Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Parallel Computing Method for the Higher Order Tensor Renormalization
  Group   In this paper, we propose a parallel computing method for the Higher Order
Tensor Renormalization Group (HOTRG) applied to a $d$-dimensional $( d \geq 2
)$ simple lattice model. Sequential computation of the HOTRG requires $O (
\chi^{4 d - 1} )$ computational cost, where $\chi$ is bond dimension, in a step
to contract indices of tensors. When we simply distribute elements of a local
tensor to each process in parallel computing of the HOTRG, frequent
communication between processes occurs. The simplest way to avoid such
communication is to hold all the tensor elements in each process, however, it
requires $O ( \chi^{2d} )$ memory space. In the presented method, placement of
a local tensor element to more than one process is accepted and sufficient
local tensor elements are distributed to each process to avoid communication
between processes during considering computation step. For the bottleneck part
of computational cost, such distribution is achieved by distributing elements
of two local tensors to $\chi^2$ processes according to one of the indices of
each local tensor which are not contracted during considering computation. In
the case of $d \geq 3$, computational cost in each process is reduced to $O (
\chi^{4 d - 3} )$ and memory space requirement in each process is kept to be $O
( \chi^{2d - 1} )$.

16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th