Abstract
It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an -particle state. While determining which 2-particle density matrices are “-representable” is a computationally hard problem, all known extreme -representable 2-particle reduced density matrices arise from a unique -particle preimage, satisfying a conjecture established in 1972. We present explicit counterexamples to this conjecture through giving Hamiltonians with 2-body interactions which have degenerate ground states that cannot be distinguished by any 2-body operator. We relate the existence of such counterexamples to quantum error correction codes and topologically ordered spin systems.
- Received 31 October 2010
DOI:https://doi.org/10.1103/PhysRevLett.106.110501
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