Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas

• Autor(a) principal: Colcelli, A.
• Data de Publicação: 2018
• Outros Autores: Vitti, Jacopo, Mussardo, G., Trombettoni, A.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UFRN
• Texto Completo: https://repositorio.ufrn.br/handle/123456789/30470
• topic: Tonks-Girardeau gas

The scaling of the largest eigenvalue λ0 of the one-body density matrix of a system with respect to its particle number N defines an exponent C and a coefficient B via the asymptotic relation λ0 ∼ B NC. The case C = 1 corresponds to off-diagonal long-range order. For a one-dimensional homogeneous Tonks-Girardeau gas, a wellknown result also confirmed by bosonization gives instead C = 1/2. Here we investigate the inhomogeneous case, initially addressing the behavior of C in the presence of a general external trapping potential V . We argue that the value C = 1/2 characterizes the hard-core system independently of the nature of the potential V . We then define the exponents γ and β, which describe the scaling of the peak of the momentum distribution with N and the natural orbital corresponding to λ0, respectively, and we derive the scaling relation γ + 2β = C. Taking as a specific case the power-law potential V (x) ∝ x2n, we give analytical formulas for γ and β as functions of n. Analytical predictions for the coefficient B are also obtained. These formulas are derived by exploiting a recent field theoretical formulation and checked against numerical results. The agreement is excellent