Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Abstract: K1.00203 : Z$_2$ topological classification of the $S=1/2$ Heisenberg model on the two dimensional pylochlore lattice
Author:
We have investigated the $S=1/2$ Heisenberg model
on the two dimensional pyrochlore lattice [1] by using the Z$_2$
Berry phase [2]
which is quantized due to the time reversal invariance.
Since these Z$_2$ Berry phases are adiabatic invariants against
change of the physical parameters,
one can distinguish ground states when the quantized values are
different.
By suitably choosing ways of local $U(1)$ twists to define the
Berry phases,
one can show that the ground state in this system is
adiabatically connected to
a direct product state of local singlets or plaquette singlets.
We have described the basic formulation and demonstrate the validity
for finite systems using a
Lanczos diagonalization.
\\[4pt]
[1] J.-B. Fouet, M. Mambrini, P. Sindzingre, and C.Lhuillier,
Phys. Rev. B 67 (2003) 054411.\\[0pt]
[2] Y. Hatsugai, J.Phys Soc. Jpn. 73 (2004) 2604.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2011.MAR.K1.203
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