Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime

Abstract

We compute all dynamical spin-spin correlation functions for the spin-1/2 $XXZ$ anisotropic Heisenberg model in the gapless antiferromagnetic regime, using numerical sums of exact determinant representations for form factors of spin operators on the lattice. Contributions from intermediate states containing many particles and string (bound) states are included. We present modified determinant representations for the form factors valid in the general case with string solutions to the Bethe equations. Our results are such that the available sum rules are saturated to high precision. We Fourier transform our results back to real space, allowing us in particular to make a comparison with known exact formulas for equal-time correlation functions for small separations in zero field, and with predictions for the zero-field asymptotics from conformal field theory.

arXiv comment14 pages

References in corpus (30)

• Quantum Inverse Scattering Method and Correlation Functions
• Form factors of the XXZ Heisenberg spin-1/2 finite chain
• Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
• Correlation Functions of the XXZ model for $\Delta <-1$
• QKZ equation with |q|=1 and correlation functions of the XXZ model in the gapless regime
• Computation of dynamical correlation functions of Heisenberg chains in a field
• Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field
• Two-spinon dynamic structure factor of the one-dimensional S=1/2 Heisenberg antiferromagnet
• Extended quantum critical phase in a magnetized spin-1/2 antiferromagnetic chain
• Order to disorder transition in the XY-like quantum magnet Cs2CoCl4 induced by noncommuting applied fields
• Long-distance asymptotics of spin-spin correlation functions for the XXZ spin chain
• Quantum Spin Chains and Riemann Zeta Function with Odd Arguments
• Spinons in the strongly correlated copper oxide chains in SrCuO2
• Correlation amplitude for the XXZ spin chain in the disordered regime
• Exact two-spinon dynamical correlation function of the Heisenberg model
• Emptiness Formation Probability and Quantum Knizhnik-Zamolodchikov Equation
• Large distance asymptotic behavior of the emptiness formation probability of the XXZ spin-1/2 Heisenberg chain
• Three-dimensionality of field-induced magnetism in a high-temperature superconductor
• Quantum Correlations and Number Theory
• Transition rates via Bethe ansatz for the spin-1/2 Heisenberg chain
• Third-neighbor and other four-point correlation functions of spin-1/2 XXZ chain
• Next Nearest-Neighbor Correlation Functions of the Spin-1/2 XXZ Chain at Critical Region
• Third Neighbor Correlators of Spin-1/2 Heisenberg Antiferromagnet
• Exact four-spinon dynamical correlation function of the Heisenberg model
• 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
• Next Nearest-Neighbor Correlation Functions of the Spin-1/2 XXZ Chain at Massive Region
• Violation of the string hypothesis and Heisenberg XXZ spin chain
• Completeness of Bethe's states for generalized $XXZ$ model
• Large N behavior of string solutions in the Heisenberg model

Cited by in corpus (117)

• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• What is an integrable quench?
• Spectral functions in one-dimensional quantum systems at T>0
• Dynamical density-density correlations in the one-dimensional Bose gas
• Multispinon continua at zero and finite temperature in a near-ideal Heisenberg chain
• Spinons and triplons in spatially anisotropic frustrated antiferromagnets
• Physical realization of a quantum spin liquid based on a novel frustration mechanism
• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• Entanglement entropy of excited states
• One-particle dynamical correlations in the one-dimensional Bose gas
• Form factor approach to dynamical correlation functions in critical models
• Statics and dynamics of weakly coupled antiferromagnetic spin-1/2 ladders in a magnetic field
• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• Experimental Observation of Bethe Strings
• The 4-spinon dynamical structure factor of the Heisenberg chain
• Quantum quenches in the anisotropic spin-1/2 Heisenberg chain: different approaches to many-body dynamics far from equilibrium
• Spectral function of spinless fermions on a one-dimensional lattice
• Direct Observation of Magnon Fractionalization in the Quantum Spin Ladder
• Observing complex bound states in the spin-1/2 Heisenberg XXZ chain using local quantum quenches
• Constrained sampling method for analytic continuation
• Quantum quenches from integrability: the fermionic pairing model
• Correlation functions of the open XXZ chain I
• Relaxation dynamics in the gapped XXZ spin-1/2 chain
• Dynamical structure factor at small q for the XXZ spin-1/2 chain
• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• Tomonaga-Luttinger Liquid Behavior and Spinon Confinement in YbAlO${}_3$
• Correlation functions of integrable models: a description of the ABACUS algorithm
• Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
• Progress on stochastic analytic continuation of quantum Monte Carlo data
• Form factor expansion for thermal correlators
• 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
• 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
• Dynamically dominant excitations of string solutions in the spin-1/2 antiferromagnetic Heisenberg chain in magnetic fields
• Bethe Ansatz approach to quench dynamics in the Richardson model
• Thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain
• The open XXX spin chain in the SoV framework: scalar product of separate states
• Exact mesoscopic correlation functions of the pairing model
• Spatially Anisotropic Heisenberg Kagome Antiferromagnet
• Threshold singularities in the dynamic response of gapless integrable models
• Deformed strings in the Heisenberg model
• The Spin-Exchange Dynamical Structure Factor of the S=1/2 Heisenberg Chain
• Dispersions of Many-Body Bethe strings
• Quantum Critical Dynamics of a Heisenberg-Ising Chain in a Longitudinal Field: Many-Body Strings versus Fractional Excitations
• 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
• The two-spinon transverse structure factor of the gapped Heisenberg antiferromagnetic chain
• Recursive formulas for the overlaps between Bethe states and product states in XXZ Heisenberg chains
• Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables
• Overlaps with arbitrary two-site states in the XXZ spin chain
• Finite Temperature Dynamical Structure Factor of Alternating Heisenberg Chains
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Emergent many-body composite excitations of interacting spin-1/2 trimers
• Form factors of integrable Heisenberg (higher) spin chains
• Derivation of Matrix Product Ansatz for the Heisenberg Chain from Algebraic Bethe Ansatz
• Dynamical correlation functions of the XXZ model at finite temperature
• One-dimensional Quantum Spin Dynamics of Bethe String States
• Exact Form-Factor Results for the Longitudinal Structure Factor of the Massless XXZ Model in Zero Field
• Quasiparticles of spatially anisotropic triangular antiferromagnets in a magnetic field
• 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
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Quasi-soliton scattering in quantum spin chains
• Quantum criticality of spinons
• Dynamical correlation functions of the mesoscopic pairing model
• Spinons and helimagnons in the frustrated Heisenberg chain
• Bethe states on a quantum computer: success probability and correlation functions
• Open XXZ chain and boundary modes at zero temperature
• The dynamics of azurite Cu${}_3$(CO${}_3$)${}_2$(OH)${}_2$ in a magnetic field as determined by neutron scattering
• Dynamical response and dimensional crossover for spatially anisotropic antiferromagnets
• Algebraic Bethe Ansatz approach to form factors and correlation functions of the cyclic eight-vertex solid-on-solid model
• Low-energy spin dynamics in rare-earth perovskite oxides
• Dynamic properties of quantum spin chains: Simple route to complex behavior
• Is solid copper oxalate a spin chain or a mixture of entangled spin pairs?
• Von Neumann's expanding model on random graphs
• Nature of the many-body excitations in a quantum wire: theory and experiment
• Effective S=1/2 description of the S=1 chain with strong easy plane anisotropy
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Introduction to the nested algebraic Bethe ansatz
• Correlations of zero-entropy critical states in the XXZ model: integrability and Luttinger theory far from the ground state
• Magnetic excitations in the one-dimensional Heisenberg-Ising model with external fields and their experimental realizations
• The solution space of metabolic networks: producibility, robustness and fluctuations
• On singularities of dynamic response functions in the massless regime of the XXZ spin-1/2 chain
• Quantum spin chain as a potential realization of the Nersesyan-Tsvelik model
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Quasi-particle interactions in frustrated Heisenberg chains
• Adjacent Spin Operator Dynamical Structure Factor of the S=1/2 Heisenberg Chain
• Exact finite volume expectation values of $\bar{\Psi }\Psi$ in the Massive Thirring model from light-cone lattice correlators
• The dynamic structure factor in impurity-doped spin chains
• Spin Hartree-Fock approach to quantum Heisenberg antiferromagnets in low dimensions
• Spinon dynamics in quantum integrable antiferromagnets
• Form factors and correlation functions of an interacting spinless fermion model
• Lattice approach to finite volume form-factors of the Massive Thirring/Sine-Gordon model
• Singular eigenstates in the even(odd) length Heisenberg spin chain
• All correlation functions of the open XXX spin 1/2 quantum chains for unparallel boundary magnetic fields with one constraint
• Determinant formula for the field form factor in the anyonic Lieb-Liniger model
• Integrability breaking and bound states in Google's decorated XXZ circuits
• Finite size effects and 2-string deviations in the spin-1 XXZ chains
• Dynamical structure factors in the nematic phase of frustrated ferromagnetic spin chains
• Antiperiodic XXZ chains with arbitrary spins: Complete eigenstate construction by functional equations in separation of variables
• Thermodynamic limit of the two-spinon form factors for the zero field XXX chain
• Cross Validation in Stochastic Analytic Continuation
• Fine structure of the asymptotic expansion of cyclic integrals
• Exact quantum dynamics of yrast states in the finite 1D Bose gas
• Quasiparticles of string solutions in the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field
• Dynamic structure factor of a spin-1/2 Heisenberg chain with long-range interactions
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model
• Sum rules for four-spinon dynamic structure factor in XXX model
• One way to grow, many ways to shrink: the reversible Von Neumann expanding model
• Confined and deconfined spinon excitations in the rectangular-lattice quantum antiferromagnet
• Universal quasi-Fermi liquid physics of one-dimensional interacting fermions
• Dynamical correlations and nonequilibrium sum rules in photodoped Hubbard ladders
• Emergent quasi-particles of spin-1 trimer chain
• Scattering of spinon excitations by potentials in the 1D Heisenberg model