The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain

Abstract

The longitudinal spin structure factor for the XXZ-chain at small wave-vector q is obtained using Bethe Ansatz, field theory methods and the Density Matrix Renormalization Group. It consists of a peak with peculiar, non-Lorentzian shape and a high-frequency tail. We show that the width of the peak is proportional to q^2 for finite magnetic field compared to q^3 for zero field. For the tail we derive an analytic formula without any adjustable parameters and demonstrate that the integrability of the model directly affects the lineshape.

4 pages, 3 figures, published version

References in corpus (19)

• Transport and conservation laws
• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Form factors of the XXZ Heisenberg spin-1/2 finite chain
• Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}
• Density matrix renormalization group algorithms with a single center site
• Computation of dynamical correlation functions of Heisenberg chains in a field
• The thermal conductivity of the spin-1/2 XXZ chain at arbitrary temperature
• Dynamic response of one-dimensional interacting fermions
• Low energy effective Hamiltonian for the XXZ spin chain
• Two-spinon dynamic structure factor of the one-dimensional S=1/2 Heisenberg antiferromagnet
• Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime
• Conductivity of a clean one-dimensional wire
• 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
• Drude Weight at Finite Temperatures for Some Non-Integrable Quantum Systems in One Dimension
• Transition rates via Bethe ansatz for the spin-1/2 Heisenberg chain
• Evaluation of Dynamic spin structure factor for the spin-1/2 XXZ chain in a magnetic field
• Transition rates via Bethe ansatz for the spin-1/2 planar XXZ antiferromagnet

Cited by in corpus (121)

• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Universal theory of nonlinear Luttinger liquids
• Matrix product simulations of non-equilibrium steady states of quantum spin chains
• What is an integrable quench?
• Dynamical density-density correlations in the one-dimensional Bose gas
• Dynamics of Fractionalization in Quantum Spin Liquids
• Entanglement entropy of excited states
• Form factor approach to dynamical correlation functions in critical models
• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• Exact edge singularities and dynamical correlations in spin-1/2 chains
• The 4-spinon dynamical structure factor of the Heisenberg chain
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
• Constrained sampling method for analytic continuation
• Correlation functions of the open XXZ chain I
• Dynamical structure factor at small q for the XXZ spin-1/2 chain
• Cavity-Heisenberg spin chain quantum battery
• Progress on stochastic analytic continuation of quantum Monte Carlo data
• Decoherence Dynamics in Low-Dimensional Cold Atom Interferometers
• Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations
• Form factor approach to the asymptotic behavior of correlation functions in critical models
• Multipartite entanglement detection via structure factors
• New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain
• Exact prefactors in static and dynamic correlation functions of 1D quantum integrable models: applications to the Calogero-Sutherland, Lieb-Liniger and XXZ models
• Lanczos algorithm with Matrix Product States for dynamical correlation functions
• Dynamically dominant excitations of string solutions in the spin-1/2 antiferromagnetic Heisenberg chain in magnetic fields
• Anomalous relaxation and the high-temperature structure factor of XXZ spin chains
• The Drude weight of the spin-1/2 XXZ chain: density matrix renormalization group versus exact diagonalization
• Thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain
• Spin-charge separation in one-dimensional fermion systems beyond the Luttinger liquid theory
• The open XXX spin chain in the SoV framework: scalar product of separate states
• Excitation spectrum of the Lieb-Liniger model
• Non-Equilibrium Universality in the Heating Dynamics of Interacting Luttinger Liquids
• Threshold Singularities in the One Dimensional Hubbard Model
• Threshold singularities in the dynamic response of gapless integrable models
• One-dimensional liquid ${}^4$He: dynamical properties beyond Luttinger liquid theory
• The Luttinger liquid and integrable models
• Low-temperature asymptotics of integrable systems in an external field
• Antiperiodic dynamical 6-vertex model I: Complete spectrum by SOV, matrix elements of the identity on separate states and connections to the periodic 8-vertex model
• From confined spinons to emergent fermions: Observation of elementary magnetic excitations in a transverse-field Ising chain
• Form factors in SU(3)-invariant integrable models
• Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables
• Method to characterize spinons as emergent elementary particles
• Transverse spectral functions and Dzyaloshinskii-Moriya interactions in XXZ spin chains
• The algebraic Bethe ansatz for scalar products in SU(3)-invariant integrable models
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Confinement and Deconfinement of Spinons in Two Dimensions
• Luttinger liquids with curvature: Density correlations and Coulomb drag effect
• Prethermalization and Thermalization of a Quenched Interacting Luttinger Liquid
• Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid
• Spin-charge coupling in quantum wires at zero magnetic field
• Bosonization approach to charge and spin dynamics of 1D fermions with band-curvature
• Equilibrium dynamics of the XX chain
• Form factors of integrable Heisenberg (higher) spin chains
• Dynamical correlation functions of the XXZ model at finite temperature
• Scalar products of Bethe vectors in models with $\mathfrak{gl}(2|1)$ symmetry 2. Determinant representation
• Low-energy excitations of a one-dimensional Bose gas with weak contact repulsion
• Class of exactly soluble models of one-dimensional spinless fermions and its application to the Tomonaga-Luttinger Hamiltonian with nonlinear dispersion
• Successes and failures of Bethe Ansatz Density Functional Theory
• Kinetics of mobile impurities and correlation functions in one-dimensional superfluids at finite temperature
• Exact Form-Factor Results for the Longitudinal Structure Factor of the Massless XXZ Model in Zero Field
• Dynamical Functions of a 1D Correlated Quantum Liquid
• Multiple Actions of the Monodromy Matrix in $\mathfrak{gl}(2|1)$-Invariant Integrable Models
• Dynamics of a Heisenberg spin chain in the quantum critical regime: NMR experiment versus effective field theory
• Real-time dynamics in the one-dimensional Hubbard model
• Spin-Dynamics of the antiferromagnetic S=1/2-Chain at finite magnetic Fields and intermediate Temperatures
• Thermal conductivity of the one-dimensional Fermi-Hubbard model
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Tracking the effects of interactions on spinons in gapless Heisenberg chains
• On the form factors of local operators in the lattice sine-Gordon model
• Low temperature dynamics of nonlinear Luttinger liquids
• Spinons and helimagnons in the frustrated Heisenberg chain
• Dynamical response and dimensional crossover for spatially anisotropic antiferromagnets
• Spin-charge separated quasiparticles in one dimensional quantum fluids
• Dynamic structure factor of the spin-1/2 XXZ chain in a transverse field
• Long time correlations of nonlinear Luttinger liquids
• Decay of Bogoliubov quasiparticles in a nonideal one-dimensional Bose gas
• Viscous Dissipation in One-Dimensional Quantum Liquids
• Nature of the many-body excitations in a quantum wire: theory and experiment
• Effective mass of elementary excitations in Galilean-invariant integrable models
• Damping of zero sound in Luttinger liquids
• Dynamic structure factor of Luttinger liquids with quadratic energy dispersion and long-range interactions
• Dynamic properties of quantum spin chains: Simple route to complex behavior
• Scalar products in models with GL(3) trigonometric R-matrix. Highest coefficient
• One-Dimensional Fermions with neither Luttinger-Liquid nor Fermi-Liquid Behavior
• Kinetic Theory for Interacting Luttinger Liquids
• Scalar products of Bethe vectors in the 8-vertex model
• Spectral edge mode in interacting one-dimensional systems
• Correlations of zero-entropy critical states in the XXZ model: integrability and Luttinger theory far from the ground state
• Spectrum of elementary excitations in Galilean-invariant integrable models
• Measuring post-quench entanglement entropy through density correlations
• Recursive Method for the Density of States in One Dimension
• Fate of classical solitons in one-dimensional quantum systems
• The Two-Band Luttinger Liquid with Spin-Orbit Coupling: Applications to Monatomic Chains on Surfaces
• Relaxation of phonons in the Lieb-Liniger gas by dynamical refermionization
• Lattice vs. continuum theory of the periodic Heisenberg chain
• Current Density Functional Theory for one-dimensional fermions
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Ground-state phase diagram for a system of interacting, $D(D_3)$ non-Abelian anyons
• Mobile impurity approach to the optical conductivity in the Hubbard chain
• The dynamic structure factor in impurity-doped spin chains
• Solitons in a one-dimensional Wigner crystal
• Scalar products in models with $GL(3)$ trigonometric $R$-matrix. General case
• Boundary versus bulk behavior of time-dependent correlation functions in one-dimensional quantum systems
• Form factors and correlation functions of an interacting spinless fermion model
• All correlation functions of the open XXX spin 1/2 quantum chains for unparallel boundary magnetic fields with one constraint
• Boson decay and the dynamical structure factor for the XXZ chain at finite magnetic field
• Antiperiodic XXZ chains with arbitrary spins: Complete eigenstate construction by functional equations in separation of variables
• Cross Validation in Stochastic Analytic Continuation
• Luttinger parameters of interacting fermions in 1D at high energies
• Plasmon localization and relaxation, and thermal transport in one-dimensional conductors
• Dynamic structure factor of a spin-1/2 Heisenberg chain with long-range interactions
• Dynamical spin structure factor of one-dimensional interacting fermions
• RPAE versus RPA for the Tomonaga model with quadratic energy dispersion
• Dressed excitations, thermodynamics and relaxation in the 1D XXZ Heisenberg model
• One-dimensional interacting electrons beyond the Dzyaloshinskii-Larkin theorem
• Spin-orbit and impurity scattering in an integrable electron model: Exact results for dynamic correlations
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Keldysh pseudo-fermion functional renormalization group for quantum magnetism
• Investigating the roots of the nonlinear Luttinger liquid phenomenology