The aim of this thesis is to evaluate correlation functions of twist elds in mixed states in two-dimensional integrable models of quantum eld theory (QFT). We construct the \Liouville space" for general models of QFT in general mixed states associated to diagonal density matrices, and de ne mixed-state form factors in Liouville space. We then specialize to two concrete models: the Ising model and U(1) Dirac model. Using a novel method based on deriving and solving a system of nonlinear functional di erential equations, we obtain exact mixed-state form factors of twist elds, in both models. These form factors are in agreement with nite-temperature form factors which correspond to the thermal Gibbs state. We then write down mixed-state correlation functions for these elds in terms of the full form factor expansions with respect to the vacuum in Liouville space. Under weak analytic conditions on the eigenvalues of the density matrix, they are exact large-distance expansions. We apply the results in the Ising model to analyze large-distance behaviours of two-point functions of order and disorder elds in generalized Gibbs ensembles and nonequilibrium steady states. In particular, we nd non-equilibrium form factors have branch cuts in rapidity space and the leading large-distance behaviour of two-point functions admit oscillations in the log of the distance between elds. Using the results in the Dirac model and the relation between the Ising and Dirac models, we deduce the Reyi entropy for even integer n. Finally, as an extra work, we deduce the high- and low-temperature limit of the exact current at non-equilibrium steady states in general integrable models of quantum eld theory with diagonal scatterings.
Mixed-State Correlation Functions of Twist Fields in Two-Dimensional Integrable Models of Quantum Field Theory
Chen, Y. (Author). 2016
Student thesis: Doctoral Thesis › Doctor of Philosophy