Free fermions, KdV charges, generalised Gibbs ensembles and modular transforms
arXiv:2111.13950 · doi:10.1007/JHEP06(2022)036
Abstract
In this paper we consider the modular properties of generalised Gibbs ensembles in the Ising model, realised as a theory of one free massless fermion. The Gibbs ensembles are given by adding chemical potentials to chiral charges corresponding to the KdV conserved quantities. (They can also be thought of as simple models for extended characters for W-algebras). The eigenvalues and Gibbs ensembles for the charges can be easily calculated exactly using their expression as bilinears in the fermion fields. We re-derive the constant term in the charges, previously found by zeta-function regularisation, from modular properties. We expand the Gibbs ensembles as a power series in the chemical potentials and find the modular properties of the corresponding expectation values of polynomials of KdV charges. This leads us to an asymptotic expansion of the Gibbs ensemble calculated in the opposite channel. We obtain the same asymptotic expansion using Dijkgraaf's results for chiral partition functions. By considering the corresponding TBA calculation, we are led to a conjecture for the exact closed-form expression of the GGE in the opposite channel. This has the form of a trace over multiple copies of the fermion Fock space. We give analytic and numerical evidence supporting our conjecture.
arXiv comment36 pages, 3 figures. Typos corrected
References in corpus (19)
- Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
- Quasilocal charges in integrable lattice systems
- Excited states by analytic continuation of TBA equations
- Generalized Gibbs Ensembles for Quantum Field Theories
- Higher Spin Black Holes from CFT
- Partition functions of higher spin black holes and their CFT duals
- TBA and TCSA with boundaries and excited states
- Chiral Deformations of Conformal Field Theories
- Excited-state thermodynamics
- Form Factors of the Elementary Field in the Bullough-Dodd Model
- Thermal Correlation Functions of KdV Charges in 2D CFT
- A general transformation formula for conformal fields
- Spectra of non-hermitian quantum spin chains describing boundary induced phase transitions
- Exact generalized partition function of 2D CFTs at large central charge
- On Truncated Generalized Gibbs Ensembles in the Ising Field Theory
- Eigensystem and Full Character Formula of the W_{1+infinity} Algebra with c=1
- Modular properties of characters of the W3 algebra
- Massless integrable quantum field theories and massless scattering in 1+1 dimensions
- The quadratic formula made hard: A less radical approach to solving equations