Exact edge singularities and dynamical correlations in spin-1/2 chains

Abstract

Exact formulas for the singularities of the dynamical structure factor, S^{zz}(q,omega), of the S=1/2 xxz spin chain at all q and any anisotropy and magnetic field in the critical regime are derived, expressing the exponents in terms of the phase shifts which are known exactly from the Bethe ansatz solution. We also study the long time asymptotics of the self-correlation function <0|S_j^z(t)S_j^z(0)|0>. Utilizing these results to supplement very accurate time-dependent Density Matrix Renormalization Group (DMRG) for short to moderate times, we calculate S^{zz}(q,omega) to very high precision.

4 pages, 1 figure, 1 table, published version

References in corpus (7)

• Real time evolution using the density matrix renormalization group
• Time-step targetting methods for real-time dynamics using DMRG
• Dynamic response of one-dimensional interacting fermions
• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• Dynamic structure factor of the Calogero-Sutherland model
• Spin diffusion and the anisotropic spin-1/2 Heisenberg chain

Cited by in corpus (10)

• Universal theory of nonlinear Luttinger liquids
• Spectral functions in one-dimensional quantum systems at T>0
• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Spectral function of spinless fermions on a one-dimensional lattice
• Exact exponents of edge singularities in dynamic correlation functions of 1D Bose gas
• Threshold singularities in the dynamic response of gapless integrable models
• Successes and failures of Bethe Ansatz Density Functional Theory
• Dynamical Functions of a 1D Correlated Quantum Liquid
• Dynamic structure factor of Luttinger liquids with quadratic energy dispersion and long-range interactions