Phase transitions in partial summation methods: Results from the 3D Hubbard model

Abstract

The accurate determination of magnetic phase transitions in electronic systems is an important task of solid state theory. While numerically exact results are readily available for model systems such as the half-filled 3D Hubbard model, the complexity of real materials requires additional approximations, such as the restriction to certain classes of diagrams in perturbation theory, that reduce the precision with which magnetic properties are described. In this work, we examine the description of magnetic properties in second order perturbation theory, GW, FLEX, and two TMatrix approximations to numerically exact CT-QMC reference data. We assess finite-size effects and compare periodic lattice simulations to cluster embedding. We find that embedding substantially improves finite size convergence. However, by analyzing different partial summation methods we find no systematic improvement in the description of magnetic properties, with most methods considered in this work predicting first-order instead of continuous transitions, leading us to the conclusion that non-perturbative methods are necessary for the accurate determination of magnetic properties and phase transitions.

14 pages, 12 figures

References in corpus (20)

• Continuous-time Monte Carlo methods for quantum impurity models
• The Hubbard Model
• Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms
• The Hubbard model: A computational perspective
• Continuous-time auxiliary field Monte Carlo for quantum impurity models
• Pairing symmetry in a two-orbital Hubbard model on a square lattice
• Thermodynamics of the 3D Hubbard model on approach to the Neel transition
• Sub-matrix updates for the Continuous-Time Auxiliary Field algorithm
• Finite temperature quantum embedding theories for correlated systems
• On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime
• Compressibility of a fermionic Mott insulator of ultracold atoms
• Dual Fermion Approach to Susceptibility of Correlated Lattice Fermions
• Spectral properties of the three-dimensional Hubbard model
• On the separability of dynamical and non-local correlations in three dimensions
• Interpretation of multiple solutions in fully iterative GF2 and GW schemes using local analysis of two-particle density matrices
• Evaluation of two-particle properties within finite-temperature self-consistent one-particle Green's function methods: theory and application to GW and GF2
• Superconductivity due to spin fluctuations originating from multiple Fermi surfaces in a double chain superconductor Pr${}_2$Ba${}_4$Cu${}_7$O${}_{15-\delta }$}
• Efficient fluctuation exchange approach to low-temperature spin fluctuations and superconductivity: from the Hubbard model to Na${}_x$CoO${}_2\cdot y$H${}_2$O
• Fictive Impurity Approach to Dynamical Mean Field Theory: a Strong-Coupling Investigation
• Short-Range Correlations and Cooling of Ultracold Fermions in the Honeycomb Lattice

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• Magnetic, thermodynamic, and dynamical properties of the three-dimensional fermionic Hubbard model: A comprehensive Monte Carlo study
• Extended Metal-Insulator Crossover with Strong Antiferromagnetic Spin Correlation in Half-Filled 3D Hubbard Model
• Excitations and spectra from equilibrium real-time Green's functions
• Magnetic phase diagram of the three-dimensional doped Hubbard model
• Electronic correlations and long-range magnetic ordering in NiO tuned by pressure
• Ising phase transitions and thermodynamics of correlated fermions in a two-dimensional spin-dependent lattice potential
• Thermodynamics of the Hubbard Model on the Bethe Lattice
• Heating and cooling in self-consistent many-body simulations
• Single- and two-particle finite size effects in interacting lattice systems
• Evaluating second-order phase transitions with Diagrammatic Monte Carlo: Néel Transition in the doped three-dimensional Hubbard model
• Variational Diagrammatic Monte-Carlo Built on Dynamical Mean-Field Theory
• Nonpertubative Many-Body Theory for the Two-Dimensional Hubbard Model at Low Temperature: From Weak to Strong Coupling Regimes