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:1504.05090 · Journal of Physics Conference Series

Deciding the fate of the false Mott transition in two dimensions by exact quantum Monte Carlo methods

D. Rost, Nils Blümer

Published Sep 28, 2015• 1 citation
arXivHTMLPDF

Abstract

We present an algorithm for the computation of unbiased Green functions and selfenergies for quantum lattice models, free from systematic errors and valid in the thermodynamic limit. The method combines direct lattice simulations using the Blankenbecler-Scalapino-Sugar quantum Monte Carlo (BSS-QMC) approach with controlled multigrid extrapolation techniques. We show that the half-filled Hubbard model is insulating at low temperatures even in the weak- coupling regime; the previously claimed Mott transition at intermediate coupling does not exist.

DOI
10.1088/1742-6596/640/1/012047

Related papers

Exact diagonalization approach to correlated fermions in infinite dimensions: Mott transition and superconductivity

Michel Caffarel, Werner Krauth

We present a powerful method for calculating the thermodynamic properties of infinite-dimensional Hubbard-type models using an exact diagonalization of an Anderson model with a finite number of sites. The resolution obtained for Green's functions is far superior to that of quantum Monte Carlo calculations. We apply the method to the half-filled Hubbard model for a discussion of the metal-insulator transition, and to the two-band Hubbard model where we find direct evidence for the existence of a superconducting instability at low temperatures.

Physical Review Letters•Mar 7, 1994•634 citations

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

Alexander Sushchyev, Stefan Weßel

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.

arXiv:2205.09512•Physical review. B./Physical review. B•Oct 12, 2022•14 citations

Momentum-dependent pseudogaps in the half-filled two-dimensional Hubbard model

D. Rost, Elena V. Gorelik, Fakher F. Assaad +1 more

We compute unbiased spectral functions of the two-dimensional Hubbard model by extrapolating Green functions, obtained from determinantal quantum Monte Carlo simulations, to the thermodynamic and continuous time limits. Our results clearly resolve the pseudogap at weak to intermediate coupling, originating from a momentum selective opening of the charge gap. A characteristic pseudogap temperature ${T}^{*}$, determined consistently from the spectra and from the momentum dependence of the imaginary-time Green functions, is found to match the dynamical mean-field critical temperature, below which antiferromagnetic fluctuations become dominant. Our results identify a regime where pseudogap physics is within reach of experiments with cold fermions on optical lattices.

arXiv:1205.6788•Physical Review B•Oct 4, 2012•54 citations

Fate of the false Mott-Hubbard transition in two dimensions

Thomas Schäfer, F. Geles, D. Rost +6 more

We have studied the impact of nonlocal electronic correlations at all length scales on the Mott-Hubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining dynamical vertex approximation, lattice quantum Monte Carlo, and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling, irrespective of the preformation of localized or short-range magnetic moments. This is the reason why the two-dimensional Hubbard model has a paramagnetic phase which is insulating at low enough temperatures for any (finite) interaction and no Mott-Hubbard transition is observed.

arXiv:1405.7250•Physical Review B•Mar 3, 2015•178 citations

Quantum Monte Carlo Simulation of the two-dimensional ionic Hubbard model

B. Martinie

The Quantum Monte Carlo simulations of the ionic Hubbard model on a two-dimensional square lattice at half filling were performed. The method based on the direct-space, proposed by Suzuki and al., Hirsch and al., was used. Cycles of increasing and decreasing values of the Coulomb interaction $ U $ were performed for fixed temperature ($ kT=0.01 $). Results indicate that, at low temperature, the two insulator phases are separated by a metallic phase for weak to intermediate values of the staggered potential $ Δ$. For large Coulomb repulsion the system is in a Mott insulator with an antiferromagnetism order. On increasing and decreasing the Coulomb interaction $ U $ the metal-Mott insulator transition shows an hysteresis phenomenon while the metal-band insulator transition is continue. For large $ Δ$ it seems that the metallic region shrinks to a single metallic point. However, the band insulator to the Mott insulator transition is not direct for the studied model. A phase diagram is drawn for the temperature $ kT=0.01 $. For $ Δ=0.5 $ cycles of increasing and decreasing temperature were programmed for different values of the Coulomb interaction $ U $ . A behaviour change appears for $ U\simeq 1.75 $. This suggests that a crossover line divides the metallic region of the phase diagram.

arXiv:1002.0325•Feb 1, 2010•0 citations

The Mott metal-insulator transition in half-filled two-dimensional Hubbard models

P Sahebsara

We study the Mott transition in the two dimensional Hubbard model by using the variational cluster approximation. The transition potential obtained is roughly Uc ≈ 2 and 6 for square and triangular lattices, respectively. A comparison between results of this approximation and other quantum cluster methods is presented. Our zero-temperature calculation at strong coupling show that the transition on the triangular and square lattices occur at lower values of compared with other numerical techniques such as DMFT, CDMFT, and DCA. We also study the thermodynamic limit by an extrapolation to infinite size.

•Jun 1, 2008•2 citations
We present an algorithm for the computation of unbiased Green functions and selfenergies for quantum lattice models, free from systematic errors and valid in the thermodynamic limit. The method combines direct lattice simulations using the Blankenbecler-Scalapino-Sugar quantum Monte Carlo (BSS-QMC) approach with controlled multigrid extrapolation techniques. We show that the half-filled Hubbard model is insulating at low temperatures even in the weak- coupling regime; the previously claimed Mott transition at intermediate coupling does not exist.
We present a powerful method for calculating the thermodynamic properties of infinite-dimensional Hubbard-type models using an exact diagonalization of an Anderson model with a finite number of sites. The resolution obtained for Green's functions is far superior to that of quantum Monte Carlo calculations. We apply the method to the half-filled Hubbard model for a discussion of the metal-insulator transition, and to the two-band Hubbard model where we find direct evidence for the existence of a superconducting instability at low temperatures.
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.
We compute unbiased spectral functions of the two-dimensional Hubbard model by extrapolating Green functions, obtained from determinantal quantum Monte Carlo simulations, to the thermodynamic and continuous time limits. Our results clearly resolve the pseudogap at weak to intermediate coupling, originating from a momentum selective opening of the charge gap. A characteristic pseudogap temperature T∗{T}^{*}T∗, determined consistently from the spectra and from the momentum dependence of the imaginary-time Green functions, is found to match the dynamical mean-field critical temperature, below which antiferromagnetic fluctuations become dominant. Our results identify a regime where pseudogap physics is within reach of experiments with cold fermions on optical lattices.
We have studied the impact of nonlocal electronic correlations at all length scales on the Mott-Hubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining dynamical vertex approximation, lattice quantum Monte Carlo, and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling, irrespective of the preformation of localized or short-range magnetic moments. This is the reason why the two-dimensional Hubbard model has a paramagnetic phase which is insulating at low enough temperatures for any (finite) interaction and no Mott-Hubbard transition is observed.
The Quantum Monte Carlo simulations of the ionic Hubbard model on a two-dimensional square lattice at half filling were performed. The method based on the direct-space, proposed by Suzuki and al., Hirsch and al., was used. Cycles of increasing and decreasing values of the Coulomb interaction $ U $ were performed for fixed temperature ($ kT=0.01 $). Results indicate that, at low temperature, the two insulator phases are separated by a metallic phase for weak to intermediate values of the staggered potential $ Δ$. For large Coulomb repulsion the system is in a Mott insulator with an antiferromagnetism order. On increasing and decreasing the Coulomb interaction $ U $ the metal-Mott insulator transition shows an hysteresis phenomenon while the metal-band insulator transition is continue. For large $ Δ$ it seems that the metallic region shrinks to a single metallic point. However, the band insulator to the Mott insulator transition is not direct for the studied model. A phase diagram is drawn for the temperature $ kT=0.01 $. For $ Δ=0.5 $ cycles of increasing and decreasing temperature were programmed for different values of the Coulomb interaction $ U $ . A behaviour change appears for $ U\simeq 1.75 $. This suggests that a crossover line divides the metallic region of the phase diagram.
We study the Mott transition in the two dimensional Hubbard model by using the variational cluster approximation. The transition potential obtained is roughly Uc ≈ 2 and 6 for square and triangular lattices, respectively. A comparison between results of this approximation and other quantum cluster methods is presented. Our zero-temperature calculation at strong coupling show that the transition on the triangular and square lattices occur at lower values of compared with other numerical techniques such as DMFT, CDMFT, and DCA. We also study the thermodynamic limit by an extrapolation to infinite size.