Volume-Independent Spectral Stability of Energy-Truncated Effective Hamiltonians in Quantum Spin Systems
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914543158951936 |
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| author | Ukai, Ayumi |
| author_facet | Ukai, Ayumi |
| contents | We prove a volume-uniform effective-Hamiltonian theorem for bounded finite-range quantum spin systems on possibly infinite lattices. For any finite target region, we construct an energy-truncated Hamiltonian and prove a volume-uniform spectral-overlap bound controlling the leakage of its low-energy spectral subspace into the high-energy spectral subspace of the original Hamiltonian. The bound may contain non-exponential spectral-window terms, but its cutoff-dependent remainder decays exponentially in the cutoff.
In finite volume, this yields stability of low-lying eigenvalues, with eigenvalue errors controlled by the exponentially small cutoff-dependent remainder. In infinite volume, we prove the corresponding spectral-overlap estimate in the GNS representation of an infinite-volume ground state. Thus, for bounded finite-range interactions, we extend and strengthen the effective-Hamiltonian mechanism of Arad, Kuwahara, and Landau by replacing the finite-volume operator-norm formulation with a volume-uniform spectral-overlap formulation applicable in the thermodynamic limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07410 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Volume-Independent Spectral Stability of Energy-Truncated Effective Hamiltonians in Quantum Spin Systems Ukai, Ayumi Mathematical Physics Statistical Mechanics Spectral Theory 82B10, 81Q10, 47A10 We prove a volume-uniform effective-Hamiltonian theorem for bounded finite-range quantum spin systems on possibly infinite lattices. For any finite target region, we construct an energy-truncated Hamiltonian and prove a volume-uniform spectral-overlap bound controlling the leakage of its low-energy spectral subspace into the high-energy spectral subspace of the original Hamiltonian. The bound may contain non-exponential spectral-window terms, but its cutoff-dependent remainder decays exponentially in the cutoff. In finite volume, this yields stability of low-lying eigenvalues, with eigenvalue errors controlled by the exponentially small cutoff-dependent remainder. In infinite volume, we prove the corresponding spectral-overlap estimate in the GNS representation of an infinite-volume ground state. Thus, for bounded finite-range interactions, we extend and strengthen the effective-Hamiltonian mechanism of Arad, Kuwahara, and Landau by replacing the finite-volume operator-norm formulation with a volume-uniform spectral-overlap formulation applicable in the thermodynamic limit. |
| title | Volume-Independent Spectral Stability of Energy-Truncated Effective Hamiltonians in Quantum Spin Systems |
| topic | Mathematical Physics Statistical Mechanics Spectral Theory 82B10, 81Q10, 47A10 |
| url | https://arxiv.org/abs/2605.07410 |