Initial states in integrable quantum field theory quenches from an integral equation hierarchy

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Description:	Takacs, G (Budapest University of Technology and Economics) Friday 15th January 2016 - 11:30 to 12:30


Created:	2016-01-27 14:29
Collection:	Mathematical Aspects of Quantum Integrable Models in and out of Equilibrium
Publisher:	Isaac Newton Institute
Copyright:	Takacs, G
Language:	eng (English)


Abstract:	Co-authors: David X. Horvath (Budapest University of Technology and Economics), Spyros Sotiriadis (SISSA) We consider the problem of determining the initial state of integrable quantum field theory quenches in terms of the post-quench eigenstates. The corresponding overlaps are a fundamental input to most exact methods to treat integrable quantum quenches. We construct and examine an infinite integral equation hierarchy based on the form factor bootstrap, proposed earlier as a set of conditions determining the overlaps. Using quenches of the mass and interaction in Sinh-Gordon theory as a concrete example, we present theoretical arguments that the state has the squeezed coherent form expected for integrable quenches, and supporting an Ansatz for the solution of the hierarchy. Moreover we also develop an iterative method to solve numerically the lowest equation of the hierarchy. The iterative solution along with extensive numerical checks performed using the next equation of the hierarchy provides a strong numerical evidence that the proposed Ansatz gives a very good approximation for the solution. Related Links http://www.sciencedirect.com/science/article/pii/S0550321315004095 - Nuclear Physics B902 (2016) 508-547

Abstract:

Co-authors: David X. Horvath (Budapest University of Technology and Economics), Spyros Sotiriadis (SISSA)

We consider the problem of determining the initial state of integrable quantum field theory quenches in terms of the post-quench eigenstates. The corresponding overlaps are a fundamental input to most exact methods to treat integrable quantum quenches. We construct and examine an infinite integral equation hierarchy based on the form factor bootstrap, proposed earlier as a set of conditions determining the overlaps. Using quenches of the mass and interaction in Sinh-Gordon theory as a concrete example, we present theoretical arguments that the state has the squeezed coherent form expected for integrable quenches, and supporting an Ansatz for the solution of the hierarchy. Moreover we also develop an iterative method to solve numerically the lowest equation of the hierarchy. The iterative solution along with extensive numerical checks performed using the next equation of the hierarchy provides a strong numerical evidence that the proposed Ansatz gives a very good approximation for the solution.

Related Links

http://www.sciencedirect.com/science/article/pii/S0550321315004095 - Nuclear Physics B902 (2016) 508-547

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