Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userExcitation Spectrum Gap and Spin-Wave Stiffness of XXZ Heisenberg Chains: Global Renormalization-Group Calculation
99
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The anisotropic XXZ spin-1/2 Heisenberg chain is studied using renormalization-group theory. The specific heats and nearest-neighbor spin-spin correlations are calculated thoughout the entire temperature and anisotropy ranges in both ferromagnetic and antiferromagnetic regions, obtaining a global description and quantitative results. We obtain, for all anisotropies, the antiferromagnetic spin-liquid spin-wave velocity and the Isinglike ferromagnetic excitation spectrum gap, exhibiting the spin-wave to spinon crossover. A number of characteristics of purely quantum nature are found: The in-plane interaction s_i^x s_j^x + s_i^y s_j^y induces an antiferromagnetic correlation in the out-of-plane s_i^z component, at higher temperatures in the antiferromagnetic XXZ chain, dominantly at low temperatures in the ferromagnetic XXZ chain, and, in-between, at all temperatures in the XY chain. We find that the converse effect also occurs in the antiferromagnetic XXZ chain: an antiferromagnetic s_i^z s_j^z interaction induces a correlation in the s_i^xy component. As another purely quantum effect, (i) in the antiferromagnet, the value of the specific heat peak is insensitive to anisotropy and the temperature of the specific heat peak decreases from the isotropic (Heisenberg) with introduction of either type (Ising or XY) anisotropy; (ii) in complete contrast, in the ferromagnet, the value and temperature of the specific heat peak increase with either type of anisotropy.
rate research
Read More
We numerically investigate elementary excitations of the Heisenberg alternating-spin chains with two kinds of spins 1 and 1/2 antiferromagnetically coupled to each other. Employing a recently developed efficient Monte Carlo technique as well as an exact diagonalization method, we verify the spin-wave argument that the model exhibits two distinct excitations from the ground state which are gapless and gapped. The gapless branch shows a quadratic dispersion in the small-momentum region, which is of ferromagnetic type. With the intention of elucidating the physical mechanism of both excitations, we make a perturbation approach from the decoupled-dimer limit. The gapless branch is directly related to spin 1s, while the gapped branch originates from cooperation of the two kinds of spins.
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
High resolution Neutron Spin Echo (NSE) spectroscopy was used to investigate the dynamics of an 3D Heisenberg ferromagnet in the exchange-controlled regime over a broad range of temperatures and momentum transfer. These results allow for the first time an extensive comparison between the experimental dynamical critical behavior and the predictions of the Renormalization Group (RG) theory. The agreement is exhaustive and surprising as the RG theory accounts not only for the critical relaxation but also for the shape crossover towards an exponential diffusive relaxation when moving from the critical to the hydrodynamic regime above $T_C$.
We employ an adaptation of a strong-disorder renormalization-group technique in order to analyze the ferro-paramagnetic quantum phase transition of Ising chains with aperiodic but deterministic couplings under the action of a transverse field. In the presence of marginal or relevant geometric fluctuations induced by aperiodicity, for which the critical behavior is expected to depart from the Onsager universality class, we derive analytical and asymptotically exact expressions for various critical exponents (including the correlation-length and the magnetization exponents, which are not easily obtainable by other methods), and shed light onto the nature of the ground state structures in the neighborhood of the critical point. The main results obtained by this approach are confirmed by finite-size scaling analyses of numerical calculations based on the free-fermion method.
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
