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arXiv:1901.02054 · Physical review. B./Physical review. B

Competing charge and magnetic order in fermionic multicomponent systems

Mohsen Hafez-Torbati, Walter Hofstetter

Published Jul 26, 2019• 14 citations
arXivHTMLPDF

Abstract

We consider the fermionic $\mathrm{SU}(3)$ Hubbard model on the triangular lattice at $1/3$ filling in the presence of a three-sublattice staggered potential which provides the possibility to investigate the competition of charge and magnetic order in three-component systems. We show that, depending on the strength of the staggered potential $\mathrm{\ensuremath{\Delta}}$, the Hubbard interaction $U$ destabilizes the band insulator at small $U$ into the Mott insulator at large $U$ in three different ways with different intermediate phases. This leads to a rich phase diagram in the $U\text{\ensuremath{-}}\mathrm{\ensuremath{\Delta}}$ plane. Our results indicate that multicomponent systems show not only exotic states in the Mott regime as has been considered previously, but also interesting competition between charge and magnetic orders which can lead to the emergence of charge-ordered magnetic insulators and charge-ordered magnetic metals.

DOI
10.1103/physrevb.100.035133

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We consider the fermionic SU(3)\mathrm{SU}(3)SU(3) Hubbard model on the triangular lattice at 1/31/31/3 filling in the presence of a three-sublattice staggered potential which provides the possibility to investigate the competition of charge and magnetic order in three-component systems. We show that, depending on the strength of the staggered potential \ensuremathΔ\mathrm{\ensuremath{\Delta}}\ensuremathΔ, the Hubbard interaction UUU destabilizes the band insulator at small UUU into the Mott insulator at large UUU in three different ways with different intermediate phases. This leads to a rich phase diagram in the U\ensuremath-\ensuremathΔU\text{\ensuremath{-}}\mathrm{\ensuremath{\Delta}}U\ensuremath-\ensuremathΔ plane. Our results indicate that multicomponent systems show not only exotic states in the Mott regime as has been considered previously, but also interesting competition between charge and magnetic orders which can lead to the emergence of charge-ordered magnetic insulators and charge-ordered magnetic metals.
We consider SU(3) fermions on the triangular lattice in the presence of a gauge potential which stabilizes a quantum Hall insulator (QHI) at the density of one particle per lattice site. We investigate the effect of the Hubbard interaction, favoring magnetic long-range order, and a three-sublattice potential (TSP), favoring a normal insulator (NI), on the system. For a weak TSP we find that the Hubbard interaction drives the QHI into a three-sublattice magnetic Mott insulator (MMI). For intermediate values of the TSP we identify two transition points upon increasing the Hubbard interaction. The first transition is from the NI to the QHI and the second transition is from the QHI to the MMI. For large values of the TSP a charge-ordered magnetic insulator (COMI) emerges between the NI and the QHI, leading to an interaction-driven COMI-to-QHI transition.
In the past few decades, tremendous efforts have been made toward understanding the exotic physics emerging from competition between various ordering tendencies in strongly correlated systems. Employing state-of-the-art quantum Monte Carlo simulation, we investigate an interacting SU(N) fermionic model with varying interaction strength and value of N, and we unveil the ground-state phase diagram of the model exhibiting a plethora of exotic phases. For small values of N-namely, N=2, 3-the ground state is an antiferromagnetic (AFM) phase, whereas in the large-N limit, a staggered valence bond solid (VBS) order is dominant. For intermediate values of N such as N=4, 5, remarkably, our study reveals that distinct VBS orders appear in the weak and strong coupling regimes. More fantastically, the competition between staggered and columnar VBS ordering tendencies gives rise to a Mott insulating phase without spontaneous symmetry breaking (SSB), existing in a large interacting parameter regime, which is consistent with a gapped quantum spin liquid. Our study not only provides a platform to investigate the fundamental physics of quantum many-body systems-it also offers a novel route toward searching for exotic states of matter such as quantum spin liquid in realistic quantum materials.
The variational cluster approximation is used to study the ground-state properties and single-particle spectra of the three-component fermionic Hubbard model defined on the two-dimensional square lattice at half filling. First, we show that either a paired Mott state or color-selective Mott state is realized in the paramagnetic system, depending on the anisotropy in the interaction strengths, except around the SU(3) symmetric point, where a paramagnetic metallic state is maintained. Then, by introducing Weiss fields to observe spontaneous symmetry breakings, we show that either a color-density-wave state or color-selective antiferromagnetic state is realized depending on the interaction anisotropy and that the first-order phase transition between these two states occurs at the SU(3) point. We moreover show that these staggered orders originate from the gain in potential energy (or Slater mechanism) near the SU(3) point but originate from the gain in kinetic energy (or Mott mechanism) when the interaction anisotropy is strong. The staggered orders near the SU(3) point disappear when the next-nearest-neighbor hopping parameters are introduced, indicating that these orders are fragile, protected only by the Fermi surface nesting.
By performing exact quantum Monte Carlo simulations of a model of interacting Dirac Fermions with staggered potential, we reveal a novel intermediate phase where the electronic correlations drive a band insulator metallic, and at a larger interaction, drive the metal-to-Mott insulator. We also show that the Mott insulating phase is antiferromagnetic. A complete phase diagram is achieved by studying the phase transitions at large staggered potential and interaction strengths, which shows that the intermediate state is robust and occupies a large part of the phase diagram and that it should be more feasible to be detected experimentally.
We investigate the phases of the ionic Hubbard model in a two-dimensional square lattice using determinant quantum Monte Carlo. At half-filling, when the interaction strength or the staggered potential dominates, we find Mott and band insulators, respectively. When these two energies are of the same order, we find a metallic region. Charge and magnetic structure factors demonstrate the presence of antiferromagnetism only in the Mott region, although the externally imposed density modulation is present everywhere in the phase diagram. Away from half-filling, other insulating phases are found. Kinetic energy correlations do not give clear signals for the existence of a bond-ordered phase.
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.