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From Ground States to Local Hamiltonians · Around

2011

From Ground States to Local Hamiltonians

Chen, Jianxin, Ji, Zhengfeng, Zeng, Bei et al.

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Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states.

In practical situations, one would be mainly interested in local Hamiltonians with certain interaction patterns, such as nearest neighbour interactions on some type of lattices.
A necessary condition for a space $V$ to be the ground-state space of some local Hamiltonian with a given interaction pattern, is that the maximally mixed state supported on $V$ is uniquely determined by its reduced density matrices associated with the given pattern, based on the principle of maximum entropy.
However, it is unclear whether this condition is in general also sufficient.

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