Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic
  potential   A major challenge in modern physics is to accurately describe strongly
interacting quantum many-body systems. One-dimensional systems provide
fundamental insights since they are often amenable to exact methods. However,
no exact solution is known for the experimentally relevant case of external
confinement. Here, 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 wavefunction. 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.

27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph