Abstract
We investigate, using the density matrix renormalization group, the evolution of the Nagaoka state with $t'$ hoppings that frustrate the hole kinetic energy in the $U=\infty$ Hubbard model on the anisotropic triangular lattice and the square lattice with second-nearest neighbor hoppings. We find that the Nagaoka ferromagnet survives up to a rather small $t'_c/t \sim 0.2.$ At this critical value, there is a transition to an antiferromagnetic phase, that depends on the lattice: a ${\bf Q}=(Q,0)$ spiral order, that continuously evolves with $t'$, for the triangular lattice, and the usual ${\bf Q}=(\pi,\pi)$ N\'eel order for the square lattice. Remarkably, the local magnetization takes its classical value for all considered $t'$ ($t'/t \le 1$). Our results show that the recently found classical kinetic antiferromagnetism, a perfect counterpart of Nagaoka ferromagnetism, is a generic phenomenon in these kinetically frustrated electronic systems.
Highlights
Nagaoka’s theorem[1] stands almost alone as a rigorous result about itinerant magnetism
Since the seminal work by Nagaoka[1], a lot of effort has been dedicated to the study of Nagaoka ferromagnetism stability beyond the constraints of the theorem
Large-scale density matrix renormalization group (DMRG) calculations[5], among others[4,6,7] seem to have solved the problem, unless for the square lattice, as they predict the existence of Nagaoka ferromagnetism up to critical hole density δc 0.2
Summary
Nagaoka’s theorem[1] stands almost alone as a rigorous result about itinerant magnetism It predicts the existence of a fully polarized ferromagnetic state as the unique ground state of the U = ∞ Hubbard model, when one hole is doped away half-filling and certain connectivity conditions are satisfied. Nagaoka’s theorem requires that Sloop = 1, where Sloop is the sign of the hopping amplitudes around the smallest loop of the lattice When this condition is not fulfilled the hole kinetic energy is frustrated. We found another example of kinetic antiferromagnetism, a (π, π) Neel order as the ground state of the square Hubbard model with second-nearest neighbor hopping t = t > 0, and we uncovered the classical nature of these antiferromagnets[14]. At the end of this work, we briefly mention some recent experimental proposals
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