Quantum

Translation-Invariant Pure States with Exotic Half-Chain Factors

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 20/10/2026, 04:13:24 UTC.

Briefings

A 2026 arXiv preprint constructs translation-invariant pure fermionic states on a 1D lattice with half-chain von Neumann algebras of type II_infty or III_lambda (0<lambda<=1). These states are unique ground states of gapless parent Hamiltonians with superpolynomially decaying interactions. The study reveals that interval entanglement entropy growth rates vary widely, challenging the link between entropy scaling and factor type. A separate result establishes a dichotomy for gauge-invariant quadratic Hamiltonians: ground states either have type I half-chain factors or exhibit logarithmic entropy growth with type III_1 factors.

Key points

• Translation-invariant pure fermionic states on a 1D lattice were constructed with half-chain von Neumann algebras of type II_infty or III_lambda (0<lambda<=1).
• These states are unique ground states of gapless parent Hamiltonians with superpolynomially decaying interactions, demonstrating that such factors need not be of type I or III.

Context

This research addresses the classification of translation-invariant pure states in quantum spin chains, specifically identifying new factor types for half-chain von Neumann algebras that were previously thought to be limited to type I or III.

Limitations

The evidence is an arXiv preprint (arXiv:2610.24154v1) from October 2026, meaning it is unverified and subject to potential revision. The study relies on AI assistance for the counterexample discovery, introducing uncertainty regarding the robustness of that specific finding. The evidence does not provide specific numerical values for entanglement entropy growth rates or exact interaction strengths, only qualitative descriptions like 'superpolynomially decaying'. The source does not include experimental data or further validation.

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