Thermal form factors of the XXZ chain and the large-distance asymptotics of its temperature dependent correlation functions

Abstract

We derive expressions for the form factors of the quantum transfer matrix of the spin-1/2 XXZ chain which are suitable for taking the infinite Trotter number limit. These form factors determine the finitely many amplitudes in the leading asymptotics of the finite-temperature correlation functions of the model. We consider form-factor expansions of the longitudinal and transversal two-point functions. Remarkably, the formulae for the amplitudes are in both cases of the same form. We also explain how to adapt our formulae to the description of ground state correlation functions of the finite chain. The usefulness of our novel formulae is demonstrated by working out explicit results in the high- and low-temperature limits. We obtain, in particular, the large-distance asymptotics of the longitudinal two-point functions for small temperatures by summing up the asymptotically most relevant terms in the form factor expansion of a generating function of the longitudinal correlation functions. As expected the leading term in the expansion of the corresponding two-point functions is in accordance with conformal field theory predictions. Here it is obtained for the first time by a direct calculation.

51 pages, one figure, v2: minor revisions and corrections

References in corpus (6)

• Form factor approach to dynamical correlation functions in critical models
• Hidden Grassmann Structure in the XXZ Model II: Creation Operators
• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• Hidden Grassmann Structure in the XXZ Model III: Introducing Matsubara direction
• Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field
• High temperature expansion of emptiness formation probability for isotropic Heisenberg chain

Cited by in corpus (39)

• Correlation functions and transport coefficients in generalised hydrodynamics
• Full Counting Statistics in the Transverse Field Ising Chain
• The open XXX spin chain in the SoV framework: scalar product of separate states
• Thermal form-factor approach to dynamical correlation functions of integrable lattice models
• Low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain
• 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
• Exact real-time longitudinal correlation functions of the massive XXZ chain
• Equilibrium dynamics of the XX chain
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• Quantum Phase Transition in a Quantum Ising Chain at Nonzero Temperatures
• On form-factor expansions for the XXZ chain in the massive regime
• Correlation lengths of the repulsive one-dimensional Bose gas
• Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
• Thermal form factor approach to the ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime
• Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
• A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime
• Effective free-fermionic form factors and the XY spin chain
• High-temperature analysis of the transverse dynamical two-point correlation function of the XX quantum-spin chain
• Thermodynamics of the spin-$1/2$ Heisenberg-Ising chain at high temperatures: a rigorous approach
• Low-temperature spectrum of correlation lengths of the XXZ chain in the antiferromagnetic massive regime
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• Scalar product of twisted XXX modified Bethe vectors
• Late-time large-distance asymptotics of the transverse correlation functions of the XX chain in the space-like regime
• Statistical mechanics of integrable quantum spin systems
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Asymptotic behaviour of two-point functions in multi-species models
• Form factors of bound states in the XXZ chain
• Exact finite volume expectation values of $\bar{\Psi }\Psi$ in the Massive Thirring model from light-cone lattice correlators
• Lattice approach to finite volume form-factors of the Massive Thirring/Sine-Gordon model
• The LeClair-Mussardo series and nested Bethe Ansatz
• Thermal form-factor expansion of the dynamical two-point functions of local operators in integrable quantum chains
• Thermodynamic limit of the two-spinon form factors for the zero field XXX chain
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Finite volume form factors in integrable theories
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint
• Exact Matrix Elements of the Field Operator in the Thermodynamic Limit of the Lieb-Liniger Model
• Space-like asymptotics of the thermal two-point functions of the XXZ spin-1/2 chain
• Fourth-neighbour two-point functions of the XXZ chain and the Fermionic basis approach