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Register a new userDynamic correlations of antiferromagnetic spin-1/2 XXZ chains at arbitrary temperature from complete diagonalization
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All eigenstates and eigenvalues are determined for the spin- 1/2 $XXZ$ chain $H = 2J sum_i ( S_{i}^{x} S_{i + 1}^{x} + S_{i}^{y} S_{i + 1}^{y} + Delta S_i^z S_{i + 1}^{z})$ for rings with up to N=16 spins, for anisotropies $Delta=0 , cos(0.3pi)$, and 1. The dynamic spin pair correlations $< S_{l+n}^{mu}(t) S_l^{mu} > , (mu=x,z)$, the dynamic structure factors $S^{mu}(q,omega)$, and the intermediate structure factors $I^{mu}(q,t)$ are calculated for arbitrary temperature T. It is found, that for all T, $S^{z}(q,omega)$ is mainly concentrated on the region $|omega| < varepsilon_2(q)$, where $varepsilon_2(q)$ is the upper boundary of the two-spinon continuum, although excited states corresponding to a much broader frequency spectrum contribute. This is also true for the Haldane-Shastry model and the frustrated Heisenberg model. The intermediate structure factors $I^{mu}(q,t)$ for $Delta eq 0$ show exponential decay for high T and large q. Within the accessible time range, the time-dependent spin correlation functions do not display the long-time signatures of spin diffusion.
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Using (infinite) density matrix renormalization group techniques, ground state properties of antiferromagnetic S=1 Heisenberg spin chains with exchange and single-site anisotropies in an external field are studied. The phase diagram is known to display a plenitude of interesting phases. We elucidate quantum phase transitions between the supersolid and spin-liquid as well as the spin-liquid and the ferromagnetic phases. Analyzing spin correlation functions in the spin-liquid phase, commensurate and (two distinct) incommensurate regions are identified.
In the easy-plane regime of XXZ spin chains, spin transport is ballistic, with a Drude weight that has a discontinuous fractal dependence on the value of the anisotropy $Delta = cos pi lambda$ at nonzero temperatures. We show that this structure necessarily implies the divergence of the low-frequency conductivity for generic irrational values of $lambda$. Within the framework of generalized hydrodynamics, we show that in the high-temperature limit the low-frequency conductivity at a generic anisotropy scales as $sigma(omega) sim 1/sqrt{omega}$; anomalous response occurs because quasiparticles undergo Levy flights. For rational values of $lambda$, the divergence is cut off at low frequencies and the corrections to ballistic spin transport are diffusive. We also use our approach to recover that at the isotropic point $Delta=1$, spin transport is superdiffusive with $sigma(omega) sim omega^{-1/3}$. We support our results with extensive numerical studies using matrix-product operator methods.
We study the finite-size behavior of the low-lying excitations of spin-1/2 Heisenberg chains with dimerization and next-to-nearest neighbors interaction, J_2. The numerical analysis, performed using density-matrix renormalization group, confirms previous exact diagonalization results, and shows that, for different values of the dimerization parameter delta, the elementary triplet and singlet excitations present a clear scaling behavior in a wide range of ell=L/xi (where L is the length of the chain and xi is the correlation length). At J_2=J_2c, where no logarithmic corrections are present, we compare the numerical results with finite-size predictions for the sine-Gordon model obtained using Luschers theory. For small delta we find a very good agreement for ell > 4 or 7 depending on the excitation considered.
This work is devoted to the investigation of nontrivial transport properties in many-body quantum systems. Precisely, we study transport in the steady state of spin-1/2 Heisenberg XXZ chains, driven out of equilibrium by two magnetic baths with fixed, different magnetization. We take grad
A few paradigmatic one-dimensional lattice-statistical spin models have recently attracted a vigorous scientific interest owing to their peculiar thermodynamic behavior, which is highly reminiscent of a temperature-driven phase transition. The pseudotransitions of one-dimensional lattice-statistical spin models differ from actual phase transitions in several important aspects: the first-order derivatives of the Gibbs free energy such as entropy or magnetization exhibit near a pseudo-transition an abrupt continuous change instead of a true discontinuity, whereas the second-order derivatives of the Gibbs free energy such as specific heat or susceptibility display near a pseudo-transition a vigorous finite peak instead of an actual power-law divergence. In the present chapter we will comprehensively examine a pseudo-critical behavior of the spin-1/2 Ising diamond and tetrahedral chains by a detailed examination of basic magnetothermodynamic quantities such as the entropy, specific heat and susceptibility. It will be demonstrated that density plots of these magnetothermodynamic quantities provide a useful tool for establishing a finite-temperature diagram, which clearly delimits boundaries between individual quasi-phases in spite of a lack of true spontaneous long-range order at any nonzero temperature. It is suggested that a substantial difference between the degeneracies of two ground states of the spin-1/2 Ising diamond and tetrahedral chains is an essential prerequisite for observation of a relevant pseudo-critical behavior in a close vicinity of their ground-state phase boundary.
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