Evolution of Nagaoka phase with kinetic energy frustrating hopping

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 = ∞ 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.

Balance and frustration in strongly correlated itinerant electron systems: An extension of Nagaoka's theorem

“…In this context it is interesting to note the recent discovery that on some kinetically frustrated lattices antiferromagnetic states with magnetization near the classical limit occur in the Nagaoka limit [6][7][8][9]. Again here releasing the frustration in the orbital part of the wave function appears to play a crucial role [7].…”

“…Balance considers this. On the other hand, it is known that kinetic frustration can lead to antiferromagnetic states in the infinite-U limit [6][7][8][9]. A staggered magnetic flux can be used to control the degree of kinetic frustration, driving the ground state of certain models from magnetic to antiferromagnetic [9].…”

Understanding one-dimensional topological Kondo insulator: poor man’s non-uniform antiferromagnetic mean-field theory versus quantum Monte Carlo simulation

“…[5] 4 Model with extra conduction electron band For 1D p-PAM, its ground-state is the well-established Haldane phase. [16,17] Since it is a (symmetry-protected) topological state, the Haldane phase itself is robust against weak interaction and perturbation. So, it is interesting to see whether there exists a quantum phase transition from Haldane phase to other non-trivial or trivial state of matter in the 1D p-PAM.…”

“…Furthermore, these results are verified by an independent density matrix renormalization group study. [17] In addition, we have also studied the finite temperature physics of p-PAM by finite-T QMC simulation, [18] and its nonequilibrium dynamics has been calculated in Ref. [19].…”

Local entanglement and string order parameter in dimerized models

“…They reconstructed SOP for identification of the SPT phase in band insulators and studied the robustness of the SOP against perturbation terms [13]. More recently, SOP was used to identify the Haldane phase in a 1D bosonic lattice, a topological Kondo insulator and a Kitaev Ladder [14][15][16], demonstrating their solid application for non-spin systems. However, these works were performed numerically using DMRG [17,18] and SOPs were not evaluated analytically.…”