Temperature dependence of the NMR spin-lattice relaxation rate for spin-1/2 chains

Abstract

We use recent developments in the framework of time dependent matrix product state method (t-MPS) to compute the NMR relaxation rate $1/T_1$ for spin-1/2 chains under magnetic field and for different Hamiltonians (XXX, XXZ, isotropically dimerized). We compute numerically the temperature dependence of the $1/T_1$. We consider both gapped and gapless phases, and also the proximity of quantum critical points. At temperatures much lower than the typical exchange energy scale our results are in excellent agreement with analytical results, such as the ones derived from the Tomonaga-Luttinger liquid (TLL) theory and bosonization which are valid in this regime. We also cover the regime for which the temperature $T$ is comparable to the exchange coupling. In this case analytical theories are not appropriate but this regime is relevant for various new compounds with exchange couplings in the range of tens of Kelvin. For the gapped phases, either the fully polarized phase for spins chains or the low magnetic field phase for the dimerized systems, we find an exponential decrease in $\Delta /(k_{B}T)$ of the relaxation time and can compute the gap $\Delta$. Close to the quantum critical point our results are in good agreement with the a scaling behavior based on the existence of free excitations.

References in corpus (15)

• The density-matrix renormalization group in the age of matrix product states
• Real time evolution using the density matrix renormalization group
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Bose-Einstein Condensation in Magnetic Insulators
• Controlling Luttinger liquid physics in spin ladders under a magnetic field
• Conservation laws, integrability and transport in one-dimensional quantum systems
• 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
• Quantum critical dynamics of a S = 1/2 antiferromagnetic Heisenberg chain studied by 13C-NMR spectroscopy
• Temperature dependence of the NMR relaxation rate 1/T_1 for quantum spin chains
• Luttinger-Liquid Behavior in the Alternating Spin-Chain System Copper Nitrate
• Quantum Critical Scaling for a Heisenberg Spin-$1/2$ Chain around Saturation

Cited by in corpus (15)

• Anomalous spin diffusion in one-dimensional antiferromagnets
• Dynamical properties of the $S=\frac{1}{2}$ random Heisenberg chain
• Temperature dependence of the NMR relaxation rate 1/T_1 for quantum spin chains
• Continuous matrix product operator approach to finite temperature quantum states
• One-dimensional quantum systems at finite temperatures can be simulated efficiently on classical computers
• 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
• 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
• Finite temperature dynamical correlations for the dimerized spin-1/2 chain
• Low dimensional correlations under thermal fluctuations
• Numerical study of the temperature dependence of the NMR relaxation rate across the superfluid-Bose glass transition in one dimension
• Site-selective observation of spin dynamics of a Tomonaga-Luttinger liquid in frustrated Heisenberg chains