The Hubbard Model: A Computational Perspective

TL;DR: In this article , the authors show that for precision-placed atoms in silicon with strong Coulomb confinement, they can engineer a minimum of six all-epitaxial in-plane gates to tune the energy levels across a linear array of ten quantum dots to realize both the trivial and the topological phases of the many-body Su-Schrieffer-Heeger (SSH) model.

TL;DR: In this paper, large-scale ground-state density matrix renormalization group (DMRG) calculations on t-J cylinders with circumferences 6 and 8 were performed to determine a rough phase diagram that appears to approximate the two-dimensional (2D) system.

TL;DR: In this paper , an efficient, low-depth variational quantum algorithm with few parameters can reproduce important qualitative features of medium-size instances of the Fermi-Hubbard model.

Abstract: Unidirectional ("stripe") charge density wave order has now been established as a ubiquitous feature in the phase diagram of the cuprate high-temperature superconductors, where it generally competes with superconductivity. Nonetheless, on theoretical grounds it has been conjectured that stripe order (or other forms of "optimal" inhomogeneity) may play an essential positive role in the mechanism of high-temperature superconductivity. Here, we report density matrix renormalization group studies of the Hubbard model on long four- and six-leg cylinders, where the hopping matrix elements transverse to the long direction are periodically modulated-mimicking the effect of putative period 2 stripe order. We find that even modest amplitude modulations can enhance the long-distance superconducting correlations by many orders of magnitude and drive the system into a phase with a substantial spin gap and superconducting quasi-long-range order with a Luttinger exponent, [Formula: see text].

TL;DR: A review of the metal-insulator transition can be found in this article, where a pedagogical introduction to the subject is given, as well as a comparison between experimental results and theoretical achievements.

TL;DR: The dynamical mean field theory of strongly correlated electron systems is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition.

TL;DR: In this paper, the Hartree-Fock approximation of the correlation problem for the d-and f-bands was applied to a simple, approximate model for the interaction of electrons in narrow energy bands.

TL;DR: The density matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems as mentioned in this paper.