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arXiv:2610.20846

Entanglement of superpositions in zero-energy subspace: insights from stabilizer theory

Konstantin Antipin, Richik Sengupta

quant-phSubmitted Oct 14, 2026• Announced Oct 16, 2026• 0 citations
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Abstract

Exact zero-energy eigenstates built from entangled dimers have recently been found in a large class of spin Hamiltonians. While the individual states have a simple structure, their superpositions can have very different entanglement properties. In this work, we study these superpositions for geometrically local spin-1/2 chains with periodic boundary conditions. Using stabilizer theory and polynomial methods, we characterize the subspace they span and find the minimum entanglement entropy between two halves of the chain. For Hamiltonians generated by a single local Pauli interaction with noncommuting translates, this minimum obeys a volume law at fixed interaction range. The structure of the least-entangled superpositions also suggests further exact eigenstate constructions, including zero-energy states separable between the two halves of the chain and states at nonzero energies.

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43 pages, 5 figures

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Exact zero-energy eigenstates built from entangled dimers have recently been found in a large class of spin Hamiltonians. While the individual states have a simple structure, their superpositions can have very different entanglement properties. In this work, we study these superpositions for geometrically local spin-1/2 chains with periodic boundary conditions. Using stabilizer theory and polynomial methods, we characterize the subspace they span and find the minimum entanglement entropy between two halves of the chain. For Hamiltonians generated by a single local Pauli interaction with noncommuting translates, this minimum obeys a volume law at fixed interaction range. The structure of the least-entangled superpositions also suggests further exact eigenstate constructions, including zero-energy states separable between the two halves of the chain and states at nonzero energies.
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Entanglement entropy obeys area law scaling for typical physical quantum systems. This may naively be argued to follow from the locality of interactions. We show that this is not the case by constructing an explicit simple spin chain Hamiltonian with nearest-neighbor interactions that presents an entanglement volume scaling law. This non-translational model is contrived to have couplings that force the accumulation of singlet bonds across the half-chain. This configuration of the couplings is suggested by real-space renormalization group arguments. Computation of the entanglement entropy is performed by mapping the system to free fermions and diagonalizing numerically its correlation matrix. An analytical relationship between the entanglement entropy and the Frobenius norm of the correlation matrix is also established. Our result is complementary to the known relationship between non-translational invariant, nearest-neighbor interacting Hamiltonians and quantum Merlin–Arthur (QMA)-complete problems.
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