Structure of the Hilbert-space of the infinite-dimensional Hubbard model

TL;DR

This paper develops an iterative method to explicitly construct the symmetry-adapted subspace of the ground state in the infinite-dimensional Hubbard model, connecting it to impurity problems and providing highly accurate estimates.

Contribution

It introduces a novel iterative procedure based on symmetrized transition operators for analyzing the Hubbard model's ground state in infinite dimensions.

Findings

Constructed the nontrivial symmetry-adapted subspace explicitly.

Linked the transition operators to the impurity model mapping.

Achieved estimates for the Hubbard model with 0.1% accuracy.

Abstract

An iterative procedure for the explicit construction of the nontrivial subspace of all symmetry-adapted configurations with non-zero weight in the ground-state of the infinite-dimensional Hubbard model is developed on the basis of a symmetrized representation of the transition operators on a sequence of Bethe-Lattices of finite depth. The relation ship between these operators and the well known mapping of the infinite-dimensional Hubbard model onto an effective impurity problem coupled to a (self-consistent) bath on non-interacting electrons is given. As an application we calculate the properties of various Hubbard stars and give estimates for the half-filled Hubbard model with up to 0.1% accuracy.