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  "path": "/abs/2604.13026v1",
  "publishedAt": "2026-04-15T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Kunal Marwaha",
    "James Sud"
  ],
  "textContent": "**Authors:** Kunal Marwaha, James Sud\n\nWe study the computational complexity of 2-local Hamiltonian problems generated by a positive-weight symmetric interaction term, encompassing many canonical problems in statistical mechanics and optimization. We show these problems belong to one of three complexity phases: QMA-complete, StoqMA-complete, and reducible to a new problem we call EPR*. The phases are physically interpretable, corresponding to the energy level ordering of the local term. The EPR* problem is a simple generalization of the EPR problem of King. Inspired by empirically efficient algorithms for EPR, we conjecture that EPR* is in BPP. If true, this would complete the complexity classification of these problems, and imply EPR* is the transition point between easy and hard local Hamiltonians. Our proofs rely on perturbative gadgets. One simple gadget, when recursed, induces a renormalization-group-like flow on the space of local interaction terms. This gives the correct complexity picture, but does not run in polynomial time. To overcome this, we design a gadget based on a large spin chain, which we analyze via the Jordan-Wigner transformation.",
  "title": "A complexity phase transition at the EPR Hamiltonian"
}