On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain

Abstract

We consider the problem of computing form factors of the massless XXZ Heisenberg spin-1/2 chain in a magnetic field in the (thermodynamic) limit where the size M of the chain becomes large. For that purpose, we take the particular example of the matrix element of the third component of spin between the ground state and an excited state with one particle and one hole located at the opposite ends of the Fermi interval (umklapp-type term). We exhibit its power-law decrease in terms of the size of the chain M, and compute the corresponding exponent and amplitude. As a consequence, we show that this form factor is directly related to the amplitude of the leading oscillating term in the long-distance asymptotic expansion of the two-point correlation function of the third component of spin.

28 pages

References in corpus (1)

• Spinon excitations in the XX chain: spectra, transition rates, observability

Cited by in corpus (56)

• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Form factor approach to dynamical correlation functions in critical models
• Form factor approach to the asymptotic behavior of correlation functions in critical models
• The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
• Exact prefactors in static and dynamic correlation functions of 1D quantum integrable models: applications to the Calogero-Sutherland, Lieb-Liniger and XXZ models
• Mean values of local operators in highly excited Bethe states
• Nonuniversal prefactors in correlation functions of 1D quantum liquids
• Thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain
• Thermal form-factor approach to dynamical correlation functions of integrable lattice models
• Thermal form factors of the XXZ chain and the large-distance asymptotics of its temperature dependent correlation functions
• Long-distance asymptotic behaviour of multi-point correlation functions in massless quantum models
• Low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain
• GL(3)-Based Quantum Integrable Composite Models. II. Form Factors of Local Operators
• On the thermodynamic limit of form factor expansions of dynamical correlation functions in the massless regime of the XXZ spin $1/2$ chain
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• On determinant representations of scalar products and form factors in the SoV approach: the XXX case
• Equilibrium dynamics of the XX chain
• Zero modes method and form factors in quantum integrable 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
• Quenching the magnetic flux in 1d fermionic ring: Loschmidt echo and edge singularity
• On the form factors of local operators in the lattice sine-Gordon model
• 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
• A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime
• 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
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• On the absorption of microwaves by the one-dimensional spin-1/2 Heisenberg-Ising magnet
• Scalar product of twisted XXX modified Bethe vectors
• Correlations of zero-entropy critical states in the XXZ model: integrability and Luttinger theory far from the ground state
• On singularities of dynamic response functions in the massless regime of the XXZ spin-1/2 chain
• Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals
• Functions Characterizing the Ground State of the XXZ Spin-1/2 Chain in the Thermodynamic Limit
• 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
• Asymptotic behaviour of two-point functions in multi-species models
• Form factors of bound states in the XXZ chain
• Nested Algebraic Bethe Ansatz in integrable models: recent results
• Spinon decay in the spin-1/2 Heisenberg chain with weak next nearest neighbour exchange
• 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
• Spinon dynamics in quantum integrable antiferromagnets
• All correlation functions of the open XXX spin 1/2 quantum chains for unparallel boundary magnetic fields with one constraint
• 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
• Asymptotic analysis of the form-factors of quantum spin chains
• On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Non-Equilibrium Steady State of the Lieb-Liniger model: multiple-integral representation of the time evolved many-body wave-function
• Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots
• Correlation functions of the XXZ spin chain with the twisted boundary condition
• Threshold singularities in the XXZ- spin chain
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint