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

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.

A comment added

References in corpus (9)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Solving the Simplest Theory of Quantum Gravity
• "Light-cone" dynamics after quantum quenches in spin chains
• Current operators in integrable spin chains: lessons from long range deformations
• The collision rate ansatz for the classical Toda lattice
• Collision rate ansatz for quantum integrable systems
• Thermal transport in $T\bar{T}$-deformed conformal field theories: from integrability to holography
• Free energy fluxes and the Kubo-Martin-Schwinger relation

Cited by in corpus (16)

• Non-Hermitian Hamiltonian Deformations in Quantum Mechanics
• Field Theory of Interacting Boundary Gravitons
• $T\bar{T}$ flow as characteristic flows
• The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations
• Note on the nonrelativistic $T\bar{T}$ deformation
• Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy
• $T\bar{T}$ deformation on multiquantum mechanics and regenesis
• New classical integrable systems from generalized $T\bar{T}$-deformations
• Integrable Crosscap States: From Spin Chains to 1D Bose Gas
• Adiabatic gauge potential and integrability breaking with free fermions
• $T\overline{T}$ deformations and the width of fundamental particles
• $T\bar{T}$ deformations and the pp wave correspondence
• $T\bar{T}$ deformation of Calogero-Sutherland model via dimensional reduction
• Krylov Complexity Under Hamiltonian Deformations and Toda Flows
• Scattering matrix for current-current deformations of the (2,2s+1) RSOS models
• $\text{T}\bar{\text{T}}$-deformed Nonlinear Schrödinger