Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Description of (Spin) Hall Conductances on Brillouin Zone
  Lattices : Quantum Phase Transitions and Topological Changes   It is widely accepted that topological quantities are useful to describe
quantum liquids in low dimensions. The (spin) Hall conductances are typical
examples. They are expressed by the Chern numbers, which are topological
invariants given by the Berry connections of the ground states. We present a
topological description for the (spin) Hall conductances on a discretized
Brillouin Zone. At the same time, it is quite efficient in practical numerical
calculations for concrete models. We demonstrate its validity in a model with
quantum phase transitions. Topological changes supplemented with the transition
is also described in the present lattice formulation.

7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an