August 4th-7th, 2014
Yukawa Institute for Theoretical Physics, Kyoto University
"Entanglement behavior of two-dimensional quantum models"
Shu Tanaka (YITP)
We investigated entanglement behavior of two-dimensional quantum systems whose ground state can be exactly obtained.
One is the entanglement properties of two-dimensional VBS (Valence-Bond-Solid) state
which is the ground state of the AKLT Hamiltonian[1,2].
Entanglement spectrum of the VBS state on square lattice is similar
to the energy dispersion of the one-dimensional antiferromagnetic Heisenberg model.
To consider the entanglement properties more detail, we introduced a new measure called nested entanglement entropy[2,3].
We found that the central charge of the entanglement Hamiltonian of the VBS state on square lattice is c=1
which is the same value as the one-dimensional Heisenberg model.
Next we considered the entanglement behavior of hard-core quantum lattice gas model with nearest-neighbor exclusion[4].
We focused on the entanglement properties at a certain point and found that critical phenomena in two-dimensional Ising
and three-state Potts models appear in the entanglement properties of the model depending on the lattice geometry.
References:
[1] H. Katsura, N. Kawashima, A. N. Kirillov, V. E. Korepin, and S. Tanaka, J.
Phys. A 43, 255303 (2010).
[2] J. Lou, S. Tanaka, H. Katsura, and N. Kawashima, Phys. Rev. B 84, 245128 (2011).
[3] S. Tanaka, Interdisciplinary Information Sciences 19, 101 (2013).
[4] S. Tanaka, R. Tamura, and H. Katsura, Phys. Rev. A 86, 032326 (2012).
Designed by CSS.Design Sample