Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The density-matrix renormalization group in the age of matrix product
  states   The density-matrix renormalization group method (DMRG) has established itself
over the last decade as the leading method for the simulation of the statics
and dynamics of one-dimensional strongly correlated quantum lattice systems. In
the further development of the method, the realization that DMRG operates on a
highly interesting class of quantum states, so-called matrix product states
(MPS), has allowed a much deeper understanding of the inner structure of the
DMRG method, its further potential and its limitations. In this paper, I want
to give a detailed exposition of current DMRG thinking in the MPS language in
order to make the advisable implementation of the family of DMRG algorithms in
exclusively MPS terms transparent. I then move on to discuss some directions of
potentially fruitful further algorithmic development: while DMRG is a very
mature method by now, I still see potential for further improvements, as
exemplified by a number of recently introduced algorithms.

28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex