Strongly interacting confined quantum systems in one dimension

TL;DR

This paper introduces a new energy-functional method to solve strongly interacting one-dimensional quantum systems in arbitrary traps, revealing magnetic states and correlations relevant for quantum manipulation.

Contribution

It provides a novel approach to exactly solve strongly interacting 1D quantum systems in any confining geometry, including full spectra and eigenstates.

Findings

Presence of ferro- and anti-ferromagnetic states in small systems

Calculation of spatial correlations in strongly interacting systems

Potential for quantum control of magnetic correlations

Abstract

In one dimension, the study of magnetism dates back to the dawn of quantum mechanics when Bethe solved the famous Heisenberg model that describes quantum behaviour in magnetic systems. In the last decade, one-dimensional systems have become a forefront area of research driven by the realization of the Tonks-Girardeau gas using cold atomic gases. Here we prove that one-dimensional fermionic and bosonic systems with strong short-range interactions are solvable in arbitrary confining geometries by introducing a new energy-functional technique and obtaining the full spectrum of energies and eigenstates. As a first application, we calculate spatial correlations and show how both ferro- and anti-ferromagnetic states are present already for small system sizes that are prepared and studied in current experiments. Our work demonstrates the enormous potential for quantum manipulation of magnetic correlations at the microscopic scale.