Excitation Spectrum Gap and Spin-Wave Stiffness of XXZ Heisenberg Chains: Global Renormalization-Group Calculation

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.

arXiv commentNew results added to text and figures. 12 pages, 18 figures, 3 tables. Published version

References in corpus (10)

• Gap generation in the XXZ model in a transverse magnetic field
• Integrability of quantum chains: theory and applications to the spin-1/2 $XXZ$ chain
• Density matrices for finite segments of Heisenberg chains of arbitrary length
• Third-neighbor and other four-point correlation functions of spin-1/2 XXZ chain
• Correlation functions of the spin-1/2 anti-ferromagnetic Heisenberg chain: exact calculation via the generating function
• Exact thermodynamic limit of short-range correlation functions of the antiferromagnetic $XXZ$-chain at finite temperatures
• Curie and Neel Temperatures of Quantum Magnets
• High Temperature Expansion for a Chain Model
• Two Superconducting Phases in the d=3 Hubbard Model: Phase Diagram and Specific Heat from Renormalization-Group Calculations
• Spin correlation functions and susceptibilities in the easy-plane XXZ chain

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• Phase Separation and Charge-Ordered Phases of the d = 3 Falicov-Kimball Model at T>0: Temperature-Density-Chemical Potential Global Phase Diagram from Renormalization-Group Theory
• Frustrated Further-Neighbor Antiferromagnetic and Electron-Hopping Interactions in the d=3 tJ Model: Finite-Temperature Global Phase Diagrams from Renormalization-Group Theory