Effective free-fermionic form factors and the XY spin chain
Oleksandr Gamayun, Nikolai Iorgov, Yu. Zhuravlev
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.
Topics & Concepts
Series (stratigraphy)FermionChain (unit)MathematicsLattice (music)Series expansionSimple (philosophy)QuantumPhysicsQuantum mechanicsSpin (aerodynamics)Fredholm determinantPhase (matter)Mathematical physicsClassical XY modelStatistical physicsPhase transitionCorrelation function (quantum field theory)Exact solutions in general relativityPure mathematicsWave functionElementary functionQuantum many-body systemsPhysics of Superconductivity and MagnetismAlgebraic structures and combinatorial models