



@article {1443,
	title = {Correlations in excited states of local Hamiltonians},
	journal = {Physical Review A},
	volume = {85},
	year = {2012},
	month = {2012/4/9},
	abstract = {  Physical properties of the ground and excited states of a $k$-local
Hamiltonian are largely determined by the $k$-particle reduced density matrices
($k$-RDMs), or simply the $k$-matrix for fermionic systems---they are at least
enough for the calculation of the ground state and excited state energies.
Moreover, for a non-degenerate ground state of a $k$-local Hamiltonian, even
the state itself is completely determined by its $k$-RDMs, and therefore
contains no genuine ${>}k$-particle correlations, as they can be inferred from
$k$-particle correlation functions. It is natural to ask whether a similar
result holds for non-degenerate excited states. In fact, for fermionic systems,
it has been conjectured that any non-degenerate excited state of a 2-local
Hamiltonian is simultaneously a unique ground state of another 2-local
Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version
of this conjecture states that any non-degenerate excited state of a 2-local
Hamiltonian is uniquely determined by its 2-matrix among all the pure
$n$-particle states. We construct explicit counterexamples to show that both
conjectures are false. It means that correlations in excited states of local
Hamiltonians could be dramatically different from those in ground states. We
further show that any non-degenerate excited state of a $k$-local Hamiltonian
is a unique ground state of another $2k$-local Hamiltonian, hence is uniquely
determined by its $2k$-RDMs (or $2k$-matrix).
},
	doi = {10.1103/PhysRevA.85.040303},
	url = {http://arxiv.org/abs/1106.1373v2},
	author = {Jianxin Chen and Zhengfeng Ji and Zhaohui Wei and Bei Zeng}
}
@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}
}
@article {1441,
	title = {The LU-LC conjecture is false},
	year = {2007},
	month = {2007/09/09},
	abstract = {  The LU-LC conjecture is an important open problem concerning the structure of
entanglement of states described in the stabilizer formalism. It states that
two local unitary equivalent stabilizer states are also local Clifford
equivalent. If this conjecture were true, the local equivalence of stabilizer
states would be extremely easy to characterize. Unfortunately, however, based
on the recent progress made by Gross and Van den Nest, we find that the
conjecture is false.
},
	url = {http://arxiv.org/abs/0709.1266v2},
	author = {Zhengfeng Ji and Jianxin Chen and Zhaohui Wei and Mingsheng Ying}
}
