We show that even in $d=\ensuremath{\infty}$ dimensions the Hubbard model, when scaled properly, describes nontrivial correlations among fermions. Diagrammatic treatments are found to be substantially simpler than in finite dimensions. The weak-coupling correlation energy is seen to be a good approximation for that in $d=3$ . Recent approximations based on slave-boson techniques are recovered by the exact evaluation of explicit variational wave functions in $d=\ensuremath{\infty}$.We show that even in $d=\ensuremath{\infty}$ dimensions the Hubbard model, when scaled properly, describes nontrivial correlations among fermions. Diagrammatic treatments are found to be substantially simpler than in finite dimensions. The weak-coupling correlation energy is seen to be a good approximation for that in $d=3$. Recent approximations based on slave-boson techniques are recovered by the exact evaluation of explicit variational wave functions in $d=\ensuremath{\infty}$.

Physical Review LettersJan 16, 19892,347 citations

Correlated Electron Systems in the Limit of Infinite Dimensions

Marcelo J. Rozenberg

Jan 1, 19940 citations

Bootstrap embedding for interacting electrons in phonon coherent-state mean field

Shariful Islam, Joel Bierman, Yuan Liu

We develop a Fermi-Bose bootstrap embedding framework for the ground state of interacting electrons coupled to a phonon mean field. The method combines bootstrap embedding for correlated electrons with a self-consistent coherent-state mean-field treatment for phonons. This method models the interacting electron-phonon problem as a system of correlated electrons traveling in a self-consistently specified potential landscape, allowing for efficient treatment of large lattice systems. Convergence of the methods for fragment size and total system size is demonstrated for the one-dimensional Hubbard-Holstein model for up to 350 sites. Finite-size scaling is performed to extrapolate to the infinite system size. Benchmarking against the density matrix renormalization group for a small 8-site system at half- and quarter-filling shows an orders-of-magnitude runtime advantage. The comparison further reveals that the method performs best in regimes dominated by localization, such as the Mott insulating phase and the strong-coupling tiny polaron regime, where the local embedding ansatz is still valid. However, due to the mean-field treatment for phonons, we find limitations of our methods in the weakly coupled delocalized region and at the Peierls transition, where quantum phonon fluctuations and long-range kinetic correlations become substantial.We develop a Fermi-Bose bootstrap embedding framework for the ground state of interacting electrons coupled to a phonon mean field. The method combines bootstrap embedding for correlated electrons with a self-consistent coherent-state mean-field treatment for phonons. This method models the interacting electron-phonon problem as a system of correlated electrons traveling in a self-consistently specified potential landscape, allowing for efficient treatment of large lattice systems. Convergence of the methods for fragment size and total system size is demonstrated for the one-dimensional Hubbard-Holstein model for up to 350 sites. Finite-size scaling is performed to extrapolate to the infinite system size. Benchmarking against the density matrix renormalization group for a small 8-site system at half- and quarter-filling shows an orders-of-magnitude runtime advantage. The comparison further reveals that the method performs best in regimes dominated by localization, such as the Mott insulating phase and the strong-coupling tiny polaron regime, where the local embedding ansatz is still valid. However, due to the mean-field treatment for phonons, we find limitations of our methods in the weakly coupled delocalized region and at the Peierls transition, where quantum phonon fluctuations and long-range kinetic correlations become substantial.

arXiv:2603.11463The Journal of Chemical PhysicsMar 26, 20260 citations

Physical Theory for One-Dimensional Correlated Electron Systems

Nelson Oyindenyifa Nenuwe

World Academy of Science, Engineering and Technology, International Journal of Mathematical and Computational SciencesMay 2, 20160 citations

d=3

. Recent approximations based on slave-boson techniques are recovered by the exact evaluation of explicit variational wave functions in $d=\ensuremath{\infty}$.