# 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} }

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

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, MathematicsJournal 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, MathematicsSciPost 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

- Physics, Mathematics
- 2021

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, PhysicsPhysical 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

- PhysicsJournal 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…

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