arXiv:1510.08232 · Nuclear Physics B

On form factors of boundary changing operators

Zoltán Bajnok, László Holló

Published Feb 9, 2016• 9 citations

Abstract

We develop a form factor bootstrap program to determine the matrix elements of local, boundary condition changing operators. We propose axioms for these form factors and determine their solutions in the free boson and Lee–Yang models. The sudden change in the boundary condition, caused by an operator insertion, can be interpreted as a local quench and the form factors provide the overlap of any state before the quench with any outgoing state after the quench.

DOI: 10.1016/j.nuclphysb.2016.02.007

Related papers

Expectation values after an integrable boundary quantum quench

Zoltán Bajnok, Dávid Fülepi, Máté Lencsés

A bstract We investigate an integrable boundary quench, in which one integrable boundary condition is suddenly switched to another. We develop a general framework for analyzing the resulting real-time dynamics based on form factors of bulk and boundary-changing operators. We first study the problem at the conformal point of the Lee-Yang model and then extend the analysis to its massive perturbation, where we examine the time evolution of the pre-quench vacuum and compute the vacuum-to-vacuum matrix elements of local operators inserted after the quench. The analytical results are validated by numerical calculations using the truncated conformal space approach adapted to boundary-changing situations.

arXiv:2605.04823Journal of High Energy PhysicsAug 17, 20260 citations

Explicit boundary form factors: The scaling Lee–Yang model

László Holló, Zoltan Laczko, Zoltán Bajnok

We provide explicit expressions for boundary form factors in the boundary scaling Lee–Yang model for operators with the mildest ultraviolet behavior for all integrable boundary conditions. The form factors of the boundary stress tensor take a determinant form, while the form factors of the boundary primary field contain additional explicit polynomials.

arXiv:1405.3820Nuclear Physics BJul 23, 20143 citations

Form factors of descendant operators in the massive Lee–Yang model

Gesualdo Delfino A, Giuliano Niccoli

The form factors of the descendant operators in the massive Lee–Yang model are determined up to level 7. This is first done by exploiting the conserved quantities of the integrable theory to generate the solutions for the descendants starting from the lowest non-trivial solutions in each operator family. We then show that the operator space generated in this way, which is isomorphic to the conformal one, coincides, level by level, with that implied by the S -matrix through the form factor bootstrap. The solutions that we determine satisfy asymptotic conditions carrying the information about the level that we conjecture to hold for all the operators of the model.

arXiv:hep-th/0501173Journal of Statistical Mechanics Theory and ExperimentApr 12, 200517 citations

THE “BOOTSTRAP PROGRAM” FOR INTEGRABLE QUANTUM FIELD THEORIES IN 1 + 1 DIMENSIONS

H. Babujian, M. Karowski

The purpose of the "bootstrap program" is to construct integrable quantum field theories in 1+1 dimensions in terms of their Wightman functions explicitly. As an input the integrability and general assumptions of local quantum field theories are used. The object is to be achieved in tree steps: 1) The S-matrix is obtained using a qualitative knowledge of the particle spectrum and the Yang-Baxter equations. 2) Matrix elements of local operators are calculated by means of the "form factor program" using the S-matrix as an input. 3) The Wightman functions are calculated by taking sums over intermediate states. The first step has been performed for a large number of models and also the second one for several models. The third step is unsolved up to now. Here the program is illustrated in terms of the sine-Gordon model alias the massive Thirring model. Exploiting the "off-shell" Bethe Ansatz we propose general formulae for form factors. For example the n-particle matrix element for all higher currents are given and in particular all eigenvalues of the higher conserved charges are calculated. Furthermore quantum operator equations are obtained in terms of their matrix elements, in particular the quantum sine-Gordon field equation. Exact expressions for the finite wave function and mass renormalization constants are calculated.

arXiv:hep-th/0110261WORLD SCIENTIFIC eBooksApr 1, 20029 citations

Spectrum of local boundary operators from boundary form factor bootstrap

M. Szőts, G. Takács

arXiv:hep-th/0703226Nuclear Physics BApr 30, 200710 citations

FACTORIZED CHARACTERS AND FORM FACTORS OF DESCENDANT OPERATORS IN PERTURBED CONFORMAL SYSTEMS

Philippe Christe

We determine which characters of minimal models factorize into an infinite product like the one of the spin operator in the Ising model. In particular, all characters in the Ising model and in the nonunitary minimal Lee-Yang model factorize. This information is used to determine form factors of descendant operators, especially in the scaling Lee-Yang model.

International Journal of Modern Physics ADec 10, 199129 citations