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

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.