@article {1454,
title = {Ground-State Spaces of Frustration-Free Hamiltonians},
journal = {Journal of Mathematical Physics},
volume = {53},
year = {2012},
month = {2012/01/01},
pages = {102201},
abstract = { We study the ground-state space properties for frustration-free Hamiltonians.
We introduce a concept of {\textquoteleft}reduced spaces{\textquoteright} to characterize local structures of
ground-state spaces. For a many-body system, we characterize mathematical
structures for the set $\Theta_k$ of all the $k$-particle reduced spaces, which
with a binary operation called join forms a semilattice that can be interpreted
as an abstract convex structure. The smallest nonzero elements in $\Theta_k$,
called atoms, are analogs of extreme points. We study the properties of atoms
in $\Theta_k$ and discuss its relationship with ground states of $k$-local
frustration-free Hamiltonians. For spin-1/2 systems, we show that all the atoms
in $\Theta_2$ are unique ground states of some 2-local frustration-free
Hamiltonians. Moreover, we show that the elements in $\Theta_k$ may not be the
join of atoms, indicating a richer structure for $\Theta_k$ beyond the convex
structure. Our study of $\Theta_k$ deepens the understanding of ground-state
space properties for frustration-free Hamiltonians, from a new angle of reduced
spaces.
},
doi = {10.1063/1.4748527},
url = {http://arxiv.org/abs/1112.0762v1},
author = {Jianxin Chen and Zhengfeng Ji and David Kribs and Zhaohui Wei and Bei Zeng}
}