the presence or absence of spin Drude weights. For ladders, we observe that all models studied are normal conductors with no ballistic contribution. Nonetheless, only the high-temperature spin conductivity of XX ladders has a simple diffusive, Drude-like form, while Heisenberg ladders exhibit a more complicated low-frequency behavior. We compute the dc spin conductivity down to temperatures of the order of $T\ensuremath{\sim}0.5J$, where J is the exchange coupling along the legs of the ladder. We further extract mean-free paths and discuss our results in relation to thermal conductivity measurements on quantum magnets.
Based on numerical simulations, a study of the high temperature, finite frequency, thermal conductivity kappa(omega) of spin-1/2 ladders is presented. The exact diagonalization and a novel Lanczos technique are employed. The conductivity spectra, analyzed as a function of rung coupling, point to a nondiverging dc limit but to an unconventional low frequency behavior. The results are discussed in perspective with recent experiments indicating a significant magnetic contribution to the energy transport in quasi-one-dimensional compounds.
In this thesis, I use a quantum Monte Carlo (QMC) method based on the stochastic series expansion (SSE) to study transport, quantum phase diagrams, and dynamics of several one- and quasi-one-dimensional spin systems, including spin-1/2 and spin-1 chains, a frustrated four-leg spin tube, and N-leg spin-1/2 ladders. I establish a diffusive channel for the finite temperature spin transport of the spin-1/2 antiferromagnetic Heisenberg chain. Extensive finite size studies are detailed, allowing to extract the diffusion kernel in the thermodynamic limit. The diffusion is found to exhibit no anomalous exponent, moreover it is shown to survive for finite values of exchange anisotropy and magnetic fields, however with a strong suppression away from the isotropic point and for increasing magnetic fields. In the case of the spin-1 chain, I obtain the quantum phase diagram and spin dynamics in the combined presence of finite single-ion anisotropies and external magnetic fields. I also prove the existence of magnon modes and multi-particle continua and determine their evolutions as a function of anisotropies and magnetic fields. Moreover, I calculate the magnetic field dependence of the nuclear magnetic relaxation as a function of the single ion anisotropy. For the quasi-one-dimensional spin system of a frustrated four-leg tube, I investigate the regime of large rung coupling, where QMC is applicable. I evaluate the uniform spin susceptibility and the dynamic structure factor and show that in this regime the spin-tube exhibts a crossover from a gapped effective antiferromagnetic spin-2 chain behavior with massive magnons to a gapless Luttinger liquid phase with spinon excitations. Finally, I investigate the spin dynamics of N-leg spin-1/2 ladders with spacially isotropic interactions for N=1,..,5. I obtain the low-lying excitations of the spin ladders as a function of the number of legs and show that they exhibt an even-odd oscillation which is consistent with Haldane's conjecture and other known results for the thermodynamics of spin ladders.
We investigate the dynamical transfer of bipartite entanglement through a two-leg spin-1/2 ladder governed by the anisotropic Heisenberg (XXZ-type) model with a selective magnetic field applied exclusively to the mediating rungs. Starting from a maximally entangled initial rung pair, we demonstrate high-fidelity entanglement transfer to the terminal pair (F_max = 0.9998 for N = 3 rung pairs), with the intermediate rungs remaining effectively disentangled throughout. The dynamics is governed by two independent timescales: a fast carrier oscillation at frequency omega_fast = 2*sqrt(1 + 4d^2) J (set by local rung physics, field-independent) and a slow transfer envelope with period T_slow = 2.37 h/J^2 (set by virtual inter-rung coupling, field-dependent). The effective inter-rung coupling J_eff = alpha(d,g) J^2/h is derived via second-order perturbation theory through two parallel virtual paths. We systematically study the effects of magnetic field strength, Hamiltonian anisotropy, and initial state on transfer quality, establish a global parameter space map of the fidelity, and demonstrate robustness under uncorrelated coupling disorder (mean F_max > 0.998 for delta <= 10%). All results are obtained by exact diagonalisation for systems of up to N = 5 rung pairs; extension to larger systems requires tensor-network methods such as DMRG. Compared to one-dimensional chain proposals, the ladder geometry enables a spatially selective control mechanism that suppresses intermediate entanglement while preserving coherent transfer, providing a distinct route to engineered quantum channels.
We theoretically study the magnetic excitations in a frustrated two-leg spin-ladder system, in which antiferromagnetic exchange interactions act on the nearest-neighbor and next-nearest-neighbor bonds in the leg direction, and on the nearest-neighbor bonds in the rung direction. A dynamical spin correlation function at zero temperature is calculated using the dynamical density-matrix renormalization-group method for possible magnetic phases, i.e., columnar-dimer and rung-singlet phases. The columnar-dimer phase is characterized by multispinon excitations with a spin gap, whereas the rung-singlet phase is dominated by the triplet excitation in the rung direction. One major difference found between these two phases appears in the spectral weight of magnetic excitations, in particular, the bonding and antibonding modes in the rung direction. Therefore, we can distinguish one phase from the other by the difference in the spectral weight. Furthermore, we examine the effect of frustration on both modes in the rung-singlet phase with a perturbation theory from the strong coupling limit. The antibonding mode is shown to be stable against frustration, and a wave number with minimum excitation energy is shifted from being commensurate to being incommensurate. In contrast, the bonding mode is merged into the continuum excitation of multiple triplet excitations by increasing frustration. By comparing our results with inelastic neutron scattering experiments for BiCu2PO6, the magnitude of the magnetic exchange interactions and the ground state will be determined.