Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable quantum spin chains with free fermionic and parafermionic
  spectrum   We present a general study of the large family of exact integrable quantum
chains with multispin interactions introduced recently in \cite{AP2020}. The
exact integrability follows from the algebraic properties of the energy density
operators defining the quantum chains. The Hamiltonians are characterized by a
parameter $p=1,2,\dots$ related to the number of interacting spins in the
multispin interaction. In the general case the quantum spins are of infinite
dimension. In special cases, characterized by the parameter $N=2,3,\ldots$, the
quantum chains describe the dynamics of $Z(N)$ quantum spin chains. The
simplest case $p=1$ corresponds to the free fermionic quantum Ising chain
($N=2$) or the $Z(N)$ free parafermionic quantum chain. The eigenenergies of
the quantum chains are given in terms of the roots of special polynomials, and
for general values of $p$ the quantum chains are characterized by a free
fermionic ($N=2$) or free parafermionic ($N>2$) eigenspectrum. The models have
a special critical point when all coupling constants are equal. At this point
the ground-state energy is exactly calculated in the bulk limit, and our
analytical and numerical analyses indicate that the models belong to
universality classes of critical behavior with dynamical critical exponent $z =
(p+1)/N$ and specific-heat exponent $\alpha = \max\{0,1-(p+1)/N\}$.

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The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci