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:1404.1885 · Physical Review B

Signatures of coherent electronic quasiparticles in the paramagnetic Mott insulator

Mats Granath, Johan Schött

Published Dec 17, 2014• 17 citations
arXivHTMLPDF

Abstract

We study the Mott insulating state of the half-filled paramagnetic Hubbard model within dynamical mean field theory using a recently formulated stochastic and nonperturbative quantum impurity solver. The method is based on calculating the impurity self energy as a sample average over a representative distribution of impurity models solved by exact diagonalization. Due to the natural parallelization of the method, millions of poles are readily generated for the self energy which allows us to work with very small pole-broadening $\ensuremath{\eta}$. Solutions at small and large $\ensuremath{\eta}$ are qualitatively different; solutions at large $\ensuremath{\eta}$ show featureless Hubbard bands whereas solutions at small $\ensuremath{\eta}\ensuremath{\le}0.001$ (in units of half bare band width) show a band of electronic quasiparticles with very small quasiparticle weight at the inner edge of the Hubbard bands. The validity of the results are supported by agreement within statistical error ${\ensuremath{\sigma}}_{\text{QMC}}\ensuremath{\sim}{10}^{\ensuremath{-}4}$ on the imaginary frequency axis with calculations using a continuous time quantum Monte Carlo solver. Nevertheless, convergence with respect to finite size of the stochastic exact diagonalization solver remains to be rigourously established.

DOI
10.1103/physrevb.90.235129

Related papers

Benchmarkings for a semiclassical impurity solver for dynamical-mean-field theory: Self-energies and magnetic transitions of the single-orbital Hubbard model

Satoshi Okamoto, Andreas Fuhrmann, Armin Comanac +1 more

An investigation is presented of the utility of semiclassical approximations for solving the quantum-impurity problems arising in the dynamical-mean-field approach to correlated-electron models. The method is based on performing an exact numerical integral over the zero-Matsubara-frequency component of the spin part of a continuous Hubbard-Stratonovich field, along with a spin-field-dependent steepest descent treatment of the charge part. We test this method by applying it to one- or two-site approximations to the single-band Hubbard model with different band structures, and comparing the results to quantum Monte Carlo and simplified exact diagonalization calculations. The resulting electron self-energies, densities of states, and magnetic transition temperatures show reasonable agreement with the quantum Monte Carlo simulation over wide parameter ranges, suggesting that the semiclassical method is useful for obtaining a reasonable picture of the physics in situations where other techniques are too expensive.

arXiv:cond-mat/0502067•Physical Review B•Jun 24, 2005•17 citations

Dynamical density-matrix renormalization group for the Mott–Hubbard insulator in high dimensions

Satoshi Nishimoto, Florian Gebhard, Eric Jeckelmann

We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number in the paramagnetic insulating phase at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity Anderson model with a bath whose properties have to be determined self-consistently. For a controlled and systematic implementation of the self-consistency scheme we use the fixed-energy (FE) approach to the DMFT. In FE-DMFT the onset and the width of the Hubbard bands are adjusted self-consistently but the energies of the bath levels are kept fixed relatively to both band edges during the calculation of self-consistent hybridization strengths between impurity and bath sites. Using the dynamical density-matrix renormalization group method (DDMRG) we calculate the density of states with a resolution ranging from 3% of the bare bandwidth $W=4t$ at high energies to 0.5% in the vicinity of the gap. The DDMRG resolution and accuracy for the density of states and the gap is superior to those obtained with other numerical methods in previous DMFT investigations. We find that the Mott gap closes at a critical coupling $U_{\rm c}/t=4.45 \pm 0.05$. At $U=4.5t$, we observe prominent shoulders near the onset of the Hubbard bands. They are the remainders of the quasi-particle resonance in the metallic phase which appears to split when the gap opens at $U_{\rm c}$.

arXiv:cond-mat/0406666•Journal of Physics Condensed Matter•Sep 21, 2004•61 citations

Dynamical mean-field theory of the Anderson-Hubbard model with local and nonlocal disorder in tensor formulation

Andreas Weh, Yi Zhang, A. Östlin +7 more

To explore correlated electrons in the presence of local and nonlocal disorder, the Blackman-Esterling-Berk method for averaging over off-diagonal disorder is implemented into dynamical mean-field theory using tensor notation. The impurity model combining disorder and correlations is solved using the recently developed fork tensor-product state solver, which allows one to calculate the single particle spectral functions on the real-frequency axis. In the absence of off-diagonal hopping, we establish exact bounds of the spectral function of the noninteracting Bethe lattice with coordination number $Z$. In the presence of interaction, the Mott insulating paramagnetic phase of the one-band Hubbard model is computed at zero temperature in alloys with site- and off-diagonal disorder. When the Hubbard $U$ parameter is increased, transitions from an alloy band insulator through a correlated metal into a Mott insulating phase are found to take place.

arXiv:2105.06971•Physical review. B./Physical review. B•Jul 16, 2021•12 citations

Orbital-selective Mott transitions in a doped two-band Hubbard model

Eberhard Jakobi, Nils Blümer, P. G. J. van Dongen

We extend previous studies on orbital-selective Mott transitions in the paramagnetic state of the half-filled degenerate two-band Hubbard model to the general doped case, using a high-precision quantum Monte Carlo dynamical mean-field theory solver. For sufficiently strong interactions, orbital-selective Mott transitions as a function of total band filling are clearly visible in the band-specific fillings, quasiparticle weights, double occupancies, and spectra. The results are contrasted with those of single-band models for similar correlation strengths.

arXiv:0906.2966•Physical Review B•Sep 9, 2009•28 citations

Distributional exact diagonalization formalism for quantum impurity models

Mats Granath, Hugo U. R. Strand

We develop a method for calculating the self-energy of a quantum impurity coupled to a continuous bath by stochastically generating a distribution of finite Anderson models that are solved by exact diagonalization, using the noninteracting local spectral function as a probability distribution for the sampling. The method enables calculation of the full analytic self-energy and single-particle Green's function in the complex frequency plane, without analytic continuation, and can be used for both finite and zero temperature at arbitrary fillings. Results are in good agreement with imaginary frequency data from continuous-time quantum Monte Carlo calculations for the single-impurity Anderson model and the two-orbital Hubbard model within dynamical mean-field theory (DMFT) as well as real frequency data for self-energy of the single-band Hubbard model within DMFT using the numerical renormalization group. The method should be applicable to a wide range of quantum impurity models and particularly useful when high-precision real frequency results are sought.

arXiv:1201.6160•Physical Review B•Sep 10, 2012•36 citations

Quasi-continuous-time impurity solver for the dynamical mean-field theory with linear scaling in the inverse temperature

D. Rost, Fakher F. Assaad, Nils Blümer

We present an algorithm for solving the self-consistency equations of the dynamical mean-field theory (DMFT) with high precision and efficiency at low temperatures. In each DMFT iteration, the impurity problem is mapped to an auxiliary Hamiltonian, for which the Green function is computed by combining determinantal quantum Monte Carlo (BSS-QMC) calculations with a multigrid extrapolation procedure. The method is numerically exact, i.e., yields results which are free of significant Trotter errors, but retains the BSS advantage, compared to direct QMC impurity solvers, of linear (instead of cubic) scaling with the inverse temperature. The new algorithm is applied to the half-filled Hubbard model close to the Mott transition; detailed comparisons with exact diagonalization, Hirsch-Fye QMC, and continuous-time QMC are provided.

arXiv:1303.2004•Physical Review E•May 29, 2013•16 citations
We study the Mott insulating state of the half-filled paramagnetic Hubbard model within dynamical mean field theory using a recently formulated stochastic and nonperturbative quantum impurity solver. The method is based on calculating the impurity self energy as a sample average over a representative distribution of impurity models solved by exact diagonalization. Due to the natural parallelization of the method, millions of poles are readily generated for the self energy which allows us to work with very small pole-broadening \ensuremathη\ensuremath{\eta}\ensuremathη. Solutions at small and large \ensuremathη\ensuremath{\eta}\ensuremathη are qualitatively different; solutions at large \ensuremathη\ensuremath{\eta}\ensuremathη show featureless Hubbard bands whereas solutions at small \ensuremathη\ensuremath≤0.001\ensuremath{\eta}\ensuremath{\le}0.001\ensuremathη\ensuremath≤0.001 (in units of half bare band width) show a band of electronic quasiparticles with very small quasiparticle weight at the inner edge of the Hubbard bands. The validity of the results are supported by agreement within statistical error \ensuremathσQMC\ensuremath∼10\ensuremath−4{\ensuremath{\sigma}}_{\text{QMC}}\ensuremath{\sim}{10}^{\ensuremath{-}4}\ensuremathσQMC​\ensuremath∼10\ensuremath−4 on the imaginary frequency axis with calculations using a continuous time quantum Monte Carlo solver. Nevertheless, convergence with respect to finite size of the stochastic exact diagonalization solver remains to be rigourously established.
An investigation is presented of the utility of semiclassical approximations for solving the quantum-impurity problems arising in the dynamical-mean-field approach to correlated-electron models. The method is based on performing an exact numerical integral over the zero-Matsubara-frequency component of the spin part of a continuous Hubbard-Stratonovich field, along with a spin-field-dependent steepest descent treatment of the charge part. We test this method by applying it to one- or two-site approximations to the single-band Hubbard model with different band structures, and comparing the results to quantum Monte Carlo and simplified exact diagonalization calculations. The resulting electron self-energies, densities of states, and magnetic transition temperatures show reasonable agreement with the quantum Monte Carlo simulation over wide parameter ranges, suggesting that the semiclassical method is useful for obtaining a reasonable picture of the physics in situations where other techniques are too expensive.
We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number in the paramagnetic insulating phase at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity Anderson model with a bath whose properties have to be determined self-consistently. For a controlled and systematic implementation of the self-consistency scheme we use the fixed-energy (FE) approach to the DMFT. In FE-DMFT the onset and the width of the Hubbard bands are adjusted self-consistently but the energies of the bath levels are kept fixed relatively to both band edges during the calculation of self-consistent hybridization strengths between impurity and bath sites. Using the dynamical density-matrix renormalization group method (DDMRG) we calculate the density of states with a resolution ranging from 3% of the bare bandwidth W=4tW=4tW=4t at high energies to 0.5% in the vicinity of the gap. The DDMRG resolution and accuracy for the density of states and the gap is superior to those obtained with other numerical methods in previous DMFT investigations. We find that the Mott gap closes at a critical coupling Uc/t=4.45±0.05U_{\rm c}/t=4.45 \pm 0.05Uc​/t=4.45±0.05. At U=4.5tU=4.5tU=4.5t, we observe prominent shoulders near the onset of the Hubbard bands. They are the remainders of the quasi-particle resonance in the metallic phase which appears to split when the gap opens at UcU_{\rm c}Uc​.
To explore correlated electrons in the presence of local and nonlocal disorder, the Blackman-Esterling-Berk method for averaging over off-diagonal disorder is implemented into dynamical mean-field theory using tensor notation. The impurity model combining disorder and correlations is solved using the recently developed fork tensor-product state solver, which allows one to calculate the single particle spectral functions on the real-frequency axis. In the absence of off-diagonal hopping, we establish exact bounds of the spectral function of the noninteracting Bethe lattice with coordination number ZZZ. In the presence of interaction, the Mott insulating paramagnetic phase of the one-band Hubbard model is computed at zero temperature in alloys with site- and off-diagonal disorder. When the Hubbard UUU parameter is increased, transitions from an alloy band insulator through a correlated metal into a Mott insulating phase are found to take place.
We extend previous studies on orbital-selective Mott transitions in the paramagnetic state of the half-filled degenerate two-band Hubbard model to the general doped case, using a high-precision quantum Monte Carlo dynamical mean-field theory solver. For sufficiently strong interactions, orbital-selective Mott transitions as a function of total band filling are clearly visible in the band-specific fillings, quasiparticle weights, double occupancies, and spectra. The results are contrasted with those of single-band models for similar correlation strengths.
We develop a method for calculating the self-energy of a quantum impurity coupled to a continuous bath by stochastically generating a distribution of finite Anderson models that are solved by exact diagonalization, using the noninteracting local spectral function as a probability distribution for the sampling. The method enables calculation of the full analytic self-energy and single-particle Green's function in the complex frequency plane, without analytic continuation, and can be used for both finite and zero temperature at arbitrary fillings. Results are in good agreement with imaginary frequency data from continuous-time quantum Monte Carlo calculations for the single-impurity Anderson model and the two-orbital Hubbard model within dynamical mean-field theory (DMFT) as well as real frequency data for self-energy of the single-band Hubbard model within DMFT using the numerical renormalization group. The method should be applicable to a wide range of quantum impurity models and particularly useful when high-precision real frequency results are sought.
We present an algorithm for solving the self-consistency equations of the dynamical mean-field theory (DMFT) with high precision and efficiency at low temperatures. In each DMFT iteration, the impurity problem is mapped to an auxiliary Hamiltonian, for which the Green function is computed by combining determinantal quantum Monte Carlo (BSS-QMC) calculations with a multigrid extrapolation procedure. The method is numerically exact, i.e., yields results which are free of significant Trotter errors, but retains the BSS advantage, compared to direct QMC impurity solvers, of linear (instead of cubic) scaling with the inverse temperature. The new algorithm is applied to the half-filled Hubbard model close to the Mott transition; detailed comparisons with exact diagonalization, Hirsch-Fye QMC, and continuous-time QMC are provided.