Dynamical response and dimensional crossover for spatially anisotropic antiferromagnets

Abstract

Theoretically challenging, the understanding of the dynamical response in quantum antiferromagnets is of great interest, in particular for both inelastic neutron scattering (INS) and nuclear magnetic resonance (NMR) experiments. In such a context, we theoretically address this question for quasi-one-dimensional quantum magnets, e.g. weakly coupled spin chains for which many compounds are available in Nature. In this class of systems, the dimensional crossover between a three-dimensional ordered regime at low temperature towards one-dimensional physics at higher temperature is a non-trivial issue, notably difficult concerning dynamical properties. Here we present a comprehensive theoretical study based on both analytical calculations (bosonization + random phase and self-consistent harmonic approximations) and numerical simulations (quantum Monte Carlo + stochastic analytic continuation) which allows us to describe the full temperature crossover for the NMR relaxation rate $1/T_1$, from one-dimensional Tomonaga-Luttinger liquid physics to the three-dimensional ordered regime, as a function of inter-chain couplings. The dynamical structure factor, directly probing the INS intensity, is also computed in the different regimes.

18 pages, 7 figures

References in corpus (18)

• The critical exponents of the superfluid transition in He4
• Controlling Luttinger liquid physics in spin ladders under a magnetic field
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Thermodynamics of the Spin Luttinger-Liquid in a Model Ladder Material
• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Dynamical structure factor at small q for the XXZ spin-1/2 chain
• Field-Controlled Magnetic Order in the Quantum Spin-Ladder System (Hpip)2CuBr4
• Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations
• Interacting Bose gases in quasi-one dimensional optical lattices
• Novel Crossover in Coupled Spin Ladders
• Temperature dependence of the NMR relaxation rate 1/T_1 for quantum spin chains
• Temperature dependence of the NMR spin-lattice relaxation rate for spin-1/2 chains
• Nuclear magnetic resonance study of the magnetic-field-induced ordered phase in the NiCl2-4SC(NH2)2 compound
• Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems
• Dimensional modulation of spontaneous magnetic order in quasi-two-dimensional quantum antiferromagnets
• Tomonaga-Luttinger liquid in quasi-one-dimensional antiferromagnet BaCo2V2O8 in magnetic fields
• Sliding phase in randomly stacked 2D superfluids/superconductors

Cited by in corpus (15)

• Detection of Kardar-Parisi-Zhang hydrodynamics in a quantum Heisenberg spin-$1/2$ chain
• Anomalous spin diffusion in one-dimensional antiferromagnets
• Spectral function of the $J_1-J_2$ Heisenberg model on the triangular lattice
• Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet
• Multipartite entanglement in the 1-D spin-$\frac{1}{2}$ Heisenberg Antiferromagnet
• Dimensional crossover and phase transitions in coupled chains: Density matrix renormalization group results
• Direct determination of the Tomonaga-Luttinger parameter $K$ in quasi-one-dimensional spin systems
• Platforms for the realization and characterization of Tomonaga-Luttinger liquids
• Domain wall melting in spin-1 chains
• Local moments versus itinerant antiferromagnetism: magnetic phase diagram and spectral properties of the anisotropic square lattice Hubbard model
• Critical Berezinskii-Kosterlitz-Thouless dynamics in the archetypal two-dimensional spin system Ba${}_2$CuSi${}_2$O${}_6$Cl${}_2$
• Numerical study of the temperature dependence of the NMR relaxation rate across the superfluid-Bose glass transition in one dimension
• Magnetic Microphase Inhomogeneity as a Thermodynamic Precursor of Ground State Phase Separation in Weakly Coupled Spin-$\frac{3}{2}$ Chains
• 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