Spin diffusion and the anisotropic spin-1/2 Heisenberg chain

Abstract

Measurements of the spin-lattice relaxation rate 1/T_1 by nuclear magnetic resonance for the one-dimensional Heisenberg antiferromagnet Sr_2CuO_3 have provided evidence for a diffusion-like contribution at finite temperature and small wave-vector. By analyzing real-time data for the auto- and nearest-neighbor spin-spin correlation functions obtained by the density-matrix renormalization group I show that such a contribution indeed exists for temperatures T>J, where J is the coupling constant, but that it becomes exponentially suppressed for T << J. I present evidence that the frequency-dependence of 1/T_1 in the Heisenberg case is smoothly connected to that in the free fermion case where the exponential suppression of the diffusion-like contribution is easily understood.

9 pages, 7 figures

References in corpus (23)

• Real time evolution using the density matrix renormalization group
• 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}
• Heat transport by lattice and spin excitations in the spin chain compounds SrCuO_2 and Sr_2CuO_3
• The thermal conductivity of the spin-1/2 XXZ chain at arbitrary temperature
• Dynamic response of one-dimensional interacting fermions
• Conductivity of a clean one-dimensional wire
• Transport in Almost Integrable Models: Perturbed Heisenberg Chains
• On the finite temperature Drude weight of the anisotropic Heisenberg chain
• Exact Correlation Amplitude for the S=1/2 Heisenberg Antiferromagnetic Chain
• 17O NMR study of q=0 spin excitations in a nearly ideal S=1/2 1D Heisenberg antiferromagnet, Sr2CuO3, up to 800 K
• Low-temperature transport in Heisenberg chains
• Coulomb drag by small momentum transfer between quantum wires
• NMR relaxation in half-integer antiferromagnetic spin chains
• 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
• Real-time dynamics at finite temperature by DMRG: A path-integral approach
• Nuclear relaxation in the spin-1/2 antiferromagnetic chain compound Sr_2CuO_3 --- comparison between theories and experiments
• Drude Weight at Finite Temperatures for Some Non-Integrable Quantum Systems in One Dimension
• Thermal conductivity of quasi-one-dimensional antiferromagnetic spin-chain materials
• NMR relaxation rates for the spin-1/2 Heisenberg chain
• Quantum-critical scaling and temperature-dependent logarithmic corrections in the spin-half Heisenberg chain

Cited by in corpus (32)

• Finite-temperature transport in one-dimensional quantum lattice models
• Minimally entangled typical quantum states at finite temperature
• Diffusion and ballistic transport in one-dimensional quantum systems
• Finite temperature dynamical DMRG and the Drude weight of spin-1/2 chains
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Spectral functions in one-dimensional quantum systems at T>0
• Exact edge singularities and dynamical correlations in spin-1/2 chains
• A real-time study of diffusive and ballistic transport in spin-1/2 chains using the adaptive time-dependent density matrix renormalization group method
• Universal spin dynamics in infinite-temperature one-dimensional quantum magnets
• Dynamical structure factor at small q for the XXZ spin-1/2 chain
• Linearized Tensor Renormalization Group Algorithm for Thermodynamics of Quantum Lattice Models
• Reducing the numerical effort of finite-temperature density matrix renormalization group transport calculations
• Many-body localization in infinite chains
• Precise evaluation of thermal response functions by optimized density matrix renormalization group schemes
• Dynamical simulation of integrable and non-integrable models in the Heisenberg picture
• Dynamical correlation functions of the XXZ model at finite temperature
• Temperature dependence of the NMR relaxation rate 1/T_1 for quantum spin chains
• Spin transport in the XXZ model at high temperatures: Classical dynamics versus quantum S=1/2 autocorrelations
• Spin-Dynamics of the antiferromagnetic S=1/2-Chain at finite magnetic Fields and intermediate Temperatures
• Tracking the effects of interactions on spinons in gapless Heisenberg chains
• Temperature dependence of the NMR spin-lattice relaxation rate for spin-1/2 chains
• Continuous matrix product operator approach to finite temperature quantum states
• Low temperature dynamics of nonlinear Luttinger liquids
• Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet
• NMR relaxation in the spin-1 Heisenberg chain
• Long time correlations of nonlinear Luttinger liquids
• NMR Response in quasi one-dimensional Spin-1/2 Antiferromagnets
• Particle number conservation in quantum many-body simulations with matrix product operators
• Dynamic structure factors of the spin-1/2 XX chain with Dzyaloshinskii-Moriya interaction
• Exact steady states of the impurity-doped XXZ spin chain coupled to dissipators
• Quantum transport under oscillatory drive with disordered amplitude
• Superdiffusion resilience in Heisenberg Chains with 2D interactions on a quantum processor