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- W4386465839 abstract "Motivated by the realization of coupled Luttinger liquids in a split condensate for quantum sine-Gordon (SG) model [Haller et al., Nature 466, 597 (2010); Schweiglet et al., Nature 545, 323 (2017); Nat. Phys. 17, 559 (2021)], here we study the phase transition in coupled condensates using the bosonization method. We show that when these condensates have different velocities ${u}_{i}$ and Luttinger parameters ${K}_{i}$, the physics is described by a generalized SG model, which is also exactly solvable. We use various approaches, including the Wilson renormalization group, correlation function, variational wave function, and the equivalent Coulomb gas methods, demonstrating the phase transition at $2=1/(4{K}_{1})+1/(4{K}_{2})$. The physical meaning of this boundary is explained by the density-phase uncertainty principle, showing how the many-body interactions drive the coupled condensates from two gapless phases to one gapless phase. The relative phase between the condensates may fundamentally affect the band structure, yet it will not affect this boundary. Furthermore, we also discuss the relevance of our result in the two-dimensional models for the Berezinskii-Kosterlitz-Thouless transition, from which the physical meaning of this boundary is self-evident. Our results can be used to study the phase transitions in one-dimensional coupled models with Fermions and Bosons, and even the Kane-Fisher model with impurities, and study their phase transitions, non-Gaussian dynamics, and thermalization, which may be of great interest in quantum simulation." @default.
- W4386465839 created "2023-09-06" @default.
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- W4386465839 date "2023-09-05" @default.
- W4386465839 modified "2023-09-30" @default.
- W4386465839 title "Generalized sine-Gordon model for coupled condensates and phase transition" @default.
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- W4386465839 doi "https://doi.org/10.1103/physrevb.108.115106" @default.
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