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

Physical review. B, Condensed matter

Coupling of quantum degrees of freedom in strongly interacting disordered electron systems

V. Janiš, D. Vollhardt

Published Dec 15, 1992• 83 citations
Publisher

Abstract

We derive the exact expression for the averaged free energy of a general class of Hubbard-type models with local, quenched disorder in the limit of high dimensions. A clear mean-field interpretation of its structure is given. Analytic results are obtained for a simplified Hubbard model with disorder. The two-particle correlation functions are shown to display a novel coupling of quantum degrees of freedom whenever genuine electron-electron correlation effects are present.

DOI
10.1103/physrevb.46.15712

Related papers

Disorder vs. Interaction in the Hubbard Model: Phase Diagram in Infinite Dimensions

V. Janiš, M. Ulmke, D. Vollhardt

The influence of local disorder on the thermodynamics of interacting electrons is studied within the infinite-dimensional disordered Hubbard model.Using a finite-temperature quantum Monte Carlo method, the averaged local moment and staggered susceptibility are calculated and the magnetic phase diagram at half-filling is constructed.From the averaged compressibility in the paramagnetic and antiferromagnetic phase we determine the metalinsulator transitions of the system.A rich transition scenario is revealed.Quite unexpectedly the disorder is found to stabilize the magnetic order in the strong-coupling limit.Randomness can significantly influence the low-temperature behaviour of interacting systems.In particular, it may lead to new phases which have no analogue in non-random systems [l].In the case of electrons, the simplest lattice model including both interactions and random potentials is the disordered Hubbard model.It is now known that even in the .mean-field.limit d + CQ [2,3] the Hubbard interaction remains dynamical [4] and leads to a highly non-trivial single-site problem with infinitely many coupled quantum degrees of freedom [5].This problem is, in fact, equivalent to an Anderson impurity model complemented by a self-consistency condition [6] and is thus amenable to numerical investigations [7] within a finite-temperature quantum Monte Carlo approach [81.In the absence of disorder this technique was already used by several groups to investigate the magnetic phase diagram [7,9], the Mott-Hubbard transition [lo, 1 1 1 and lately also superconductivity in a two-band version [12] of the Hubbard model in d = C Q ; thereby important new insight was gained.In this letter we wish to concentrate on the combined effect of disorder and interaction.We will study the effect of diagonal disorder on the low-temperature properties of the Hubbard model in d = CQ , in particular the competition between correlation-induced

Europhysics Letters (EPL)•Nov 1, 1993•25 citations

Electron Correlations in the High-Dimension Hubbard Model

H. Hasegawa

The effect of electron correlations in the infinite-dimension (d=∞) Hubbard model at finite temperatures has been investigated with the use of a theory which was recently proposed by the present author generalizing the slave-boson functional-integral method. Sublattice magnetizations, double occupancies and band-narrowing factors are computed as functions of the interaction, U, and the temperature, T. Calculated results are exact in the limits of U→0 and U→∞, and in the limits of T=0 and T→∞ they are expected to be very accurate owing to the nature of our mean-field-type theory for infinite-dimension systems. Similarities and differences between the calculated results for d=3 and d=∞ are also discussed.

Progress of Theoretical Physics Supplement•May 16, 2013•0 citations

Dynamical mean field study of the two-dimensional disordered Hubbard model

Yun Song, Rachel Wortis, W. A. Atkinson

We study the paramagnetic Anderson-Hubbard model using an extension of dynamical mean field theory (DMFT), known as statistical DMFT, that allows us to treat disorder and strong electronic correlations on equal footing. An approximate nonlocal Green's function is found for individual disorder realizations and then configuration averaged. We apply this method to two-dimensional lattices with up to 1000 sites in the strong disorder limit, where an atomic-limit approximation is made for the self-energy. We investigate the scaling of the inverse participation ratio at quarter- and half-filling, and find a nonmonotonic dependence of the localization length on the interaction strength. For strong disorder, we do not find evidence for an insulator-metal transition, and the disorder potential becomes unscreened near the Mott transition. Furthermore, strong correlations suppress the Altshuler-Aronov density of states anomaly near half-filling.

arXiv:0707.0791•Physical Review B•Feb 21, 2008•60 citations

The Hubbard Model: Exact Results in the Strong Coupling Limit

D. M. Esterling

Exact relations are derived for the Fermi Hubbard spectral weight function for infinite U at zero temperature in the thermodynamic limit for any dimension,any lattice structure and general hopping matrix. These relations involve moments of the spectral weight function but differ from similar work by (a) restricting the moments over the interesting low energy (lower Hubbard band) spectrum and (b) without any of the usual approximations (e.g. decoupling) for the requisite higher order correlation functions. The latter are determined exactly as explicit functions of the single particle correlation function in the infinite U limit. The methods behind these results have the additional virtue of simplicity - cumbersome, but entirely straightforward. In a companion paper, the relations offer rich insights into the model behavior and offer severe tests - a computer lab - of any proposed solution to the Hubbard model in the strong correlation (large finite U) region. As the electron density approaches one electron per site, then the correlation functions become local, so are trivial to compute exactly. In that limit and for the paramagnetic case, the second central moment of the spectral weight function is not zero, but quite large.

arXiv:1807.09219•Jul 24, 2018•0 citations

Effect of nonlocal interactions on the disorder-induced zero-bias anomaly in the Anderson-Hubbard model

Hong-Yi Chen, W. A. Atkinson, Rachel Wortis

To expand the framework available for interpreting experiments on disordered strongly correlated systems, and in particular to explore further the strong-coupling zero-bias anomaly found in the Anderson-Hubbard model, we ask how this anomaly responds to the addition of nonlocal electron-electron interactions. We use exact diagonalization to calculate the single-particle density of states of the extended Anderson-Hubbard model. We find that for weak nonlocal interactions the form of the zero-bias anomaly is qualitatively unchanged. The energy scale of the anomaly continues to be set by an effective hopping amplitude renormalized by the nonlocal interaction. At larger values of the nonlocal interaction strength, however, hopping ceases to be a relevant energy scale and higher energy features associated with charge correlations dominate the density of states.

arXiv:1203.5366•Physical Review B•Jun 21, 2012•4 citations

Electron Correlation in the Hubbard Modelind=∞ Dimension

Fusayoshi J. Ohkawa

The Hubbard model with strong correlation is examined. The mean-field approximation (MFA) based on the best single-site approximation (SSA) is rigorous in the limit of high dimension of d =+∞. The best SSA is reduced to solving the Anderson model. The ground state is a heavy-electron liquid, presumably superconducting, in the weak-coupling regime, which is approximately defined by g ≈ J ( Q )/4 T K <1 with J ( Q ) being the maximum value of exchange interactions and T K the Kondo temperature to show the energy scale of heavy electrons. In the strong-coupling regime defined by g >1, on the other hand, the ground state is a MFA-type antiferromagnetic state.

Journal of the Physical Society of Japan•Oct 15, 1991•46 citations
We derive the exact expression for the averaged free energy of a general class of Hubbard-type models with local, quenched disorder in the limit of high dimensions. A clear mean-field interpretation of its structure is given. Analytic results are obtained for a simplified Hubbard model with disorder. The two-particle correlation functions are shown to display a novel coupling of quantum degrees of freedom whenever genuine electron-electron correlation effects are present.
The influence of local disorder on the thermodynamics of interacting electrons is studied within the infinite-dimensional disordered Hubbard model.Using a finite-temperature quantum Monte Carlo method, the averaged local moment and staggered susceptibility are calculated and the magnetic phase diagram at half-filling is constructed.From the averaged compressibility in the paramagnetic and antiferromagnetic phase we determine the metalinsulator transitions of the system.A rich transition scenario is revealed.Quite unexpectedly the disorder is found to stabilize the magnetic order in the strong-coupling limit.Randomness can significantly influence the low-temperature behaviour of interacting systems.In particular, it may lead to new phases which have no analogue in non-random systems [l].In the case of electrons, the simplest lattice model including both interactions and random potentials is the disordered Hubbard model.It is now known that even in the .mean-field.limit d + CQ [2,3] the Hubbard interaction remains dynamical [4] and leads to a highly non-trivial single-site problem with infinitely many coupled quantum degrees of freedom [5].This problem is, in fact, equivalent to an Anderson impurity model complemented by a self-consistency condition [6] and is thus amenable to numerical investigations [7] within a finite-temperature quantum Monte Carlo approach [81.In the absence of disorder this technique was already used by several groups to investigate the magnetic phase diagram [7,9], the Mott-Hubbard transition [lo, 1 1 1 and lately also superconductivity in a two-band version [12] of the Hubbard model in d = C Q ; thereby important new insight was gained.In this letter we wish to concentrate on the combined effect of disorder and interaction.We will study the effect of diagonal disorder on the low-temperature properties of the Hubbard model in d = CQ , in particular the competition between correlation-induced
The effect of electron correlations in the infinite-dimension (d=∞) Hubbard model at finite temperatures has been investigated with the use of a theory which was recently proposed by the present author generalizing the slave-boson functional-integral method. Sublattice magnetizations, double occupancies and band-narrowing factors are computed as functions of the interaction, U, and the temperature, T. Calculated results are exact in the limits of U→0 and U→∞, and in the limits of T=0 and T→∞ they are expected to be very accurate owing to the nature of our mean-field-type theory for infinite-dimension systems. Similarities and differences between the calculated results for d=3 and d=∞ are also discussed.
We study the paramagnetic Anderson-Hubbard model using an extension of dynamical mean field theory (DMFT), known as statistical DMFT, that allows us to treat disorder and strong electronic correlations on equal footing. An approximate nonlocal Green's function is found for individual disorder realizations and then configuration averaged. We apply this method to two-dimensional lattices with up to 1000 sites in the strong disorder limit, where an atomic-limit approximation is made for the self-energy. We investigate the scaling of the inverse participation ratio at quarter- and half-filling, and find a nonmonotonic dependence of the localization length on the interaction strength. For strong disorder, we do not find evidence for an insulator-metal transition, and the disorder potential becomes unscreened near the Mott transition. Furthermore, strong correlations suppress the Altshuler-Aronov density of states anomaly near half-filling.
Exact relations are derived for the Fermi Hubbard spectral weight function for infinite U at zero temperature in the thermodynamic limit for any dimension,any lattice structure and general hopping matrix. These relations involve moments of the spectral weight function but differ from similar work by (a) restricting the moments over the interesting low energy (lower Hubbard band) spectrum and (b) without any of the usual approximations (e.g. decoupling) for the requisite higher order correlation functions. The latter are determined exactly as explicit functions of the single particle correlation function in the infinite U limit. The methods behind these results have the additional virtue of simplicity - cumbersome, but entirely straightforward. In a companion paper, the relations offer rich insights into the model behavior and offer severe tests - a computer lab - of any proposed solution to the Hubbard model in the strong correlation (large finite U) region. As the electron density approaches one electron per site, then the correlation functions become local, so are trivial to compute exactly. In that limit and for the paramagnetic case, the second central moment of the spectral weight function is not zero, but quite large.
To expand the framework available for interpreting experiments on disordered strongly correlated systems, and in particular to explore further the strong-coupling zero-bias anomaly found in the Anderson-Hubbard model, we ask how this anomaly responds to the addition of nonlocal electron-electron interactions. We use exact diagonalization to calculate the single-particle density of states of the extended Anderson-Hubbard model. We find that for weak nonlocal interactions the form of the zero-bias anomaly is qualitatively unchanged. The energy scale of the anomaly continues to be set by an effective hopping amplitude renormalized by the nonlocal interaction. At larger values of the nonlocal interaction strength, however, hopping ceases to be a relevant energy scale and higher energy features associated with charge correlations dominate the density of states.
The Hubbard model with strong correlation is examined. The mean-field approximation (MFA) based on the best single-site approximation (SSA) is rigorous in the limit of high dimension of d =+∞. The best SSA is reduced to solving the Anderson model. The ground state is a heavy-electron liquid, presumably superconducting, in the weak-coupling regime, which is approximately defined by g ≈ J ( Q )/4 T K <1 with J ( Q ) being the maximum value of exchange interactions and T K the Kondo temperature to show the energy scale of heavy electrons. In the strong-coupling regime defined by g >1, on the other hand, the ground state is a MFA-type antiferromagnetic state.