Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automatic Differentiation for Second Renormalization of Tensor Networks   Tensor renormalization group (TRG) constitutes an important methodology for
accurate simulations of strongly correlated lattice models. Facilitated by the
automatic differentiation technique widely used in deep learning, we propose a
uniform framework of differentiable TRG ($\partial$TRG) that can be applied to
improve various TRG methods, in an automatic fashion. Essentially,
$\partial$TRG systematically extends the concept of second renormalization [PRL
103, 160601 (2009)] where the tensor environment is computed recursively in the
backward iteration, in the sense that given the forward process of TRG,
$\partial$TRG automatically finds the gradient through backpropagation, with
which one can deeply "train" the tensor networks. We benchmark $\partial$TRG in
solving the square-lattice Ising model, and demonstrate its power by simulating
one- and two-dimensional quantum systems at finite temperature. The deep
optimization as well as GPU acceleration renders $\partial$TRG manybody
simulations with high efficiency and accuracy.

21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs