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arXiv:1808.03966 · Physical Review A

Resonant-driving-induced ferromagnetism in the Fermi-Hubbard model

Ning G. Sun, Pengfei Zhang, Hui Zhai

Published Apr 29, 2019• 3 citations
arXivHTMLPDF

Abstract

In this article we study quantum phases and the phase diagram of a Fermi-Hubbard model under periodic driving that has been realized in recent cold-atom experiments, in particular, when the driving frequency is nearly resonant with the interaction energy. Due to the driving, the effective Hamiltonian contains a correlated hopping term where the density occupation strongly modifies the hopping strength. Focusing on half filling, in addition to the charge- and spin-density wave phases, large regions of ferromagnetic phase and phase separation are discovered in the weakly interacting regime. The mechanism of this ferromagnetism is attributed to the correlated hopping, because the hopping strength within a ferromagnetic domain is normalized to a larger value than the hopping strength across the domain. Thus, the kinetic energy drives the system into a ferromagnetic phase. We note that this is a different mechanism, in contrast to the well-known Stoner mechanism for ferromagnetism where the ferromagnetism is driven by interaction energy.

DOI
10.1103/physreva.99.043629

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In this article we study quantum phases and the phase diagram of a Fermi-Hubbard model under periodic driving that has been realized in recent cold-atom experiments, in particular, when the driving frequency is nearly resonant with the interaction energy. Due to the driving, the effective Hamiltonian contains a correlated hopping term where the density occupation strongly modifies the hopping strength. Focusing on half filling, in addition to the charge- and spin-density wave phases, large regions of ferromagnetic phase and phase separation are discovered in the weakly interacting regime. The mechanism of this ferromagnetism is attributed to the correlated hopping, because the hopping strength within a ferromagnetic domain is normalized to a larger value than the hopping strength across the domain. Thus, the kinetic energy drives the system into a ferromagnetic phase. We note that this is a different mechanism, in contrast to the well-known Stoner mechanism for ferromagnetism where the ferromagnetism is driven by interaction energy.
While the exact phase diagram of the Fermi-Hubbard model remains poorly understood despite decades of progress, nearly 60 years ago Nagaoka proved that a single dopant in an otherwise half-filled Hubbard system can bring about ferromagnetism through kinetic means. The phenomenon was recently observed with ultracold atoms in triangular optical lattices. Here, we explore the kinetic ferromagnetism within the square lattice Hubbard model and its strong-coupling counterpart, the $t\ensuremath{-}J$ model, at finite temperatures in the thermodynamic limit via numerical linked-cluster expansions. We find evidence of ferromagnetic Nagaoka polarons at dopings up to $\ensuremath{\sim}30%$ away from half filling for a variety of interaction strengths and at temperatures as low as 0.2 of the hopping energy. We map out the boundaries of this phase through analyzing various correlation functions.
We propose using ultracold fermionic atoms trapped in a periodically shaken optical lattice as a quantum simulator of the $t\text{\ensuremath{-}}J$ Hamiltonian, which describes the dynamics in doped antiferromagnets and is thought to be relevant to the problem of high-temperature superconductivity in the cuprates. We show analytically that the effective Hamiltonian describing this system for off-resonant driving is the $t\text{\ensuremath{-}}J$ model with additional pair hopping terms, whose parameters can all be controlled by the drive. We then demonstrate numerically using tensor network methods for a one-dimensional (1D) lattice that a slow modification of the driving strength allows near-adiabatic transfer of the system from the ground state of the underlying Hubbard model to the ground state of the effective $t\text{\ensuremath{-}}J$ Hamiltonian. Finally, we report exact diagonalization calculations illustrating the control achievable on the dynamics of spin-singlet pairs in 2D lattices utilizing this technique with current cold-atom quantum-simulation technology. These results open new routes to explore the interplay between density and spin in strongly correlated fermionic systems through their out-of-equilibrium dynamics.
A broad class of correlated quantum materials features strong Hund’s coupling, yet cold-atom quantum simulators have so far focused primarily on single-orbital Fermi-Hubbard systems near a Mott insulator. Here, we show that repulsively interacting fermions loaded into the p bands of a hexagonal lattice offer a unique platform to study the interplay of “Hundness” and “Mottness.” Our theory predicts that the orbital degrees of freedom, despite geometric frustration, produce a rich phase diagram featuring a competing itinerant ferromagnetic (FM) metal and a spin-1 antiferromagnetic (AFM) insulator. While FM order is known to emerge at low fillings near the flat-band limit, we show that this itinerant ferromagnetism is remarkably robust, persisting to stronger interactions and higher fillings well beyond the flat-band regime. More importantly, we identify that near half filling, FM is stabilized by a different mechanism: the double exchange with spins aligning to avoid Hund-rule penalties at the expense of the kinetic energy of Dirac fermions. The competition between the kinetic and double-exchange energies leads to, within our approximations, a first-order transition between FM and AFM orders in the chemical potential-interaction strength plane. Our analysis suggests that p -orbital Fermi gases—as multiorbital systems with coexisting localized and itinerant spins—reveal a rich competition between correlated “Hund metals” and other unconventional states driven by quantum fluctuations.
We studied ferromagnetism in the one-dimensional Hubbard model with doubly degenerate atomic orbitals by means of the density-matrix renormalization-group method and obtained the ground-state phase diagrams. It was found that ferromagnetism is stable from low to high (0<n<1.75)(0<n<1.75)(0<n<1.75) electron density when the interactions are sufficiently strong. The quasi-long-range order of triplet superconductivity coexists with the ferromagnetic order for a strong Hund coupling region, where the interorbital interaction ${U}^{\ensuremath{'}}\ensuremath{-}J$ is attractive. At quarter-filling (n=1),(n=1),(n=1), the insulating ferromagnetic state appears, accompanying orbital quasi-long-range order. For low densities (n<1),(n<1),(n<1), ferromagnetism occurs owing to the ferromagnetic exchange interaction caused by virtual hoppings of electrons, the same as in the quarter-filled system. This comes from separation of the charge and spin-orbital degrees of freedom in the strong-coupling limit. This ferromagnetism is fragile against variation of band structure. For high densities (n>1),(n>1),(n>1), the phase diagram of the ferromagnetic phase is similar to that obtained in infinite dimensions. In this case, the double exchange mechanism is operative for stabilizing the ferromagnetic order and this long-range order is robust against variation of the band dispersion. A partially polarized state appears in the density region $1.68\ensuremath{\lesssim}n\ensuremath{\lesssim}1.75$ and phase separation occurs for n just below the half-filling (n=2).(n=2).(n=2).
Non-equilibrium control of electronic properties in condensed matter systems can result in novel phenomena. In this work, we provide a novel non-equilibrium route to realize half-metallic phases. We explore the periodically driven Hubbard model on a bipartite lattice and demonstrate that a specially designed sublattice dependent drive can transform a weakly interacting metal or insulator into a ferrimagnetic half-metal (HM). We consider a Fermi-Hubbard model with only nearest-neighbour hopping and Floquet engineer the elusive half-metal phase by driving the site potentials periodically. The drive induces staggered higher range hoppings and a staggered potential between two sublattices in the Floquet Hamiltonian. Close to the dynamical localization point, due to the suppression of nearest neighbor hopping in the driven system, an effective enhancement of various terms in the Floquet Hamiltonian, including the e-e interactions, occurs. This helps in stabilizing a broad ferrimagnetic HM phase for a wide range of drive parameters. This dynamically stabilized HM phase is a pristine platform for next-generation spintronics, topological quantum computing (specifically for engineering Majorana zero modes in hybrid nanowires) and ultrafast magnetic memory architectures.
We consider a Hubbard model with occupation dependent hopping integrals. Using the Hartree-Fock (H-F) approximation and the new Green function approach with inter-site kinetic averages included, we analyze the influence of the correlated hopping on ferromagnetic ordering. The influence of correlated hopping on the nonlocal quasiparticle energies and corresponding k-dependent spectral weights is included. In addition we obtain the shift of the spin bands which is a major factor in creating spontaneous ferromagnetism. At some parameters of the model the correlated hopping effect is strong enough to achieve saturated ferromagnetism. This state may be obtained at the asymmetric density of states (DOS) and the Fermi energy located in the region of large spectral weight near the band edge. The results are compared with DMFT-Quantum Monte Carlo calculations and with the Hubbard III approximation which includes the correlated hopping effect.