Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measurement-induced criticality and entanglement clusters: a study of 1D
  and 2D Clifford circuits   Entanglement transitions in quantum dynamics present a novel class of phase
transitions in non-equilibrium systems. When a many-body quantum system
undergoes unitary evolution interspersed with monitored random measurements,
the steady-state can exhibit a phase transition between volume and area-law
entanglement. There is a correspondence between measurement-induced transitions
in non-unitary quantum circuits in $d$ spatial dimensions and classical
statistical mechanical models in $d+1$ dimensions. In certain limits these
models map to percolation, but there is analytical and numerical evidence to
suggest that away from these limits the universality class should generically
be distinct from percolation. Intriguingly, despite these arguments, numerics
on 1D qubit circuits give bulk exponents which are nonetheless close to those
of 2D percolation, with possible differences in surface behavior. In the first
part of this work we study the critical properties of 2D Clifford circuits. In
the bulk, we find many properties suggested by the percolation picture,
including matching bulk exponents, and an inverse power-law for the critical
entanglement growth, $S(t,L) \sim L(1 - a/t)$, which saturates to an area-law.
We then utilize a graph-state based algorithm to analyze in 1D and 2D the
critical properties of entanglement clusters in the steady state. We show that
in a model with a simple geometric map to percolation, the projective
transverse field Ising model, the entanglement clusters are governed by
percolation surface exponents. However, in the Clifford models we find large
deviations in the cluster exponents from those of surface percolation,
highlighting the breakdown of any possible geometric map to percolation. Given
the evidence for deviations from the percolation universality class, our
results raise the question of why nonetheless many bulk properties behave
similarly to percolation.

21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph