The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations

Doyon, Benjamin; Durnin, Joseph; Yoshimura, Takato

doi:10.21468/SciPostPhys.13.3.072

SciPost Physics

The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations

Benjamin Doyon, Joseph Durnin, Takato Yoshimura

SciPost Phys. 13, 072 (2022) · published 28 September 2022

doi: 10.21468/SciPostPhys.13.3.072
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Abstract

We introduce an extension of the generalised $T\bar{T}$-deformation described by Smirnov-Zamolodchikov, to include the complete set of extensive charges. We show that this gives deformations of S-matrices beyond CDD factors, generating arbitrary functional dependence on momenta. We further derive from basic principles of statistical mechanics the flow equations for the free energy and all free energy fluxes. From this follows, without invoking the microscopic Bethe ansatz or other methods from integrability, that the thermodynamics of the deformed models are described by the integral equations of the thermodynamic Bethe-Ansatz, and that the exact average currents take the form expected from generalised hydrodynamics, both in the classical and quantum realms.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.13.3.072
TI  - The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations
PY  - 2022/09/28
UR  - https://scipost.org/SciPostPhys.13.3.072
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 13
IS  - 3
SP  - 072
A1  - Doyon, Benjamin
AU  - Durnin, Joseph
AU  - Yoshimura, Takato
AB  - We introduce an extension of the generalised $T\bar{T}$-deformation described by Smirnov-Zamolodchikov, to include the complete set of extensive charges. We show that this gives deformations of S-matrices beyond CDD factors, generating arbitrary functional dependence on momenta. We further derive from basic principles of statistical mechanics the flow equations for the free energy and all free energy fluxes. From this follows, without invoking the microscopic Bethe ansatz or other methods from integrability, that the thermodynamics of the deformed models are described by the integral equations of the thermodynamic Bethe-Ansatz, and that the exact average currents take the form expected from generalised hydrodynamics, both in the classical and quantum realms.
ER  -

@Article{10.21468/SciPostPhys.13.3.072,
	title={{The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations}},
	author={Benjamin Doyon and Joseph Durnin and Takato Yoshimura},
	journal={SciPost Phys.},
	volume={13},
	pages={072},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.13.3.072},
	url={https://scipost.org/10.21468/SciPostPhys.13.3.072},
}

Cited by 8

Authors / Affiliations: mappings to Contributors and Organizations

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¹ Benjamin Doyon,
¹ Joseph Durnin,
² Takato Yoshimura

Funder for the research work leading to this publication

Engineering and Physical Sciences Research Council [EPSRC]