Intermediate temperature dynamics of one-dimensional Heisenberg antiferromagnets

Abstract

We present a general theory for the intermediate temperature (T) properties of Heisenberg antiferromagnets of spin-S ions on p-leg ladders, valid for 2Sp even or odd. Following an earlier proposal for 2Sp even (Damle and Sachdev, cond-mat/9711014), we argue that an integrable, classical, continuum model of a fixed-length, 3-vector applies over an intermediate temperature range; this range becomes very wide for moderate and large values of 2Sp. The coupling constants of the effective model are known exactly in terms of the energy gap above the ground state (for 2Sp even) or a crossover scale (for 2Sp odd). Analytic and numeric results for dynamic and transport properties are obtained, including some exact results for the spin-wave damping. Numerous quantitative predictions for neutron scattering and NMR experiments are made. A general discussion on the nature of T>0 transport in integrable systems is also presented: an exact solution of a toy model proves that diffusion can exist in integrable systems, provided proper care is taken in approaching the thermodynamic limit.

38 pages, including 12 figures

References in corpus (17)

• Transport and conservation laws
• Susceptibility of the Spin 1/2 Heisenberg Antiferromagnetic Chain
• Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}
• Spin dynamics and transport in gapped one-dimensional Heisenberg antiferromagnets at nonzero temperatures
• Properties of lightly doped t-J two-leg ladders
• Low energy effective Hamiltonian for the XXZ spin chain
• Susceptibility and Low Temperature Thermodynamics of Spin-1/2 Heisenberg Ladders
• Experimental Evidence of a Haldane Gap in an S = 2 Quasi-linear Chain Antiferromagnet
• Spin diffusion and the spin 1/2 XXZ chain at $T=\infty$ from exact diagonalization
• Dynamics of the spin-half Heisenberg chain at intermediate temperatures
• Spin Dependence of Correlations in Two-Dimensional Quantum Heisenberg Antiferromagnets
• Nuclear relaxation in the spin-1/2 antiferromagnetic chain compound Sr_2CuO_3 --- comparison between theories and experiments
• Dimensional Crossover in Quantum Antiferromagnets
• Monte Carlo Study of Correlations in Quantum Spin Chains at Non-Zero Temperature
• Quantum-critical scaling and temperature-dependent logarithmic corrections in the spin-half Heisenberg chain
• Low-Energy Properties of Antiferromagnetic Spin-1/2 Heisenberg Ladders with an Odd Number of Legs
• Correlation Lengths in Quantum Spin Ladders

Cited by in corpus (16)

• 17O NMR study of q=0 spin excitations in a nearly ideal S=1/2 1D Heisenberg antiferromagnet, Sr2CuO3, up to 800 K
• Dephasing-induced diffusive transport in anisotropic Heisenberg model
• Modes of magnetic resonance in the spin liquid phase of Cs2CuCl4
• Anomalous scaling of conductivity in integrable fermion systems
• Comment on "Spin Transport properties of the quantum one-dimensional non-linear sigma model"
• Spin transport properties of the quantum one-dimensional non-linear sigma model : an application to Haldane gap systems
• Integrable Mott insulators driven by finite electric field
• Diffusive transport in spin-1 chains at high temperatures
• Coexistence of Anomalous and Normal Diffusion in Integrable Mott Insulators
• Spin transport in the Neel and collinear antiferromagnetic phase of the two dimensional spatial and spin anisotropic Heisenberg model on a square lattice
• The hydrodynamic theory of dynamical correlation functions in the XX chain
• Hydrodynamics of R-charged D1-branes
• 63Cu NQR evidence of dimensional crossover to anisotropic 2d regime in S= 1/2 three-leg ladder Sr2Cu3O5
• Thermodynamics of Two-Dimensional Ideal Ferromagnets - Three-Loop Analysis
• A semi-classical approach to electron spin resonance in quantum spin systems
• Spinor Bose gas in an elongated trap