One-body reduced density matrix of trapped impenetrable anyons in one dimension

Abstract

We study the one-body reduced density matrix of a system of $N$ one-dimensional impenetrable anyons trapped by a harmonic potential. To this purpose we extend two methods developed to tackle related problems, namely the determinant approach and the replica method. While the former is the basis for exact numerical computations at finite $N$, the latter has the advantage of providing an analytic asymptotic expansion for large $N$. We show that the first few terms of such expansion are sufficient to reproduce the numerical results to an excellent accuracy even for relatively small $N$, thus demonstrating the effectiveness of the replica method.

16 pages, 5 figures; v2 typos fixed, matches published version

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Cited by in corpus (23)

• Emergence of curved light-cones in a class of inhomogeneous Luttinger liquids
• Conformal field theory on top of a breathing one-dimensional gas of hard core bosons
• Exact dynamics following an interaction quench in a one-dimensional anyonic gas
• One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance
• Anyonic tight-binding models of parafermions and of fractionalized fermions
• Subsystem trace distance in low-lying states of $(1+1)$-dimensional conformal field theories
• Ground State Properties of the One-Dimensional Unconstrained Pseudo-Anyon Hubbard Model
• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Probing the exchange statistics of one-dimensional anyon models
• Correlation functions of one-dimensional strongly interacting two-component gases
• Universal off-diagonal long-range order behaviour for a trapped Tonks-Girardeau gas
• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases
• Three-body interaction effects on the ground state of one-dimensional anyons
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Spin-incoherent Luttinger liquid of one-dimensional SU($\kappa$) fermions
• One-dimensional hard-core anyon gas in a harmonic trap at finite temperature
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• Determinant formula for the field form factor in the anyonic Lieb-Liniger model
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases
• Bardeen-Cooper-Schrieffer State Representation and Pairing in the Fermionic Tonks-Girardeau Gas
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
• One-dimensional anyons in relativistic field theory