Effective free-fermionic form factors and the XY spin chain

Abstract

We introduce effective form factors for one-dimensional lattice fermions with arbitrary phase shifts. We study tau functions defined as series of these form factors. On the one hand we perform the exact summation and present tau functions as Fredholm determinants in the thermodynamic limit. On the other hand simple expressions of form factors allow us to present the corresponding series as integrals of elementary functions. Using this approach we re-derive the asymptotics of static correlation functions of the XY quantum chain at finite temperature.

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• Correlation functions and transport coefficients in generalised hydrodynamics
• Exact full counting statistics for the staggered magnetization and the domain walls in the XY spin chain
• Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
• Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
• The hydrodynamic theory of dynamical correlation functions in the XX chain
• Closed hierarchy of Heisenberg equations in integrable models with Onsager algebra
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• Finite temperature spin diffusion in the Hubbard model in the strong coupling limit
• Mobile impurity in a one-dimensional gas at finite temperatures
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• The relevant excitations for the one-body function in the Lieb-Liniger model
• On Landauer--Büttiker formalism from a quantum quench
• Kubo-Martin-Schwinger relation for an interacting mobile impurity
• Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
• Dynamical correlation functions in the Ising field theory
• Two-spinon effects on the thermal Tonks-Girardeau gas