Universal relation between the dispersion curve and the ground-state correlation length in 1D antiferromagnetic quantum spin systems

Abstract

We discuss an universal relation $\epsilon (i\kappa )=0$ with $\mathrm{Re}\kappa =1/\xi$ in 1D quantum spin systems with an excitation gap, where $\epsilon (k)$ is the dispersion curve of the low-energy excitation and $\xi$ is the correlation length of the ground-state. We first discuss this relation for integrable models such as the Ising model in a transverse filed and the XYZ model. We secondly make a derivation of the relation for general cases, in connection with the equilibrium crystal shape in the corresponding 2D classical system. We finally verify the relation for the S=1 bilinear-biquadratic spin chain and $S=1/2$ zigzag spin ladder numerically.

6 pages, 2 figures, PRB accepted

References in corpus (10)

• Density matrix algorithm for the calculation of dynamical properties of low dimensional systems
• Physical Meaning of the Affleck-Kennedy-Lieb-Tasaki S=1 Quantum spin chain
• Large-Scale Numerical Evidence for Bose Condensation in the S=1 Antiferromagnetic Chain in a Strong Field
• Middle-Field Cusp Singularities in the Magnetization Process of One-Dimensional Quantum Antiferromagnets
• Density matrix renormalisation group study of the correlation function of the bilinear-biquadratic spin-1 chain
• Delta-Function Bose Gas Picture of S=1 Antiferromagnetic Quantum Spin Chains Near Critical Fields
• Antiferromagnetic Zigzag Spin Chain in Magnetic Fields at Finite Temperatures
• Variational and DMRG studies of the Frustrated Antiferromagnetic Heisenberg S=1 Quantum Spin Chain
• Transition from Haldane Phase to Spin Liquid and Incommensurate Correlation in Spin-1/2 Heisenberg Chains
• Commensurate and incommensurate correlations in Haldane gap antiferromagnets

Cited by in corpus (11)

• The density-matrix renormalization group
• New Trends in Density Matrix Renormalization
• Lanczos algorithm with Matrix Product States for dynamical correlation functions
• Spinon excitation and Möbius boundary condition in S=1/2 antiferromagnetic Heisenberg spin ladder with zigzag structure
• Dispersive Excitations in the One-Dimensional Ionic Hubbard Model
• Continuous similarity transformation for critical phenomena: easy-axis antiferromagnetic XXZ model
• Determination of Boundary Scattering, Intermagnon Scattering, and the Haldane Gap in Heisenberg Chains
• Correlation length of the 1D Hubbard Model at half-filling : equal-time one-particle Green's function
• Infinite boundary conditions for response functions and limit cycles in iDMRG, demonstrated for bilinear-biquadratic spin-1 chains
• Quantitative description of long-range order in the anisotropic spin-1/2 Heisenberg antiferromagnet on the square lattice
• Effective One-Dimensional Models from Matrix Product States