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$\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas

by Yunfeng Jiang

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Submission summary

Authors (as registered SciPost users): Yunfeng Jiang
Submission information
Preprint Link: https://arxiv.org/abs/2011.00637v3  (pdf)
Date accepted: 2022-04-22
Date submitted: 2022-03-07 02:07
Submitted by: Jiang, Yunfeng
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
Approach: Theoretical

Abstract

$\mathrm{T}\overline{\mathrm{T}}$ deformation was originally proposed as an irrelevant solvable deformation for 2d relativistic quantum field theories (QFTs). The same family of deformations can also be defined for integrable quantum spin chains which was first studied in the context of integrability in AdS/CFT. In this paper, we construct such deformations for yet another type of models, which describe a collection of particles moving in 1d and interacting in an integrable manner. The prototype of such models is the Lieb-Liniger model. This shows that such deformations can be defined for a very wide range of systems. We study the finite volume spectrum and thermodynamics of the $\mathrm{T}\overline{\mathrm{T}}$-deformed Lieb-Liniger model. We find that for one sign of the deformation parameter $(\lambda<0)$, the deformed spectrum becomes complex when the volume of the system is smaller than certain critical value, signifying the break down of UV physics. For the other sign $(\lambda>0)$, there exists an upper bound for the temperature, similar to the Hagedorn behavior of the $\mathrm{T}\overline{\mathrm{T}}$ deformed QFTs. Both behaviors can be attributed to the fact that $\mathrm{T}\overline{\mathrm{T}}$ deformation changes the size the particles. We show that for $\lambda>0$, the deformation increases the spaces between particles which effectively increases the volume of the system. For $\lambda<0$, $\mathrm{T}\overline{\mathrm{T}}$ deformation fattens point particles to finite size hard rods. This is similar to the observation that the action of $\mathrm{T}\overline{\mathrm{T}}$-deformed free boson is the Nambu-Goto action, which describes bosonic strings -- also an extended object with finite size.

Author comments upon resubmission

I would like to thank the referee for the helpful comment.

I added a few sentences which includes the comment below (27) and a footnote which acknowledge the referee for the helpful suggestion.

List of changes

Few sentences are added below (27) to include the comment from the referee.

A footnote added on page 9 to acknowledge the referee for this useful suggestion.

Published as SciPost Phys. 12, 191 (2022)


Reports on this Submission

Anonymous Report 2 on 2022-3-29 (Invited Report)

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The paper can be published.

  • validity: -
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Anonymous Report 1 on 2022-3-15 (Invited Report)

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The author has amended the paper following the suggestions of the referees

Requested changes

none

  • validity: high
  • significance: high
  • originality: high
  • clarity: top
  • formatting: excellent
  • grammar: good

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