We study the infinite U Hubbard model with one hole doped away half-filling, in triangular and square lattices with frustrated hoppings that invalidate Nagaoka's theorem, by means of the density matrix renormalization group. We find that these kinetically frustrated models have antiferromagnetic ground states with classical local magnetization in the thermodynamic limit. We identify the mechanism of this kinetic antiferromagnetism with the release of the kinetic energy frustration as the hole moves in the established antiferromagnetic background. This release can occurs in two different ways: by a non-trivial spin-Berry phase acquired by the hole or by the effective vanishing of the hopping amplitude along the frustrating loops.Itinerant magnetism has proved to be an elusive subject in condensed matter physics, since itinerant and localized aspects of electrons need to be taken into account on equal footing. The single-band Hubbard model, originally proposed to describe metallic ferromagnetism [1], has also been associated with antiferromagnetism of kinetic exchange origin close to half-filling. While virtual kinetic processes favor antiferromagnetism, it is a rule of thumb to link real kinetic processes with ferromagnetism [2]. However, there exist only few exact results ensuring the existence of itinerant ferromagnetism [3, 4]. Among them, the most renowned is Nagaoka's theorem [3], which assert that the saturated ferromagnetic state is the unique ground state when one hole is doped on the half-filled Hubbard model with infinite U Coulomb repulsion. Furthermore, a connectivity condition must be fulfilled for the validity of Nagaoka's theorem: the sign of the hopping amplitudes around the smallest closed loop of the lattice must be positive, otherwise the hole kinetic energy will be frustrated and the saturated ferromagnetic state will no longer be the ground state. Kinetic energy frustration is a quantum mechanical phenomenon without classical analog, easily understood in certain tight-binding models where an electron can not gain the full kinetic energy −z|t|, due to quantum interferences [5, 6]. This kind of frustration has been considerably less studied than the magnetic one, although recent works indicate that its effects may lead to rich physics, such as, robust superconductivity in strongly repulsive fermionic system [7] and spontaneous time-reversal symmetry breakings [8], among others [9, 10].In a seminal work, Haerter and Shastry [7] have found a 120 • antiferromagnetic Néel order as the ground state of the U = ∞ triangular lattice Hubbard model when the hole motion is frustrated (t > 0), uncovering a new mechanism for itinerant magnetism. In this Letter, we further characterize this kinetic antiferromagnetism and we describe its microscopic origin, analyzing generic kinetically frustrated electronic models for which, in the limit of infinite Coulomb repulsion and one hole doped away halffilling, the Nagaoka's theorem is not valid. In particular, we study the ground state of two Hubbard models: one ...

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 = ∞ 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 ∼ 0.2. At this critical value, there is a transition to an antiferromagnetic phase, that depends on the lattice: a Q = (Q, 0) spiral order, that continuously evolves with t , for the triangular lattice, and the usual Q = (π, π) Néel order for the square lattice. Remarkably, the local magnetization takes its classical value for all considered t (t /t ≤ 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.