On form-factor expansions for the XXZ chain in the massive regime

Abstract

We study the large-volume-$L$ limit of form factors of the longitudinal spin operators for the XXZ spin-$1/2$ chain in the massive regime. We find that the individual form factors decay as $L^{-n}$, $n$ being an even integer counting the number of physical excitations -- the holes -- that constitute the excited state. Our expression allows us to derive the form-factor expansion of two-point spin-spin correlation functions in the thermodynamic limit $L\to +\infty$. The staggered magnetisation appears naturally as the first term in this expansion. We show that all other contributions to the two-point correlation function are exponentially small in the large-distance regime.

47 pages, 3 figures, V2 minor modifications and few missprints corrected

References in corpus (2)

• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas

Cited by in corpus (23)

• Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the Bose-Hubbard and XXZ models
• Thermal form-factor approach to dynamical correlation functions of integrable lattice models
• Equilibrium dynamics of the XX chain
• 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
• Phase structure of the 1+1 dimensional massive Thirring model from matrix product states
• Kink confinement in the antiferromagnetic XXZ spin-1/2 chain in a weak staggered magnetic field
• Entanglement spreading after local fermionic excitations in the XXZ chain
• Asymptotic behaviour of two-point functions in multi-species models
• Spin conductivity of the XXZ chain in the antiferromagnetic massive regime
• Form factors of bound states in the XXZ chain
• Spinon confinement in the gapped antiferromagnetic XXZ spin-1/2 chain
• Interaction distance in the extended XXZ model
• Asymptotics of correlation functions of the Heisenberg-Ising chain in the easy-axis regime
• The LeClair-Mussardo series and nested Bethe Ansatz
• Thermodynamic limit of the two-spinon form factors for the zero field XXX chain
• Thermal form-factor expansion of the dynamical two-point functions of local operators in integrable quantum chains
• Finite-size scaling on the torus with periodic projected entangled-pair states
• Scaling in the massive antiferromagnetic XXZ spin-1/2 chain near the isotropic point
• Asymptotic analysis of the form-factors of quantum spin chains
• Confinement of spinons in the XXZ spin-1/2 chain in presence of the transverse magnetic field
• Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots
• Space-like asymptotics of the thermal two-point functions of the XXZ spin-1/2 chain