QKZ equation with |q|=1 and correlation functions of the XXZ model in the gapless regime

Abstract

An integral solution to the quantum Knizhnik-Zamolodchikov ($q$KZ) equation with $|q|=1$ is presented. Upon specialization, it leads to a conjectural formula for correlation functions of the XXZ model in the gapless regime. The validity of this conjecture is verified in special cases, including the nearest neighbor correlator with an arbitrary coupling constant, and general correlators in the XXX and XY limits.

References in corpus (1)

• Counting the local fields in SG theory.

Cited by in corpus (178)

• Quantum discord and quantum phase transition in spin chains
• Exact expectation values of local fields in quantum sine-Gordon model
• Liouville Field Theory -- A decade after the revolution
• Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
• On the quantum inverse scattering problem
• What is an integrable quench?
• Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field
• Timelike Boundary Liouville Theory
• $q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series
• Rolling Tachyons from Liouville theory
• Low energy effective Hamiltonian for the XXZ spin chain
• Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime
• Essays on the theory of elliptic hypergeometric functions
• Long-distance asymptotics of spin-spin correlation functions for the XXZ spin chain
• Master equation for spin-spin correlation functions of the XXZ chain
• Hidden Grassmann structure in the XXZ model
• The Importance of being Odd
• The half-infinite XXZ chain in Onsager's approach
• Multi-point Local Height Probabilities in the Integrable RSOS Model
• Correlation functions of the open XXZ chain I
• On the reduced density matrix for a chain of free electrons
• Dynamical structure factor at small q for the XXZ spin-1/2 chain
• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• Correlation amplitude for the XXZ spin chain in the disordered regime
• Form factor approach to the asymptotic behavior of correlation functions in critical models
• Dynamical correlation functions of the XXZ spin-1/2 chain
• 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
• Emptiness Formation Probability for the One-Dimensional Isotropic XY Model
• Emptiness formation probability of the XXZ spin-1/2 Heisenberg chain at Delta=1/2
• On the spectrum of Dehn twists in quantum Teichmuller theory
• Thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain
• Density matrices for finite segments of Heisenberg chains of arbitrary length
• Six-Vertex, Loop and Tiling models: Integrability and Combinatorics
• Computation of static Heisenberg-chain correlators: Control over length and temperature dependence
• Superconformal Partition Functions and Non-perturbative Topological Strings
• Correlation functions of the XXZ spin-1/2 Heisenberg chain at the free fermion point from their multiple integral representations
• Higher-Level Appell Functions, Modular Transformations, and Characters
• Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field
• Traces on the Sklyanin algebra and correlation functions of the eight-vertex model
• Reduced qKZ equation and correlation functions of the XXZ model
• Form factors in quantum integrable models with GL(3)-invariant R-matrix
• From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics
• Short-distance thermal correlations in the massive XXZ chain
• Factorization of multiple integrals representing the density matrix of a finite segment of the Heisenberg spin chain
• Quantum Correlations and Number Theory
• Excited state correlations of the finite Heisenberg chain
• Boundary spectrum in the sine-Gordon model with Dirichlet boundary conditions
• Low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain
• Correlation functions of the higher spin XXX chains
• Unit circle elliptic beta integrals
• Third-neighbor and other four-point correlation functions of spin-1/2 XXZ chain
• Permutation operators, entanglement entropy, and the XXZ spin chain in the limit Δ-> -1
• Next Nearest-Neighbor Correlation Functions of the Spin-1/2 XXZ Chain at Critical Region
• Asymptotic Behavior of the Emptiness Formation Probability in the Critical Phase of XXZ Spin Chain
• A note on the spin-1/2 XXZ chain concerning its relation to the Bose gas
• On the thermodynamic limit of form factor expansions of dynamical correlation functions in the massless regime of the XXZ spin $1/2$ chain
• Third Neighbor Correlators of Spin-1/2 Heisenberg Antiferromagnet
• Correlation functions of the spin-1/2 anti-ferromagnetic Heisenberg chain: exact calculation via the generating function
• S-duality as a beta-deformed Fourier transform
• Exact thermodynamic limit of short-range correlation functions of the antiferromagnetic $XXZ$-chain at finite temperatures
• On the physical part of the factorized correlation functions of the XXZ chain
• Form factors of integrable Heisenberg (higher) spin chains
• Next Nearest-Neighbor Correlation Functions of the Spin-1/2 XXZ Chain at Massive Region
• A Q-Operator Identity for the Correlation Functions of the Infinite XXZ Spin-Chain
• First principle approach to correlation functions of spin-1/2 Heisenberg chain : fourth-neighbor correlators
• Boundary Liouville theory at c=1
• Dynamical correlation functions of the XXZ model at finite temperature
• Long-time and large-distance asymptotic behavior of the current-current correlators in the non-linear Schrödinger model
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• Exact evaluation of density matrix elements for the Heisenberg chain
• Exact Form-Factor Results for the Longitudinal Structure Factor of the Massless XXZ Model in Zero Field
• On solutions of the KZ and qKZ equations at level zero
• Correlation functions of the half-infinite XXZ spin chain with a triangular boundary
• Matrix models with hard walls: Geometry and solutions
• Density matrix elements and entanglement entropy for the spin-1/2 XXZ chain at $\Delta$=1/2
• 5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry
• Tracking the effects of interactions on spinons in gapless Heisenberg chains
• On the form factors of local operators in the lattice sine-Gordon model
• Elliptic hypergeometric functions
• Intrinsic Jump Character of the First-Order Quantum Phase Transitions
• Non-Abelian symmetries of the half-infinite XXZ spin chain
• Elliptic algebra $A_{q,p}(\widehat{s{l}_2})$ in the scaling limit
• Correlation functions of the integrable higher-spin XXX and XXZ spin chains through the fusion method
• On the spin-spin correlation functions of the XXZ spin-1/2 infinite chain
• Counting minimal form factors of the restricted sine-Gordon model
• 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
• Finite temperature density matrix and two-point correlations in the antiferromagnetic XXZ chain
• Reflection algebra and functional equations
• Correlation functions for the Z-invariant Ising model
• Determinant representations for form factors in quantum integrable models with GL(3)-invariant R-matrix
• New formulae for solutions of quantum Knizhnik-Zamolodchikov equations on level -4
• The modular properties and the integral representations of the multiple elliptic gamma functions
• Long-distance and large-time asymptotic behaviour of dynamic correlation functions in the massless regime of the XXZ spin-1/2 chain
• Quantum-classical crossover in the spin 1/2 XXZ chain
• XX and Ising limits in integral formulae for finite temperature correlation functions of the XXZ chain
• Correlation functions of the integrable $SU(n)$ spin chain
• A common limit of super Liouville theory and minimal models
• String correlation functions of the spin-1/2 Heisenberg XXZ chain
• Emptiness formation probability at finite temperature for the isotropic Heisenberg chain
• On the calculation of the correlation functions of the ${\mathfrak{sl}}_3$-model by means of the reduced qKZ equation
• Exact results for the sigma^z two-point function of the XXZ chain at Delta=1/2
• Fifth-neighbor spin-spin correlator for the anti-ferromagnetic Heisenberg chain
• Correlation functions of the integrable isotropic spin-1 chain at finite temperature
• Theta hypergeometric integrals
• Correlation functions of the integrable isotropic spin-1 chain: algebraic expressions for arbitrary temperature
• Correlation functions of integrable $O(n)$ spin chains
• Correlation functions of the integrable spin-s chain
• Form factors of boundary fields for A(2)-affine Toda field theory
• Statistical mechanics of integrable quantum spin systems
• Generalized q-Onsager Algebras and Dynamical K-matrices
• Correlation functions by Separation of Variables: the XXX spin chain
• A Worldsheet Description of Instant Folded Strings
• Riemann-Hilbert problems for the resolved conifold
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• Check-Operators and Quantum Spectral Curves
• The massless XXZ chain with a boundary
• Accurate localization of Kosterlitz-Thouless-type quantum phase transitions for one-dimensional spinless fermions
• The 19-Vertex Model at critical regime $|q|=1$
• Diagrammatics for SU(2) invariant matrix product states
• Integrable Quantum Field Theories, in the Bulk and with a Boundary
• Determinant Formula for the Solutions of the Quantum Knizhnik-Zamolodchikov Equation with |q|=1
• Reduced qKZ equation: general case
• Multiple sine, multiple elliptic gamma functions and rational cones
• Large-distance and long-time asymptotic behavior of the reduced density matrix in the non-linear Schrödinger model
• Form factors and correlation functions of an interacting spinless fermion model
• The hyperbolic modular double and the Yang-Baxter equation
• Solvable Discrete Quantum Mechanics: q-Orthogonal Polynomials with |q|=1 and Quantum Dilogarithm
• All correlation functions of the open XXX spin 1/2 quantum chains for unparallel boundary magnetic fields with one constraint
• Nearest neighbor two-point correlation function of the $Z$-invariant eight-vertex model
• Yangian Algebras and Classical Riemann Problems
• Exact two-particle Matrix Elements in S-Matrix Preserving Deformation of Integrable QFTs
• Asymptotics of correlation functions of the Heisenberg-Ising chain in the easy-axis regime
• Central extension of the reflection equations and an analog of Miki's formula
• Density matrices in integrable face models
• Factorization of density matrices in the critical RSOS models
• Bootstrap equations and correlation functions for the Heisenberg XYZ antiferromagnet
• Classical elliptic hypergeometric functions and their applications
• A note on the high temperature expansion of the density matrix for the isotropic Heisenberg chain
• Quantum Riemann-Hilbert problems for the resolved conifold
• The integral formula for the solutions of the quantum Knizhnik-Zamolodchikov equation associated with $U_q({\widehat{sl}}_n)$ for |q|=1
• Form factors and action of U_{\sqrt{-1}}(sl_2~) on infinite-cycles
• The critical $A_{n-1}^{(1)}$ chain
• On the Quasi-Hopf structure of deformed double Yangians
• Thermodynamic limit of the two-spinon form factors for the zero field XXX chain
• Free boson representation of DY_{\hbar}(gl_N)_k
• Hierarchy of the Selberg zeta functions
• Matrix product states for $su(2)$ invariant quantum spin chains
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Finite size lattice results for the two-boundary Temperley--Lieb loop model
• Deformed Double Yangian Structures
• Generalized Cherednik-Macdonald identities
• Correlation Function and Simplified TBA Equations for XXZ Chain
• Non-Equilibrium Steady State of the Lieb-Liniger model: multiple-integral representation of the time evolved many-body wave-function
• On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model
• Asymptotic analysis of the form-factors of quantum spin chains
• Boundary timelike Liouville theory: bulk 1-point & boundary 2-point functions
• Determinat formula for solutions of the $U_q(s{l}_n)$ qKZ equation at $|q|=1$
• Quantum Knizhnik-Zamolodchikov equation associated with $U_q(A_2^{(2)})$ for $|q|=1$
• Smirnov-type integral formulae for correlation functions of the bulk/boundary XXZ model in the anti-ferromagnetic regime
• Laurent polynomial solutions of the boundary quantum Knizhnik--Zamolodchikov equation
• Supersymmetric zeta functions and determinants
• The q-twisted cohomology and the q-hypergeometric function at |q|=1
• Factorization of the Ising model form factors
• Replica-deformation of the SU(2)-invariant Thirring model via solutions of the qKZ equation
• Form factors of SU(N) invariant Thirring model
• Fourth-neighbour two-point functions of the XXZ chain and the Fermionic basis approach
• On solutions of the q-hypergeometric equation with q^{N}=1
• Two Point Correlation Functions for a Periodic Box-Ball System
• Quantum Group U_q(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain
• Geometric phase and topological phase diagram of the one-dimensional $XXZ$ Heisenberg spin chain in a longitudinal field
• Master equation for correlation functions in algebra symmetry $\mathfrak{gl}(2|1)$ related models
• Angular Quantization of the Sine-Gordon Model at the Free Fermion Point
• Barnes' type multiple Changhee q-zeta functiond
• Correlation functions of an interacting spinless fermion model at finite temperature
• Degeneration of the Elliptic Algebra $A_{q,p}(\widehat{s{l}_2})$ and Form Factors in the sine-Gordon Theory