Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-Layer Restricted Boltzmann Machine Representation of 1D Quantum
  Many-Body Wave Functions   We consider representing two classes of 1D quantum wave functions of spin
systems, including the AKLT and CFT correlator wave functions, in terms of
multi-layer restricted Boltzmann machines. In our prescription, the AKLT wave
function can be exactly represented by a 2-layer restricted Boltzmann machine
with five hidden spins per visible spin. The construction can be generalized to
prove that any MPS wave function on $N$ unit cells with finite bond dimension
can be approximated by a 2-layer restricted Boltzmann machine with
$\mathcal{O}(N)$ hidden spins within an error which scales linearly with $N$.
The Haldane-Shastry wave function or a chiral boson CFT correlator wave
function, as any Jastrow type of wave functions, can be exactly written as a
1-layer Boltzmann machine with $\mathcal{O}(N^2)$ hidden spins and $N$ visible
spins. Applying the cumulant expansion, we further find that the chiral boson
CFT correlator wave function (with small vertex operator conformal dimension
$\alpha$, i.e., $\alpha<0.1$) can be approximated, within 99.9\% accuracy up to
22 visible spins, by a 1-layer RBM with $\mathcal{O}(N)$ hidden spins. The
cumulant expansion also leads us to a physically inspiring result in which the
hidden spins of the restricted Boltzmann machine can be interpreted as the
conformal tower of the chiral boson CFT on the cylinder.

24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc