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Thermodynamics & Correlation Functions

Turn spectral data into equilibrium states, finite-volume spectra, matrix elements and physical response.

This volume will develop the subjects in the chapter map below. Use the outline to locate the methods and examples you want to study; the individual readings are still being developed.

For a worked entrance available now, the Learn sequence From Bethe states to correlations calculates normalized matrix elements and an exact five-site spin correlation. Its complete finite final-state sum makes selection rules, degeneracy and frequency signs explicit; thermodynamic-limit methods remain future coverage here.

Readings and planned coverage

CHAPTER 01

Thermodynamic limits & root densities

Planned coverage

  • Particle and hole densities

CHAPTER 02

Thermodynamic Bethe ansatz

Planned coverage

  • Dressed energies and TBA equations

CHAPTER 03

Generalized equilibrium & charge completeness

Planned coverage

  • Constructing generalized Gibbs ensembles

CHAPTER 04

Finite-volume spectra & nonlinear integral equations

Planned coverage

  • Excited-state TBA

CHAPTER 05

Matrix elements & determinant formulas

Planned coverage

  • Gaudin norms and determinant form factors

CHAPTER 06

Correlation functions & spectral response

Planned coverage

  • Dynamical structure factors

CHAPTER 07

Low-energy & scaling descriptions

Planned coverage

  • Dressed charge and Luttinger parameters

CHAPTER 08

Equilibrium entanglement

Planned coverage

  • Ground-state entanglement in integrable chains

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