Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fermionic Luttinger liquids from a microscopic perspective   We consider interacting one-dimensional, spinless Fermi gases, whose
low-energy properties are described by Luttinger liquid theory. We perform a
systematic, in-depth analysis of the relation between the macroscopic,
phenomenological parameters of Luttinger liquid effective field theory, and the
microscopic interactions of the Fermi gas. In particular, we begin by
explaining how to model effective interactions in one dimension, which we then
apply to the main forward scattering channel -- the interbranch collisions --
common to these systems. We renormalise the corresponding interbranch
phenomenological constants in favour of scattering phase shifts. Interestingly,
our renormalisation procedure shows (i) how Luttinger's model arises in a
completely natural way -- and not as a convenient approximation -- from
Tomonaga's model, and (ii) the reasons behind the interbranch coupling constant
remaining unrenormalised in Luttinger's model. We then consider the so-called
intrabranch processes, whose phenomenological coupling constant is known to be
fixed by charge conservation, but whose microscopic origin is not well
understood. We show that, contrary to general belief and common sense, the
intrabranch interactions appearing in Luttinger liquid theory do not correspond
to an intrabranch scattering channel, nor an energy shift due to intrabranch
interactions, in the microscopic theory. Instead, they are due to interbranch
processes. We finally apply our results to a particular example of an exactly
solvable model, namely the fermionic dual to the Lieb-Liniger model in the
Tonks-Girardeau and super-Tonks-Girardeau regimes.

20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn