Quantized Collective Fluctuations in Correlated Fermion Systems

TL;DR

This paper introduces Quantum FLF, an extension of the FLF method, to quantify quantum collective fluctuations in correlated fermion systems, demonstrated on a Hubbard chain.

Contribution

The paper develops Quantum FLF, incorporating bosonic Matsubara modes for better quantum collective fluctuation description in fermionic systems.

Findings

Low Matsubara frequencies significantly impact total energy and susceptibility.

Higher-frequency modes are necessary for accurate single-particle property descriptions.

Quantum FLF efficiently characterizes contributions of individual bosonic modes.

Abstract

Collective excitations in fermionic systems play a crucial role in determining their physical properties. An important challenge is to develop efficient theoretical approaches for describing these excitations and their coupling to fermionic degrees of freedom. In this work, we revisit the problem of quantifying the contributions of individual bosonic modes of collective fluctuations to observable properties of correlated fermion systems within the framework of the Fluctuating Local Field (FLF) method. Whereas the auxiliary field in this method was previously considered only classically, we formulate its systematic extension termed Quantum FLF (Q-FLF) that incorporates selected bosonic Matsubara modes, thus tailoring it to description of quantum collective fluctuations. As a testbed, we apply the approach to a half-filled one-dimensional Hubbard chain and compute the Green's function, the total energy, and the antiferromagnetic susceptibility. Our results demonstrate that the proposed scheme enables an efficient and selective characterization of the contributions of individual bosonic modes. In particular, low Matsubara frequencies are found to have a quantitative impact on integrated observables such as total energy and antiferromagnetic susceptibility. At the same time, an accurate description of single-particle properties requires inclusion of higher-frequency bosonic modes.