Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2205.09512 · Physical review. B./Physical review. B

Thermodynamics of the metal-insulator transition in the extended Hubbard model from determinantal quantum Monte Carlo

Alexander Sushchyev, Stefan Weßel

Published Oct 12, 2022• 14 citations
arXivHTMLPDF

Abstract

Using finite-temperature determinantal quantum Monte Carlo simulations, we examine the thermodynamic properties of the extended Hubbard model on the half-filled square lattice in the Slater regime at intermediate coupling. We consider both the case of nearest-neighbor interactions and long-range Coulomb interactions, for coupling strengths in which the presence of nonlocal interactions still allows us to perform sign-problem free quantum Monte Carlo simulations. In particular, we assess a recently proposed scenario from variational calculations in terms of a first-order metal-insulator transition in this interaction regime.

DOI
10.1103/physrevb.106.155121

Related papers

First-order metal-insulator transitions in the extended Hubbard model due to self-consistent screening of the effective interaction

Malte Schüler, Erik G. C. P. van Loon, Mikhail I. Katsnelson +1 more

While the Hubbard model is the standard model to study Mott metal-insulator transitions, it is still unclear to what extent it can describe metal-insulator transitions in real solids, where nonlocal Coulomb interactions are always present. By using a variational principle, we clarify this issue for short- and long-range nonlocal Coulomb interactions for half-filled systems on bipartite lattices. We find that repulsive nonlocal interactions generally stabilize the Fermi-liquid regime. The metal-insulator phase boundary is shifted to larger interaction strengths to leading order linearly with nonlocal interactions. Importantly, nonlocal interactions can raise the order of the metal-insulator transition. We present a detailed analysis of how the dimension and geometry of the lattice as well as the temperature determine the critical nonlocal interaction leading to a first-order transition: for systems in more than two dimensions with nonzero density of states at the Fermi energy the critical nonlocal interaction is arbitrarily small; otherwise, it is finite.

arXiv:1706.09644•Physical review. B./Physical review. B•Apr 23, 2018•24 citations

Ground-state phase diagram of the half-filled bilayer Hubbard model

Michael Golor, Timo Reckling, Laura Classen +2 more

Employing a combination of functional renormalization group calculations and projective determinantal quantum Monte Carlo simulations, we examine the Hubbard model on the square lattice bilayer at half filling. From this combined analysis, we obtain a comprehensive account of the ground-state phase diagram with respect to the extent of the system's metallic and (antiferromagnetically ordered) Mott-insulating as well as band-insulating regions. By means of an unbiased functional renormalization group approach, we exhibit the antiferromagnetic Mott-insulating state as the relevant instability of the free metallic state, induced by any weak finite on-site repulsion. Upon performing a careful analysis of the quantum Monte Carlo data, we resolve the difficulty of identifying this antiferromagnetic ground state for finite interlayer hopping in the weak-coupling regime, where nonmonotonic finite-size corrections are shown to relate to the two-sheeted Fermi surface structure of the metallic phase. On the other hand, quantum Monte Carlo simulations are well suited to identify the transition between the Mott-insulating phase and the band insulator in the intermediate-to-strong coupling regime. Here, we compare our numerical findings to indications for the transition region obtained from the functional renormalization group procedure.

arXiv:1409.1103•Physical Review B•Nov 18, 2014•23 citations

Extended Crossover from a Fermi Liquid to a Quasiantiferromagnet in the Half-Filled 2D Hubbard Model

Fedor Šimkovic, J. P. F. LeBlanc, Aaram J. Kim +4 more

The ground state of the Hubbard model with nearest-neighbor hopping on the square lattice at half filling is known to be that of an antiferromagnetic (AFM) band insulator for any on-site repulsion. At finite temperature, the absence of long-range order makes the question of how the interaction-driven insulator is realized nontrivial. We address this problem with controlled accuracy in the thermodynamic limit using self-energy diagrammatic determinant Monte Carlo and dynamical cluster approximation methods and show that development of long-range AFM correlations drives an extended crossover from Fermi liquid to insulating behavior in the parameter regime that precludes a metal-to-insulator transition. The intermediate crossover state is best described as a non-Fermi liquid with a partially gapped Fermi surface.

arXiv:1812.11503•Physical Review Letters•Jan 10, 2020•94 citations

Charge ordering and correlation effects in the extended Hubbard model

Hanna Terletska, Tianran Chen, Emanuel Gull

We study the half-filled extended Hubbard model on a two-dimensional square lattice using cluster dynamical mean-field theory on clusters of size 8--20. We show that the model exhibits metallic, Mott-insulating, and charge-ordered phases, and determine the location of the charge-ordering phase-transition line and the properties of the phases as a function of temperature, local interaction, and nearest-neighbor interaction. We find strong nonlocal correlations outside the charge-ordered phase and a pronounced screening effect in the vicinity of the phase transition, where nonlocal interactions push the system towards metallic behavior. In contrast, correlations in the charge-ordered phase are mostly local to the unit cell. Finally, we demonstrate how strong nonlocal electron-electron interactions can increase electron mobility by turning a charge-ordered insulator into a metal. We analyze finite-size effects and the convergence of our data to the thermodynamic limit. Control of all sources of errors allows us to assess the regime of applicability of simpler approximation schemes for systems with nonlocal interactions.

arXiv:1611.07861•Physical review. B./Physical review. B•Mar 27, 2017•71 citations

Variational Monte Carlo Study of Two-Dimensional Multi-Orbital Hubbard Model on Square Lattice

Y Takenaka, N. Kawakami

We investigate the Mott transition in a two-dimensional two-orbital Hubbard model on a square lattice at half filling by using the variational Monte Carlo method. As a variational trial wave function, we consider Gutzwiller's on-site correlations and nearest-neighbor doublon-holon correlations. We calculate the ground-state energy and the other physical quantities, all of which clearly signal a first-order Mott transition. We thus obtain the phase diagram at zero temperature, where we find the coexistence region of the metal and the Mott insulator. We discuss how Hund's coupling affects the nature of the Mott transition in this system.

Journal of Physics Conference Series•Dec 17, 2012•5 citations

Doping-dependent metal-insulator transition in a disordered Hubbard model

Lingyu Tian, Yueqi Li, Ying Liang +1 more

We study the effect of disorder and doping on the metal-insulator transition in a repulsive Hubbard model on a square lattice using the determinant quantum Monte Carlo method. First, with the aim of making our results reliable, we compute the sign problem with various parameters such as temperature, disorder, on-site interactions, and lattice size. We show that in the presence of randomness in the hopping elements, the metal-insulator transition occurs and the critical disorder strength differs at different fillings. We also demonstrate that doping is a driving force behind the metal-insulator transition.

arXiv:2106.03296•Physical review. B./Physical review. B•Jan 24, 2022•8 citations
Using finite-temperature determinantal quantum Monte Carlo simulations, we examine the thermodynamic properties of the extended Hubbard model on the half-filled square lattice in the Slater regime at intermediate coupling. We consider both the case of nearest-neighbor interactions and long-range Coulomb interactions, for coupling strengths in which the presence of nonlocal interactions still allows us to perform sign-problem free quantum Monte Carlo simulations. In particular, we assess a recently proposed scenario from variational calculations in terms of a first-order metal-insulator transition in this interaction regime.
While the Hubbard model is the standard model to study Mott metal-insulator transitions, it is still unclear to what extent it can describe metal-insulator transitions in real solids, where nonlocal Coulomb interactions are always present. By using a variational principle, we clarify this issue for short- and long-range nonlocal Coulomb interactions for half-filled systems on bipartite lattices. We find that repulsive nonlocal interactions generally stabilize the Fermi-liquid regime. The metal-insulator phase boundary is shifted to larger interaction strengths to leading order linearly with nonlocal interactions. Importantly, nonlocal interactions can raise the order of the metal-insulator transition. We present a detailed analysis of how the dimension and geometry of the lattice as well as the temperature determine the critical nonlocal interaction leading to a first-order transition: for systems in more than two dimensions with nonzero density of states at the Fermi energy the critical nonlocal interaction is arbitrarily small; otherwise, it is finite.
Employing a combination of functional renormalization group calculations and projective determinantal quantum Monte Carlo simulations, we examine the Hubbard model on the square lattice bilayer at half filling. From this combined analysis, we obtain a comprehensive account of the ground-state phase diagram with respect to the extent of the system's metallic and (antiferromagnetically ordered) Mott-insulating as well as band-insulating regions. By means of an unbiased functional renormalization group approach, we exhibit the antiferromagnetic Mott-insulating state as the relevant instability of the free metallic state, induced by any weak finite on-site repulsion. Upon performing a careful analysis of the quantum Monte Carlo data, we resolve the difficulty of identifying this antiferromagnetic ground state for finite interlayer hopping in the weak-coupling regime, where nonmonotonic finite-size corrections are shown to relate to the two-sheeted Fermi surface structure of the metallic phase. On the other hand, quantum Monte Carlo simulations are well suited to identify the transition between the Mott-insulating phase and the band insulator in the intermediate-to-strong coupling regime. Here, we compare our numerical findings to indications for the transition region obtained from the functional renormalization group procedure.
The ground state of the Hubbard model with nearest-neighbor hopping on the square lattice at half filling is known to be that of an antiferromagnetic (AFM) band insulator for any on-site repulsion. At finite temperature, the absence of long-range order makes the question of how the interaction-driven insulator is realized nontrivial. We address this problem with controlled accuracy in the thermodynamic limit using self-energy diagrammatic determinant Monte Carlo and dynamical cluster approximation methods and show that development of long-range AFM correlations drives an extended crossover from Fermi liquid to insulating behavior in the parameter regime that precludes a metal-to-insulator transition. The intermediate crossover state is best described as a non-Fermi liquid with a partially gapped Fermi surface.
We study the half-filled extended Hubbard model on a two-dimensional square lattice using cluster dynamical mean-field theory on clusters of size 8--20. We show that the model exhibits metallic, Mott-insulating, and charge-ordered phases, and determine the location of the charge-ordering phase-transition line and the properties of the phases as a function of temperature, local interaction, and nearest-neighbor interaction. We find strong nonlocal correlations outside the charge-ordered phase and a pronounced screening effect in the vicinity of the phase transition, where nonlocal interactions push the system towards metallic behavior. In contrast, correlations in the charge-ordered phase are mostly local to the unit cell. Finally, we demonstrate how strong nonlocal electron-electron interactions can increase electron mobility by turning a charge-ordered insulator into a metal. We analyze finite-size effects and the convergence of our data to the thermodynamic limit. Control of all sources of errors allows us to assess the regime of applicability of simpler approximation schemes for systems with nonlocal interactions.
We investigate the Mott transition in a two-dimensional two-orbital Hubbard model on a square lattice at half filling by using the variational Monte Carlo method. As a variational trial wave function, we consider Gutzwiller's on-site correlations and nearest-neighbor doublon-holon correlations. We calculate the ground-state energy and the other physical quantities, all of which clearly signal a first-order Mott transition. We thus obtain the phase diagram at zero temperature, where we find the coexistence region of the metal and the Mott insulator. We discuss how Hund's coupling affects the nature of the Mott transition in this system.
We study the effect of disorder and doping on the metal-insulator transition in a repulsive Hubbard model on a square lattice using the determinant quantum Monte Carlo method. First, with the aim of making our results reliable, we compute the sign problem with various parameters such as temperature, disorder, on-site interactions, and lattice size. We show that in the presence of randomness in the hopping elements, the metal-insulator transition occurs and the critical disorder strength differs at different fillings. We also demonstrate that doping is a driving force behind the metal-insulator transition.