论文标题
美元
$\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas
论文作者
论文摘要
$ \ mathrm {t} \叠加{\ mathrm {t}} $变形最初是作为2D相对论量子场理论（QFTS）的无关可解决的变形。还可以定义相同的变形系列，用于在ADS/CFT中首先研究的可集成量子自旋链。在本文中，我们为另一种模型构建了这种变形，这些变形描述了以1D的形式进行的粒子集合，并以整合的方式进行交互。这种模型的原型是Lieb-Liniger模型。这表明可以为非常广泛的系统定义此类变形。我们研究了$ \ mathrm {t} \ overline {\ mathrm {t}} $ - 变形的lieb-liniger模型的有限体积光谱和热力学。我们发现，对于变形参数$（λ<0）$的一个符号，当系统的体积小于某些临界值时，变形频谱就会变得复杂，表示紫外线物理的分解。对于其他标志$（λ> 0）$，存在温度的上限，类似于$ \ mathrm {t} \ overline {\ mathrm {t}} $变形qfts的hagedorn行为。这两种行为都可以归因于$ \ mathrm {t} \ Overline {\ Mathrm {t}} $变形改变粒子大小的事实。我们表明，对于$λ> 0 $，变形增加了粒子之间的空间，从而有效地增加了系统体积。对于$λ<0 $，$ \ mathrm {t} \ overline {\ mathrm {t}} $变形将点粒子涂成有限尺寸硬杆。这类似于观察到$ \ mathrm {t} \ Overline {\ Mathrm {t}} $的动作 - 变形的Free Boson是NAMBU-GOTO动作，它描述了玻色弦，它也是一个具有有限尺寸的扩展对象。
$\mathrm{T}\overline{\mathrm{T}}$ 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 $(λ<0)$, 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 $(λ>0)$, 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 $λ>0$, the deformation increases the spaces between particles which effectively increases the volume of the system. For $λ<0$, $\mathrm{T}\overline{\mathrm{T}}$ 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.
