scholarly journals Simple approximation for the Bethe-ansatz solution of the one-dimensional Fermi gas

1987 ◽  
Vol 35 (4) ◽  
pp. 1682-1686 ◽  
Author(s):  
M. A. Gusmão
Keyword(s):  
Bethe Ansatz ◽  
Fermi Gas ◽  
Simple Approximation ◽  
One Dimensional ◽  
Bethe Ansatz Solution ◽  
The One

Thermodynamics of the Repulsive Lieb–Liniger Model

2019 ◽  
pp. 633-640
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Bethe Ansatz ◽  
Finite Temperature ◽  
Bose Gas ◽  
Main Ingredient ◽  
Ansatz Method ◽  
One Dimensional ◽  
Bethe Ansatz Solution ◽  
The One

This chapter discusses how the Bethe ansatz solution of the one-dimensional Bose gas with repulsive δ‎-function interaction is extended to finite temperatures, the thermody- namic Bethe ansatz. The excitations of this system consist of particle and hole excitations, which can be described by the corresponding densities of Bethe ansatz roots. It shows how these Bethe ansatz root densities are used to define an appropriate expression for the entropy of the system of Bose particles, which is the main ingredient for the extension of the Bethe ansatz method to finite temperature.

scholarly journals Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential

2015 ◽  
Vol 1 (6) ◽  
pp. e1500197 ◽  
Author(s):  
Jesper Levinsen ◽  
Pietro Massignan ◽  
Georg M. Bruun ◽  
Meera M. Parish
Keyword(s):  
Fermi Gas ◽  
Harmonic Potential ◽  
Chain Model ◽  
Many Body ◽  
Exact Methods ◽  
One Dimensional ◽  
Heisenberg Spin Chain ◽  
Precise Knowledge ◽  
Short Range Repulsion ◽  
The One

A major challenge in modern physics is to accurately describe strongly interacting quantum many-body systems. One-dimensional systems provide fundamental insights because they are often amenable to exact methods. However, no exact solution is known for the experimentally relevant case of external confinement. We propose a powerful ansatz for the one-dimensional Fermi gas in a harmonic potential near the limit of infinite short-range repulsion. For the case of a single impurity in a Fermi sea, we show that our ansatz is indistinguishable from numerically exact results in both the few- and many-body limits. We furthermore derive an effective Heisenberg spin-chain model corresponding to our ansatz, valid for any spin-mixture, within which we obtain the impurity eigenstates analytically. In particular, the classical Pascal’s triangle emerges in the expression for the ground-state wave function. As well as providing an important benchmark for strongly correlated physics, our results are relevant for emerging quantum technologies, where a precise knowledge of one-dimensional quantum states is paramount.

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