Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Many Body Quantum Chaos and Dual Unitarity Round-a-Face   We propose a new type of locally interacting quantum circuits which are
generated by unitary interactions round-a-face (IRF). Specifically, we discuss
a set (or manifold) of dual-unitary IRFs with local Hilbert space dimension $d$
(DUIRF$(d)$) which generate unitary evolutions both in space and time
directions of an extended 1+1 dimensional lattice. We show how arbitrary
dynamical correlation functions of local observables can be evaluated in terms
of finite dimensional completely positive trace preserving unital maps, in
complete analogy to recently studied circuits made of dual unitary brick gates
(DUBG). In fact, we show that the simplest non-trivial (non-vanishing) local
correlation functions in dual-unitary IRF circuits involve observables
non-trivially supported on at least two sites. We completely characterise the
10-dimensional manifold of DUIRF$(2)$ for qubits ($d=2$) and provide, for
$d=3,4,5,6,7$, empirical estimates of its dimensionality based on numerically
determined dimensions of tangent spaces at an ensemble of random instances of
dual-unitary IRF gates. In parallel, we apply the same algorithm to determine
${\rm dim}\,{\rm DUBG}(d)$ and show that they are of similar order though
systematically larger than ${\rm dim}\,{\rm DUIRF}(d)$ for $d=2,3,4,5,6,7$. It
is remarkable that both sets have rather complex topology for $d\ge 3$ in the
sense that the dimension of the tangent space varies among different randomly
generated points of the set. Finally, we provide additional data on
dimensionality of the chiral extension of DUBG circuits with distinct local
Hilbert spaces of dimensions $d\neq d'$ residing at even/odd lattice sites.

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The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
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The categories of this paper are: stat
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th