aiqbench analysis
This paper provides a rigorous proof that unique gapped ground states in one-dimensional spin chains are short-range entangled, confirming the intuition that such systems lack bulk topological order. By demonstrating that these states can be transformed into product states via local Hamiltonian evolution, the work clarifies fundamental limits on entanglement structure in low-dimensional quantum many-body systems.
Pure gapped ground states of spin chains are short-range entangled
arXiv:2511.14699v3 Announce Type: replace-cross Abstract: We consider spin chains with a finite range Hamiltonian. For reasons of simplicity, the chain is taken to be infinitely long. A ground state is said to be a unique gapped ground state if its GNS Hamiltonian has a unique ground state, separated by a gap from the rest of the spectrum. By combining some powerful techniques developed in the last years, we prove that each unique gapped ground state is short-range entangled: It can be mapped into a product state by a finite time evolution map generated by a Hamiltonian with exponentially quasi-local interaction terms. This claim makes precise the common belief that one-dimensional gapped systems are topologically trivial in the bulk.
Abstract:We consider spin chains with a finite range Hamiltonian. For reasons of simplicity, the chain is taken to be infinitely long. A ground state is said to be a unique gapped ground state if its GNS Hamiltonian has a unique ground state, separated by a gap from the rest of the spectrum. By combining some powerful techniques developed in the last years, we prove that each unique gapped ground state is short-range entangled: It can be mapped into a product state by a finite time evolution map generated by a Hamiltonian with exponentially quasi-local interaction terms. This claim makes precise the common belief that one-dimensional gapped systems are topologically trivial in the bulk.
23 pages. Appendix B now contains a proof of Theorem 5.4. Section 6 was reformulated
arXiv:2511.14699 [math-ph]
(or arXiv:2511.14699v3 [math-ph] for this version)
From: Bruno De O. Carvalho [view email] [v1] Tue, 18 Nov 2025 17:38:52 UTC (70 KB) [v2] Tue, 7 Jul 2026 08:22:36 UTC (78 KB) [v3] Tue, 29 Sep 2026 18:44:01 UTC (90 KB)
Full text under the publisher's open licence · 170 words
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