Lieb-Liniger model with exponentially decaying interactions: A continuous matrix product state study

Julián Rincón, Martin Ganahl, Guifre Vidal

Research output: Contribution to journalResearch Articlepeer-review

19 Scopus citations


The Lieb-Liniger model describes one-dimensional bosons interacting through a repulsive contact potential. In this work, we introduce an extended version of this model by replacing the contact potential with a decaying exponential. Using the recently developed continuous matrix product states techniques, we explore the ground-state phase diagram of this model by examining the superfluid and density correlation functions. At weak coupling superfluidity governs the ground state, in a similar way as in the Lieb-Liniger model. However, at strong coupling quasicrystal and super-Tonks-Girardeau regimes are also found, which are not present in the original Lieb-Liniger case. Therefore the presence of the exponentially decaying potential leads to a superfluid/super-Tonks-Girardeau/quasicrystal crossover, when tuning the coupling strength from weak to strong interactions. This corresponds to a Luttinger liquid parameter in the range K(0,∞), in contrast with the Lieb-Liniger model, where K[1,), and the screened long-range potential, where K(0,1].

Original languageEnglish (US)
Article number115107
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number11
StatePublished - Sep 2 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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