Temperature dependence of the NMR relaxation rate 1/T_1 for quantum spin chains

Abstract

We present results of numerical simulations performed on one-dimensional spin chains in order to extract the so-called relaxation rate $1/T_1$ accessible through NMR experiments. Building on numerical tensor network methods using the Matrix Product States (MPS) formalism, we can follow the non-trivial crossover occurring in critical chains between the high-temperature diffusive classical regime and the low-temperature response described by the Tomonaga-Luttinger liquid (TLL) theory, for which analytical expressions are known. In order to compare analytics and numerics, we focus on a generic spin-$1/2$ XXZ chain which is a paradigm of gapless TLL, as well as a more realistic spin-$1$ anisotropic chain, modelling the DTN material, which can be either in a trivial gapped phase or in a TLL regime induced by an external magnetic field. Thus, by monitoring the finite temperature crossover, we provide quantitative limits on the range of validity of TLL theory, that will be useful when interpreting experiments on quasi one-dimensional materials.

12 pages, 6 figures

References in corpus (16)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Quantum entanglement in condensed matter systems
• Controlling Luttinger liquid physics in spin ladders under a magnetic field
• NMR relaxation rate and dynamical structure factors in nematic and multipolar liquids of frustrated spin chains under magnetic fields
• Numerical Contractor Renormalization Method for Quantum Spin Models
• Field and temperature dependence of the NMR relaxation rate in the magnetic quadrupolar liquid phase of spin-1/2 frustrated ferromagnetic chains
• Spin gap and Luttinger liquid description of the NMR relaxation in carbon nanotubes
• Dichotomy between Attractive and Repulsive Tomonaga-Luttinger Liquids in Spin Ladders
• Critical properties and Bose Einstein Condensation in dimer spin systems
• Spin diffusion and the anisotropic spin-1/2 Heisenberg chain
• Temperature dependence of the NMR spin-lattice relaxation rate for spin-1/2 chains
• Critical exponents and intrinsic broadening of the field-induced transition in NiCl${}_2$$\cdot$4SC(NH${}_2$)${}_2$
• Effective S=1/2 description of the S=1 chain with strong easy plane anisotropy
• NMR relaxation of quantum spin chains in magnetic fields
• Bose-Einstein Condensation of Magnons in NiCl2-4SC(NH2)2

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• Temperature dependence of the NMR spin-lattice relaxation rate for spin-1/2 chains
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• Continuous matrix product operator approach to finite temperature quantum states
• Finite-temperature correlations in a quantum spin chain near saturation
• Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet
• Dynamical response and dimensional crossover for spatially anisotropic antiferromagnets
• Dynamical reduction of the dimensionality of exchange interactions and the "spin-liquid" phase of $\kappa$-(BEDT-TTF)${}_{2}X$
• NMR relaxation in the spin-1 Heisenberg chain
• Phase diagram and quantum criticality of Heisenberg spin chains with Ising-like interchain couplings -- Implication to YbAlO${}_3$
• Direct determination of the Tomonaga-Luttinger parameter $K$ in quasi-one-dimensional spin systems
• Dynamical spin excitations of topological Haldane gapped phase in the $S=1$ Heisenberg antiferromagnetic chain with single-ion anisotropy
• Effects of anisotropy in spin molecular-orbital coupling on effective spin models of trinuclear organometallic complexes
• Finite temperature dynamical correlations for the dimerized spin-1/2 chain
• Zigzag materials: selective interchain couplings control the coexistence of one-dimensional physics and deviations from it
• Quantum magnetism on small-world networks
• Numerical study of the temperature dependence of the NMR relaxation rate across the superfluid-Bose glass transition in one dimension
• Ising spin-1/2 XXZ chain's quantum problems beyond the spinon paradigm
• Properties of an organic model $S=1$ Haldane chain system
• Site-selective observation of spin dynamics of a Tomonaga-Luttinger liquid in frustrated Heisenberg chains