Mixed-state Correlation Functions of Twist Fields in Two-dimensional Integrable Models of Quantum Field Theory PDF Download
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Author: Yixiong Chen Publisher: ISBN: Category : Languages : en Pages : 350
Book Description
The aim of this thesis is to evaluate correlation functions of twist fields in mixed states in two-dimensional integrable models of quantum field theory (QFT). We construct the "Liouville space" for general models of QFT in general mixed states associated to diagonal density matrices, and define mixed-state form factors in Liouville space. We then specialize to two concrete models: the Ising model and U(l) Dirac model. Using a novel method based on deriving and solving a system of nonlinear functional differential equations, we • obtain exact mixed-state form factors of twist fields, in both models. These form factors are in agreement with finite-temperature form factors which correspond to the thermal Gibbs state. We then write down mixed-state correlation functions for these fields 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 fields in generalized Gibbs ensembles and nonequilibrium steady states. In particular, we find 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 fields. 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 field theory with diagonal scatterings.
Author: Yixiong Chen Publisher: ISBN: Category : Languages : en Pages : 350
Book Description
The aim of this thesis is to evaluate correlation functions of twist fields in mixed states in two-dimensional integrable models of quantum field theory (QFT). We construct the "Liouville space" for general models of QFT in general mixed states associated to diagonal density matrices, and define mixed-state form factors in Liouville space. We then specialize to two concrete models: the Ising model and U(l) Dirac model. Using a novel method based on deriving and solving a system of nonlinear functional differential equations, we • obtain exact mixed-state form factors of twist fields, in both models. These form factors are in agreement with finite-temperature form factors which correspond to the thermal Gibbs state. We then write down mixed-state correlation functions for these fields 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 fields in generalized Gibbs ensembles and nonequilibrium steady states. In particular, we find 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 fields. 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 field theory with diagonal scatterings.
Author: Elcio Abdalla Publisher: World Scientific ISBN: 9812810153 Category : Science Languages : en Pages : 834
Book Description
The second edition of Non-Perturbative Methods in Two-Dimensional Quantum Field Theory is an extensively revised version, involving major changes and additions. Although much of the material is special to two dimensions, the techniques used should prove helpful also in the development of techniques applicable in higher dimensions. In particular, the last three chapters of the book will be of direct interest to researchers wanting to work in the field of conformal field theory and strings. This book is intended for students working for their PhD degree and post-doctoral researchers wishing to acquaint themselves with the non-perturbative aspects of quantum field theory. Contents: Free Fields; The Thirring Model; Determinants and Heat Kernels; Self-Interacting Fermionic Models; Nonlinear a Models: Classical Aspects; Nonlinear a Models OCo Quantum Aspects; Exact S-Matrices of 2D Models; The Wess-Zumino-Witten Theory; QED 2: Operator Approach; Quantum Chromodynamics; QED 2: Functional Approach; The Finite Temperature Schwinger Model; Non-Abelian Chiral Gauge Theories; Chiral Quantum Electrodynamics; Conformally Invariant Field Theory; Conformal Field Theory with Internal Symmetry; 2D Gravity and String-Related Topics. Readership: Graduate students and researchers in high energy and quantum physics."
Author: James Brian Silk Publisher: ISBN: Category : Languages : en Pages :
Book Description
The aim of this thesis is to explore correlation functions in two dimensional quantum field theories in two distinct ways. In part I a new method for calculating the differential equations parametrising the correlation functions of twist fields associated with the U (1) symmetry of the Dirac model is presented. While developing this method a new family of descendent twist fields are identified and their form factors calculated. This provides a novel way of calculating the vacuum expectation values of the primary twist fields and is shown to be entirely consistent with known results. The method of calculating the correlation functions of twist fields provides a parametrisation of several other correlation functions for various quantum states. Since this method relies on the Ward identities found in a double copy model it is hoped to have wider applications in other free fermion models. Part II concerns the truncated conformal space approach which has been developed to approximate perturbed conformal field theories. In this part the theory underpinning the approach is discussed and a working algorithm is developed for both bulk and boundary perturbed minimal models. The energy levels, mass gaps and one point functions of various models are computed using the truncated conformal space approach and are shown to be in good agreement with previous calculations. A possible method for using this approach to approximate two point functions in perturbed conformal field theories is discussed.
Author: Stefano Evangelisti Publisher: Minkowski Institute Press ISBN: 1927763096 Category : Science Languages : en Pages : 213
Book Description
This doctoral thesis analytically and numerically examines some of the most important concepts in quantum correlations in low-dimensional physics: entanglement and out-of-equilibrium dynamics. As John Bell once said: "Entanglement expresses the spooky nonlocality inherent to quantum mechanics", and its study not only concerns the foundations of any quantum theory, but also has important applications in quantum information and condensed matter theory, amongst others. The first chapters are devoted to the study of "entanglement entropies", a popular measure of the "quantumness" of a physical system. The main focus of the analysis is the one-dimensional XYZ spin-1/2 chain in equilibrium, an interacting theory which in addition to being integrable also has interesting scaling limits, such as the sine-Gordon field theory. Moving away from equilibrium the subsequent chapters deal with the dynamics of quantum correlators after an instantaneous quantum quench. The emphasis is on two different models and techniques; the transverse field Ising chain is studied using the form-factor approach and the O(3) non-linear sigma model is studied by means of the semi-classical theory. In the final chapter the author highlights an important general result: in the absence of long-range interactions in the final Hamiltonian the dynamics of a quantum system are determined by the same statistical ensemble that describes static correlations.
Author: Elcio Abdalla Publisher: World Scientific ISBN: 9814506516 Category : Science Languages : en Pages : 752
Book Description
This book is a survey of methods used in the study of two-dimensional models in quantum field theory as well as applications of these theories in physics. It covers the subject since the first model, studied in the fifties, up to modern developments in string theories, and includes exact solutions, non-perturbative methods of study, and nonlinear sigma models.
Author: Laurent Baulieu Publisher: Springer Science & Business Media ISBN: Category : Science Languages : en Pages : 440
Book Description
Many contributions to these proceeding of the May 1993 workshop are concerned with two dimensional quantum field theory. The continuous advances in the domain of two dimensional integrable theories on the lattice as well as in the continuum, including conformal field theories, Liouville field theory
Author: Changrim Ahn Publisher: World Scientific ISBN: 9814490180 Category : Science Languages : en Pages : 354
Book Description
This volume includes several lecture notes on the fundamentals and elementary techniques of integrable field theories and on their applications to low-dimensional physics systems contributed by leading scientists in the respective fields. The main topics covered are various aspects of the thermodynamic Bethe ansatz, form factors, Calogero (and related) models, sigma models, conformal boundary conditions, etc. The volume presents both pedagogical material and a current research trend in the field.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)
Author: Yixiong Chen
Author: Yixiong Chen
Author: Elcio Abdalla
Author: James Brian Silk
Author: Stefano Evangelisti
Author: Elcio Abdalla
Author: A.B. Zamolodchikov
Author: Mario Rasetti
Author: Laurent Baulieu
Author: Bert Schroer
Author: Changrim Ahn