A Possible Via For Proving The Approach Of The Hubbard Ground States Toward Stripes And Other Doping States

TL;DR

This paper proposes a method to rigorously constrain the ground states of Hubbard and t-J models using finite cluster numerical results, potentially confirming stripe formations at specific dopings.

Contribution

It introduces a new approach to establish ground state constraints based on numerical data and boundary conditions, aiding in understanding stripe and doping states.

Findings

Strong bounds can be established with non-uniform minima under periodic boundary conditions.

The approach may rigorously confirm stripe formations at 1/8 doping.

Potential to generalize to other doping levels and models.

Abstract

In this simple note, we suggest a way to rigorously establishing constraints on the form of the ground states of the Hubbard and t-J models and extended longer (yet finite) range variants for various dopings, once exact numerical results are established for these Hamiltonians on finite size clusters with two different (both open and periodic) boundary conditions. We demonstrate that strong bounds will be established if non-uniform minima subject periodic boundary conditions are found. An offshoot of our proposal might enable rigorously establishing the strong tendency toward especially stable stripe formation at the magical commensurate doping of 1/8 on the infinite lattice, as well as at other dopings.