# Effective free-fermionic form factors and the XY spin chain

@article{Gamayun2020EffectiveFF,
title={Effective free-fermionic form factors and the XY spin chain},
author={Oleksandr Gamayun and N. Z. Iorgov and Yu. Yu. Zhuravlev},
journal={arXiv: Statistical Mechanics},
year={2020}
}
• Published 3 December 2020
• Physics, Mathematics
• arXiv: Statistical Mechanics
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…
10 Citations

## Figures from this paper

On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• Physics, Mathematics
• 2021
In this work we explore an instance of the τ-function of vertex type operators, specified in terms of a constant phase shift in a free-fermionic basis. From the physical point of view this τ-function
Correlation functions and transport coefficients in generalised hydrodynamics
• Physics, Mathematics
Journal of Statistical Mechanics: Theory and Experiment
• 2022
We review the recent advances on exact results for dynamical correlation functions at large scales and related transport coefficients in interacting integrable models. We discuss Drude weights,
Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
• Physics, Mathematics
SciPost Physics
• 2022
We consider the XY spin chain with arbitrary time-dependent magnetic field and anisotropy. We argue that a certain subclass of Gaussian states, called Coherent Ensemble (CE) following [1], provides a
Closed hierarchy of Heisenberg equations in integrable models with Onsager algebra
Dynamics of a quantum system can be described by coupled Heisenberg equations. In a generic many-body system these equations form an exponentially large hierarchy that is intractable without
Exact full counting statistics for the staggered magnetization and the domain walls in the XY spin chain.
• Medicine, Physics
Physical review. E
• 2021
By determining subleading corrections in a large interval asymptotics, the applicability of conformal field theory predictions at criticality is tested, and a universal interpolation formula is derived based on the solution of a Painlevé V equation for the full counting statistics of the transverse magnetization and the domain walls.
Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
• Physics, Mathematics
• 2021
We study thermal correlation functions of the one-dimensional impenetrable lattice anyons. These correlation functions can be presented as a difference of two Fredholm determinants. To describe large
Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via a set of Heisenberg equations
• 2021
The Kitaev model on the honeycomb lattice, while being integrable via the spinfermion mapping, has generally resisted an analytical treatment of the far-fromequilibrium dynamics due to the extensive
Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations
• Physics, Mathematics
• 2021
The Kitaev model on the honeycomb lattice, while being integrable via the spinfermion mapping, has generally resisted an analytical treatment of the far-fromequilibrium dynamics due to the extensive
The hydrodynamic theory of dynamical correlation functions in the XX chain
• Physics, Mathematics
• 2021
By the hydrodynamic linear response theory, dynamical correlation functions decay as power laws along certain velocities, determined by the flux Jacobian. Such correlations are obtained by
The relevant excitations for the one-body function in the Lieb–Liniger model
• Physics
Journal of Statistical Mechanics: Theory and Experiment
• 2021
We study the ground state one-body correlation function in the Lieb–Liniger model. In the spectral representation, correlations are built from contributions stemming from different excited states of

## References

SHOWING 1-10 OF 98 REFERENCES
Finite-lattice form factors in free-fermion models
• Mathematics, Physics
• 2011
We consider the general -symmetric free-fermion model on the finite periodic lattice, which includes as special cases the Ising model on the square and triangular lattices and the -symmetric BBS
Impurity Green's function of the one-dimensional Fermi gas
• Physics, Mathematics
• 2015
Abstract We consider a one-dimensional gas of spin-1/2 fermions interacting through δ -function repulsive potential of an arbitrary strength. For the case of all fermions but one having spin up, we
Form-factors of the finite quantum XY-chain
Explicit factorized formulas for the matrix elements (form-factors) of the spin operators \sigma^x and \sigma^y between the eigenvectors of the Hamiltonian of the finite quantum periodic XY-chain in
Thermal form-factor approach to dynamical correlation functions of integrable lattice models
• Physics
• 2017
We propose a method for calculating dynamical correlation functions at finite temperature in integrable lattice models of Yang-Baxter type. The method is based on an expansion of the correlation
Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions.
• Physics, Mathematics
• 2020
We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain.
Form factor expansion for thermal correlators
• Physics, Mathematics
• 2010
We consider finite temperature correlation functions in massive integrable Quantum Field Theory. Using a regularization by putting the system in finite volume, we develop a novel approach (based on
Thermal form factors of the XXZ chain and the large-distance asymptotics of its temperature dependent correlation functions
• Mathematics, Physics
• 2013
We derive expressions for the form factors of the quantum transfer matrix of the spin- XXZ chain which are suitable for taking the infinite Trotter number limit. These form factors determine the
The XX and Ising Limits in Integral Formulas for Finite-Temperature Correlation Functions of the XXZ Chain
• Physics, Mathematics
• 2005
We consider a multiple-integral representation for a one-parameter generating function of the finite temperature Sz-Sz correlation functions of the antiferromagnetic spin-1/2 XXZ chain in the XX
Ising Correlations and Elliptic Determinants
• Physics, Mathematics
• 2010
Correlation functions of the two-dimensional Ising model on the periodic lattice can be expressed in terms of form factors—matrix elements of the spin operator in the basis of common eigenstates of
Density form factors of the 1D Bose gas for finite entropy states
• Physics
• 2014
We consider the Lieb-Liniger model for a gas of bosonic $\delta-$interacting particles. Using Algebraic Bethe Ansatz results we compute the thermodynamic limit of the form factors of the density