Symmetry-driven correlation patterns in one-dimensional periodic fermionic systems: Closed-form expressions and exact selection rules for correlation functions, entanglement entropies, and mutual information
Year: 2026
Type: article
Abstract: We present an analytical study of the spatial structure of correlations in periodic fermionic systems at the single Slater determinant level, focusing on the cyclic case. Exploiting cyclic symmetry, the transformation from localized orbitals to molecular orbitals is simultaneously a discrete Fourier transform, a Vandermonde matrix on the roots of unity, a complex Hadamard matrix, and the character table of the cyclic group Cm. Within this framework, the spatial structure of correlations is fully determined by the occupied irreducible representations (Fourier modes), independently of the specific Hamiltonian generating them. In particular, the fermionic two-point correlator is expressed as a truncated Fourier sum over the occupied orbitals, leading to exact analytical expressions for symmetric occupation patterns of Fourier modes (ℓ and -ℓ pairs), corresponding in quantum chemistry to aromatic fillings, i.e., fillings satisfying Hückel's 4n + 2 rule. For the half filling case, we derive exact spatial selection rules. In particular, the two-point correlator vanishes identically for all even distances along the ring. This property propagates to reduced density matrices and implies a complete absence of mutual information between the corresponding orbitals. These results reveal that, despite the global delocalization of molecular orbitals, the correlation structure in cyclic systems is highly non-uniform and governed by symmetry-induced interference. Although formulated in terms of cyclic lattice systems, the present results extend straightforwardly to one-dimensional fermionic chains with periodic conditions, reflecting the underlying translational symmetry of the problem. The framework, therefore, provides a Hamiltonian-independent and universal reference for understanding correlation patterns in one-dimensional periodic fermionic systems.
Source: The Journal of Chemical Physics
DOI: 10.1063/5.0350248
Author: Celestino Angeli
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G3781801761, G598502428
OpenAlex ID: W7213602689
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