Applications of Massive Integrable Quantum Field Theories to Problems in Condensed Matter Physics

Abstract

We review applications of the sine-Gordon model, the O(3) non-linear sigma model, the U(1) Thirring model, and the O(N) Gross--Neveu model to quasi one-dimensional quantum magnets, Mott insulators, and carbon nanotubes. We focus upon the determination of dynamical response functions for these problems. These quantities are computed by means of form factor expansions of quantum correlation functions in integrable quantum field theories. This approach is reviewed here in some detail.

150 pages, 35 figures, published in the I. Kogan Memorial Volume by World Scientific

Cited by in corpus (28)

• Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
• Form factors in finite volume II:disconnected terms and finite temperature correlators
• Experimental Observation of Bethe Strings
• Signatures of rare states and thermalization in a theory with confinement
• Quench dynamics near a quantum critical point: application to the sine-Gordon model
• Anomalies in the pseudogap phase of the cuprates: Competing ground states and the role of umklapp scattering
• One-point functions in massive integrable QFT with boundaries
• Finite-Temperature Form Factors: a Review
• Sine-Gordon form factors in finite volume
• Thermodynamic bootstrap program for integrable QFT's: Form factors and correlation functions at finite energy density
• Exact Thermodynamics and Transport in the Classical Sine-Gordon Model
• Spectral expansion for finite temperature two-point functions and clustering
• Self-consistent time-dependent harmonic approximation for the sine-Gordon model out of equilibrium
• Josephson oscillations in split one-dimensional Bose gases
• On the low-energy description for tunnel-coupled one-dimensional Bose gases
• Sine-Gordon multi-soliton form factors in finite volume
• Finite temperature one-point functions in non-diagonal integrable field theories: the sine-Gordon model
• Boundary form factors of the sinh-Gordon model with Dirichlet boundary conditions at the self-dual point
• Duality and Form Factors in the Thermally Deformed Two-Dimensional Tricritical Ising Model
• Fermion Bag Solitons in the Massive Gross-Neveu and Massive Nambu-Jona-Lasinio Models in 1+1 Dimensions: Inverse Scattering Analysis
• On the finite volume expectation values of local operators in the sine-Gordon model
• Dissipative dynamics in the free massive boson limit of the sine-Gordon model
• On convergence of form factor expansions in the infinite volume quantum Sinh-Gordon model in 1+1 dimensions
• Extending the Thermodynamic Form Factor Bootstrap Program: Multiple particle-hole excitations, crossing symmetry, and reparameterization invariance
• Emergent dipole field theory in atomic ladders
• Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems
• Mixed-state form factors of $U(1)$ twist fields in the Dirac theory
• Exact results, transient generalized Gibbs ensembles, and analytic approximations for spacetime propagators of massive, real scalar fields in one spatial dimension