Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singularities in fidelity surfaces for quantum phase transitions: a
  geometric perspective   The fidelity per site between two ground states of a quantum lattice system
corresponding to different values of the control parameter defines a surface
embedded in a Euclidean space. The Gaussian curvature naturally quantifies
quantum fluctuations that destroy orders at transition points. It turns out
that quantum fluctuations wildly distort the fidelity surface near the
transition points, at which the Gaussian curvature is singular in the
thermodynamic limit. As a concrete example, the one-dimensional quantum Ising
model in a transverse field is analyzed. We also perform a finite size scaling
analysis for the transverse Ising model of finite sizes. The scaling behavior
for the Gaussian curvature is numerically checked and the correlation length
critical exponent is extracted, which is consistent with the conformal
invariance at the critical point.

11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph