Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entropy, gap and a multi-parameter deformation of the Fredkin spin chain   We introduce a multi-parameter deformation of the Fredkin spin $1/2$ chain
whose ground state is a weighted superposition of Dyck paths, depending on a
set of parameters $t_i$ along the chain. The parameters are introduced in such
a way to maintain the system frustration-free while allowing to explore a range
of possible phases. In the case where the parameters are uniform, and a color
degree of freedom is added we establish a phase diagram with a transition
between an area law and a volume low. The volume entropy obtained for half a
chain is $n \log s$ where $n$ is the half-chain length and $s$ is the number of
colors. Next, we prove an upper bound on the spectral gap of the $t>1, s>1$
phase, scaling as $\Delta=O((4s)^nt^{-n^2/2})$, similar to a recent a result
about the deformed Motzkin model, albeit derived in a different way. Finally,
using an additional variational argument we prove an exponential lower bound on
the gap of the model for $t>1, s=1$, which provides an example of a system with
bounded entanglement entropy and a vanishing spectral gap.

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The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
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The categories of this paper are: physics
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th