The rotation-invariant local Hamiltonian problem in any fixed lattice dimension is QMAEXP-complete.
Commuting Local Hamiltonians on Expanders, Locally Testable Quantum codes, and the qPCP conjecture
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Understanding commuting local Hamiltonians (CLHs) is at the heart of many questions in quantum computational complexity and quantum physics: quantum error correcting codes, quantum NP, the PCP conjecture, topological order and more.
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The rotation-invariant Hamiltonian problem is QMA$_{\rm EXP}$-complete
The rotation-invariant local Hamiltonian problem in any fixed lattice dimension is QMAEXP-complete.