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

Journal of Physics C Solid State Physics

A renormalisation group study of weak disorder in the Hubbard Hamiltonian

G R Bhat, Vijay A. Singh

Published Oct 30, 1985• 6 citations
Publisher

Abstract

The authors have undertaken a real-space renormalisation group study of the weakly disordered Hubbard Hamiltonian. They find that the presence of a small correlation leads to an unexpected result: an enhancement of delocalisation which becomes more pronounced as the dimensionality increases.
DOI
10.1088/0022-3719/18/30/008

Related papers

Disorder and Interactions on a 1D Chain

Jonathan M. Carter, A. MacKinnon

It has become increasingly clear that a full understanding of the physics of electrons in disordered systems requires an approach in which both disorder and interactions are taken into account. Work on small numbers of electrons has suggested that interactions can substantially increase the localisation length in 1 dimensional systems and possibly lead to delocalisation in 2D. It has not been clear, however, to what extent these results are applicable to systems with a finite density of electrons. Among numerical approaches the transfer matrix method combined with finite size scaling has been particularly successful for non--interacting systems, whereas the density matrix renormalisation group successfully describes interacting systems. We have developed a new approach which combines elements of both these methods and have successfully applied it to spinless electrons with nearest neighbour interactions.

arXiv:cond-mat/0209213•Sep 9, 2002•0 citations

Real-space renormalization group approach to the Anderson model

Eamonn A. Campbell

Many of the most interesting electronic behaviours currently being studied are associated with strong correlations. In addition, many of these materials are disordered either intrinsically or due to doping. Solving interacting systems exactly is extremely computationally expensive, and approximate techniques developed for strongly correlated systems are not easily adapted to include disorder. As a non-interacting disordered model, it makes sense to consider the Anderson model as a first step in developing an approximate method of solution to the interacting and disordered Anderson-Hubbard model. Our renormalization group (RG) approach is modeled on that proposed by Johri and Bhatt [23]. We found an error in their work which we have corrected in our procedure. After testing the execution of the RG, we benchmarked the density of states and inverse participation ratio results against exact diagonalization. Our approach is significantly faster than exact diagonalization and is most accurate in the limit of strong disorder. Author Keywords: disorder, localization, real-space renormalization, strong correlations

Theory of Computing Systems•Jan 1, 2017•0 citations

Real-space renormalisation-group study of the one-dimensional Hubbard model

Chandan Dasgupta, Pierre M. Pfeuty

The one-dimensional Hubbard model is studied using a real-space renormalisation-group block method previously applied to other quantum systems. The authors primarily consider the half-filled band for which the ground state is found to be insulating for all non-zero values of the Hubbard interaction, in agreement with the exact solution. When the method is applied to first order in perturbation, they find that the insulating gap for small U/t behaves like exp (-At 2 /U 2 ) where U is the Hubbard interaction and t is the nearest-neighbour transfer integral. When the method is extended to second order, the authors find that for small U/t the gap behaves like (U/t) alpha with alpha approximately=11.2. The exact asymptotic behaviour of the gap ( approximately (U/t) 1/2 exp(-At/U)) is not recovered, but a good semiquantative agreement with the exact solution is obtained for both the gap and the ground state energy. Extensions to non-half-filled bands and to higher dimensions are discussed. The validity of the renormalisation group method is also discussed.

Journal of Physics C Solid State Physics•Feb 20, 1981•49 citations

Real space renormalization of the Mott-insulator to Bose-glass transition in the disordered Bose-Hubbard model

Anthony Hegg, Frank Krüger, Philip Phillips

Bulletin of the American Physical Society•Mar 19, 2013•0 citations

A new real-space renormalisation group method for interacting fermions at finite temperatures: application to the Anderson-Hubbard model. I

Arkady L. Kholodenko

A new real-space renormalisation group method is developed and tested for the case of the Anderson-Hubbard model. The development is concentrated on obtaining and subsequent analysis of one-dimensional recurrence relations which take into account the effects of interaction and temperature. The results are presented in a form that naturally permits the extension of the given treatment to the case of higher dimensions and off-diagonal bond percolation type of disorder. Although the method itself is not limited to low temperatures, actual computations were made for the case of low temperatures and weak-electron-electron coupling. For this case, the scaling expressions obtained for the ground-state energy and the energy gap are in satisfactory agreement with available exact results.

Journal of Physics C Solid State Physics•Nov 30, 1986•4 citations

Density matrix renormalisation group study of a one-dimensional quantum spin chain at non-zero temperature

Robert J. Bursill, Tao Xiang, G A Gehring

Journal of Magnetism and Magnetic Materials•Jan 1, 1998•1 citation
It has become increasingly clear that a full understanding of the physics of electrons in disordered systems requires an approach in which both disorder and interactions are taken into account. Work on small numbers of electrons has suggested that interactions can substantially increase the localisation length in 1 dimensional systems and possibly lead to delocalisation in 2D. It has not been clear, however, to what extent these results are applicable to systems with a finite density of electrons. Among numerical approaches the transfer matrix method combined with finite size scaling has been particularly successful for non--interacting systems, whereas the density matrix renormalisation group successfully describes interacting systems. We have developed a new approach which combines elements of both these methods and have successfully applied it to spinless electrons with nearest neighbour interactions.
Many of the most interesting electronic behaviours currently being studied are associated with strong correlations. In addition, many of these materials are disordered either intrinsically or due to doping. Solving interacting systems exactly is extremely computationally expensive, and approximate techniques developed for strongly correlated systems are not easily adapted to include disorder. As a non-interacting disordered model, it makes sense to consider the Anderson model as a first step in developing an approximate method of solution to the interacting and disordered Anderson-Hubbard model. Our renormalization group (RG) approach is modeled on that proposed by Johri and Bhatt [23]. We found an error in their work which we have corrected in our procedure. After testing the execution of the RG, we benchmarked the density of states and inverse participation ratio results against exact diagonalization. Our approach is significantly faster than exact diagonalization and is most accurate in the limit of strong disorder. Author Keywords: disorder, localization, real-space renormalization, strong correlations
The one-dimensional Hubbard model is studied using a real-space renormalisation-group block method previously applied to other quantum systems. The authors primarily consider the half-filled band for which the ground state is found to be insulating for all non-zero values of the Hubbard interaction, in agreement with the exact solution. When the method is applied to first order in perturbation, they find that the insulating gap for small U/t behaves like exp (-At 2 /U 2 ) where U is the Hubbard interaction and t is the nearest-neighbour transfer integral. When the method is extended to second order, the authors find that for small U/t the gap behaves like (U/t) alpha with alpha approximately=11.2. The exact asymptotic behaviour of the gap ( approximately (U/t) 1/2 exp(-At/U)) is not recovered, but a good semiquantative agreement with the exact solution is obtained for both the gap and the ground state energy. Extensions to non-half-filled bands and to higher dimensions are discussed. The validity of the renormalisation group method is also discussed.
A new real-space renormalisation group method is developed and tested for the case of the Anderson-Hubbard model. The development is concentrated on obtaining and subsequent analysis of one-dimensional recurrence relations which take into account the effects of interaction and temperature. The results are presented in a form that naturally permits the extension of the given treatment to the case of higher dimensions and off-diagonal bond percolation type of disorder. Although the method itself is not limited to low temperatures, actual computations were made for the case of low temperatures and weak-electron-electron coupling. For this case, the scaling expressions obtained for the ground-state energy and the energy gap are in satisfactory agreement with available exact results.