# One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance

## TL;DR

This paper derives an asymptotically exact expression for the one-particle density matrix of trapped one-dimensional impenetrable bosons using conformal invariance, applicable to arbitrary trapping potentials and confirming previous results in specific cases.

## Contribution

It introduces a novel approach using conformal field theory to compute the density matrix for inhomogeneous systems, extending previous methods to arbitrary traps.

## Key findings

- Exact asymptotic formula for density matrix in large particle limit
- Applicable to arbitrary trapping potentials
- Recovers known results for harmonic traps

## Abstract

The one-particle density matrix of the one-dimensional Tonks-Girardeau gas with inhomogeneous density profile is calculated, thanks to a recent observation that relates this system to a two-dimensional conformal field theory in curved space. The result is asymptotically exact in the limit of large particle density and small density variation, and holds for arbitrary trapping potentials. In the particular case of a harmonic trap, we recover a formula obtained by Forrester et al. [Phys. Rev. A 67, 043607 (2003)] from a different method.