Microscopically informed self-consistent multi-resolvent closure for dense many-body spectra
Abstract
The exact multi-resolvent hierarchy of dense many-body spectra encodes higher-order spectral-weight correlations, but closing it predictively for interacting Hamiltonians remains a challenge. We introduce the multi-resolvent self-consistency (MRSC) equations, which separate an exact algebraic hierarchy from an approximate finite-parameter closure. The exact Feshbach geometric identity organizes r-resolvent cumulants into a ladder over irreducible vertices Gamma^(r), and the projected hierarchy expresses those vertices as functionals of the cumulants. The closure works in finite parameters: a connectivity basis organizes a general Hamiltonian's seed into class amplitudes, and a causal r-fold Stieltjes representation with a moment-field identity reduce moment matching to a finite-dimensional problem closed at a predictive fixed point. On the free-fermion benchmark the tested exact identities are reproduced and the Faddeeva closure is recovered at r=1. In a blind test on the interacting Ising chain, with the exact two-resolvent data withheld, the Hamiltonian-derived closure predicts the tested probes to 0.35%-0.97%. At the observable level the exact two-resolvent sector supplies a sign-correct, energy-resolved correction to the single-resolvent baseline for the off-diagonal eigenstate-thermalization-hypothesis (ETH) variance, of order one relative to it. Closure errors organize hierarchically: a level-by-level deficit decomposition, anchor measurements of the isolatable terms, and an explicit propagation bound. The same moments further yield a diagnostic chain for the window conditions of local rotational invariance -- an exact drift-kernel identity, a proven single-state identifiability boundary, and a transferability census over couplings and realizations -- a finite-order framework, not a proof of universal emergence.
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BibTeX
@misc{huang2026microscopically,
title = {{Microscopically informed self-consistent multi-resolvent closure for dense many-body spectra}},
author = {Zhiqiang Huang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28031},
eprint = {2610.28031},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28031},
}
RIS
TY - UNPB
TI - Microscopically informed self-consistent multi-resolvent closure for dense many-body spectra
AU - Zhiqiang Huang
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28031
UR - https://arxiv.org/abs/2610.28031
AB - The exact multi-resolvent hierarchy of dense many-body spectra encodes higher-order spectral-weight correlations, but closing it predictively for interacting Hamiltonians remains a challenge. We introduce the multi-resolvent self-consistency (MRSC) equations, which separate an exact algebraic hierarchy from an approximate finite-parameter closure. The exact Feshbach geometric identity organizes r-resolvent cumulants into a ladder over irreducible vertices Gamma^(r), and the projected hierarchy expresses those vertices as functionals of the cumulants. The closure works in finite parameters: a connectivity basis organizes a general Hamiltonian's seed into class amplitudes, and a causal r-fold Stieltjes representation with a moment-field identity reduce moment matching to a finite-dimensional problem closed at a predictive fixed point. On the free-fermion benchmark the tested exact identities are reproduced and the Faddeeva closure is recovered at r=1. In a blind test on the interacting Ising chain, with the exact two-resolvent data withheld, the Hamiltonian-derived closure predicts the tested probes to 0.35%-0.97%. At the observable level the exact two-resolvent sector supplies a sign-correct, energy-resolved correction to the single-resolvent baseline for the off-diagonal eigenstate-thermalization-hypothesis (ETH) variance, of order one relative to it. Closure errors organize hierarchically: a level-by-level deficit decomposition, anchor measurements of the isolatable terms, and an explicit propagation bound. The same moments further yield a diagnostic chain for the window conditions of local rotational invariance -- an exact drift-kernel identity, a proven single-state identifiability boundary, and a transferability census over couplings and realizations -- a finite-order framework, not a proof of universal emergence.
ER -