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Correlations in excited states of local Hamiltonians · Around

2011

Correlations in excited states of local Hamiltonians

Chen, Jianxin, Ji, Zhengfeng, Wei, Zhaohui et al.

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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.

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M. B. Hastings, “Locality in Quantum Systems,” (2010), arXiv:1008.5137
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