Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free fermions in disguise   I solve a quantum chain whose Hamiltonian is comprised solely of local
four-fermi operators by constructing free-fermion raising and lowering
operators. The free-fermion operators are both non-local and highly non-linear
in the local fermions. This construction yields the complete spectrum of the
Hamiltonian and an associated classical transfer matrix. The spatially uniform
system is gapless with dynamical critical exponent z=3/2, while staggering the
couplings gives a more conventional free-fermion model with an Ising
transition. The Hamiltonian is equivalent to that of a spin-1/2 chain with
next-nearest-neighbour interactions, and has a supersymmetry generated by a sum
of fermion trilinears. The supercharges are part of a large non-abelian
symmetry algebra that results in exponentially large degeneracies. The model is
integrable for either open or periodic boundary conditions but the free-fermion
construction only works for the former, while for the latter the extended
symmetry is broken and the degeneracies split.

3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
18
The categories of this paper are: econ