Abstract
The Hubbard model represents the fundamental model for interacting quantum systems and electronic correlations. Using the two-dimensional half-filled Hubbard model at weak coupling as a testing ground, we perform a comparative study of a comprehensive set of state-of-the-art quantum many-body methods. Upon cooling into its insulating antiferromagnetic ground state, the model hosts a rich sequence of distinct physical regimes with crossovers between a high-temperature incoherent regime, an intermediate-temperature metallic regime, and a low-temperature insulating regime with a pseudogap created by antiferromagnetic fluctuations. We assess the ability of each method to properly address these physical regimes and crossovers through the computation of several observables probing both quasiparticle properties and magnetic correlations, with two numerically exact methods (diagrammatic and determinantal quantum Monte Carlo methods) serving as a benchmark. By combining computational results and analytical insights, we elucidate the nature and role of spin fluctuations in each of these regimes. Based on this analysis, we explain how quasiparticles can coexist with increasingly long-range antiferromagnetic correlations and why dynamical mean-field theory is found to provide a remarkably accurate approximation of local quantities in the metallic regime. We also critically discuss whether imaginary-time methods are able to capture the non-Fermi-liquid singularities of this fully nested system.
- Received 18 June 2020
- Revised 2 November 2020
- Accepted 21 December 2020
DOI:https://doi.org/10.1103/PhysRevX.11.011058
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Interactions between a large number of identical quantum particles, such as electrons in a solid, lead to fascinating collective phenomena. Depending on external parameters, a piece of matter may exhibit magnetism, transition from a metal to an insulator, or even become a superconductor. The paradigmatic model of this field is the Hubbard model which, despite its simplicity, presents a formidable challenge to computational and theoretical methods alike. Here, we present an extensive assessment of the wealth of computational methods that have been developed in recent years to determine the physical properties of the Hubbard model in two spatial dimensions.
The Hubbard model describes electrons hopping from one site of a crystal to another, with the electron-electron interaction present only when two electrons occupy the same site. Borrowing terminology from astrophysics, our “multimethod, multimessenger” assessment of the many methods used to tackle this model elucidates the nature and role of magnetic fluctuations and explains their implications for the theory of metallic materials with strong magnetic correlations.
This work paves the way for the improvement of existing algorithms and the development of new ones for quantum systems with strong interactions.
