Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions

Abstract

We describe a method to derive, from first principles, the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz. We apply this approach to the longitudinal spin- spin correlation function of the XXZ Heisenberg spin-1/2 chain (with magnetic field) in the disordered regime as well as to the density-density correlation func- tion of the interacting one-dimensional Bose gas. At leading order, the results confirm the Luttinger liquid and conformal field theory predictions.

arXiv comment78 pages

References in corpus (22)

• 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
• Unified Approach to Thermodynamic Bethe Ansatz and Finite Size Corrections for Lattice Models and Field Theories
• Computation of dynamical correlation functions of Heisenberg chains in a field
• On the quantum inverse scattering problem
• Integral representations for correlation functions of the XXZ chain at finite temperature
• Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field
• Low energy effective Hamiltonian for the XXZ spin chain
• Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime
• Long-distance asymptotics of spin-spin correlation functions for the XXZ spin chain
• Master equation for spin-spin correlation functions of the XXZ chain
• Exact Correlation Amplitude for the S=1/2 Heisenberg Antiferromagnetic Chain
• Correlation amplitude for the XXZ spin chain in the disordered regime
• Integral representation of the density matrix of the XXZ chain at finite temperatures
• Dynamical correlation functions of the XXZ spin-1/2 chain
• Algebraic representation of correlation functions in integrable spin chains
• Reduced qKZ equation and correlation functions of the XXZ model
• Density matrix of a finite sub-chain of the Heisenberg anti-ferromagnet
• Finite-size scaling for the S=1/2 Heisenberg Antiferromagnetic Chain
• String correlation functions of the spin-1/2 Heisenberg XXZ chain

Cited by in corpus (81)

• Fermi gases in one dimension: From Bethe Ansatz to experiments
• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• The Quench Action
• Form factor approach to dynamical correlation functions in critical models
• Quantum quenches in the anisotropic spin-1/2 Heisenberg chain: different approaches to many-body dynamics far from equilibrium
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Form factor approach to the asymptotic behavior of correlation functions in critical models
• Exact prefactors in static and dynamic correlation functions of 1D quantum integrable models: applications to the Calogero-Sutherland, Lieb-Liniger and XXZ models
• Current operators in Bethe Ansatz and Generalized Hydrodynamics: An exact quantum/classical correspondence
• Nonuniversal prefactors in correlation functions of 1D quantum liquids
• Local correlations in the 1D Bose gas from a scaling limit of the XXZ chain
• Thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain
• Thermal form factors of the XXZ chain and the large-distance asymptotics of its temperature dependent correlation functions
• Short-distance thermal correlations in the massive XXZ chain
• Long-distance asymptotic behaviour of multi-point correlation functions in massless quantum models
• One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance
• Recursive formulas for the overlaps between Bethe states and product states in XXZ Heisenberg chains
• Form factors in SU(3)-invariant integrable models
• Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas
• Theory of superfluidity and drag force in the one-dimensional Bose gas
• Low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain
• Permutation operators, entanglement entropy, and the XXZ spin chain in the limit Δ-> -1
• Universal terms in the overlap of the ground state of the spin-1/2 XXZ chain with the Néel state
• On the thermodynamic limit of form factor expansions of dynamical correlation functions in the massless regime of the XXZ spin $1/2$ chain
• 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
• Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions
• On determinant representations of scalar products and form factors in the SoV approach: the XXX case
• On the physical part of the factorized correlation functions of the XXZ chain
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• Scalar products of Bethe vectors in models with $\mathfrak{gl}(2|1)$ symmetry 2. Determinant representation
• Exact formulas for the form factors of local operators in the Lieb-Liniger model
• Universal Relations for Non Solvable Statistical Models
• On form-factor expansions for the XXZ chain in the massive regime
• Long-time and large-distance asymptotic behavior of the current-current correlators in the non-linear Schrödinger model
• Inner products in integrable Richardson-Gaudin models
• Quenching the magnetic flux in 1d fermionic ring: Loschmidt echo and edge singularity
• Correlation functions of one-dimensional bosons at low temperature
• Correlation lengths of the repulsive one-dimensional Bose gas
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Bethe vectors for models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$
• Finite-size Gap, Magnetization, and Entanglement of Deformed Fredkin Spin Chain
• On the form factors of local operators in the lattice sine-Gordon model
• Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
• Microscopic approach to a class of 1D quantum critical models
• XXZ spin-1/2 representation of a finite-U Bose-Hubbard chain at half-integer filling
• Open XXZ chain and boundary modes at zero temperature
• Thermal form factor approach to the ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime
• Algebraic Bethe Ansatz approach to form factors and correlation functions of the cyclic eight-vertex solid-on-solid model
• Finite temperature correlation functions from discrete functional equations
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Correlation functions of the integrable $SU(n)$ spin chain
• On Form Factors of the conjugated field in the non-linear Schröodinger model
• Long-distance and large-time asymptotic behaviour of dynamic correlation functions in the massless regime of the XXZ spin-1/2 chain
• Scalar products of Bethe vectors in the 8-vertex model
• On the calculation of the correlation functions of the ${\mathfrak{sl}}_3$-model by means of the reduced qKZ equation
• Scalar products and norm of Bethe vectors for integrable models based on $U_q({\widehat{\mathfrak{gl}}}_n)$
• Correlation functions of the integrable isotropic spin-1 chain at finite temperature
• Correlations of zero-entropy critical states in the XXZ model: integrability and Luttinger theory far from the ground state
• Six-vertex model on a finite lattice: integral representations for nonlocal correlation functions
• The equilibrium landscape of the Heisenberg spin chain
• Correlation functions of the integrable isotropic spin-1 chain: algebraic expressions for arbitrary temperature
• Correlation functions of the integrable spin-s chain
• Correlation functions by Separation of Variables: the XXX spin chain
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Low-density limit of dynamical correlations in the Lieb-Liniger model
• Form factors of bound states in the XXZ chain
• Ground-state phase diagram for a system of interacting, $D(D_3)$ non-Abelian anyons
• Integral formulas and antisymmetrization relations for the six-vertex model
• The propagator of the finite XXZ spin-$\frac{1}{2}$ chain
• Spinon dynamics in quantum integrable antiferromagnets
• Lattice approach to finite volume form-factors of the Massive Thirring/Sine-Gordon model
• Asymptotics of correlation functions of the Heisenberg-Ising chain in the easy-axis regime
• Fine structure of the asymptotic expansion of cyclic integrals
• The monodromy matrix in the F-basis for arbitrary six-vertex models
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Evaluation of integrals for the emptiness formation probability in the square-ice model
• Exact spectral function and nonequilibrium dynamics of the strongly interacting Hubbard model
• Fisher-Hartwig expansion for the transverse correlation function in the XX spin-1/2 chain
• Exact solution of the two-axis two-spin Hamiltonian
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint