Competing charge and magnetic order in fermionic multicomponent systems

Mohsen Hafez-Torbati and Walter Hofstetter

Phys. Rev. B 100, 035133 – Published 26 July 2019

Abstract

We consider the fermionic $SU (3)$ 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 $Δ$ , 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 $U − Δ$ 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.

Received 14 January 2019

DOI:https://doi.org/10.1103/PhysRevB.100.035133

Physics Subject Headings (PhySH)

Charge density waves Magnetic order Quantum phase transitions

Dynamical mean field theory

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Mohsen Hafez-Torbati ^* and Walter Hofstetter^†

Institut für Theoretische Physik, Goethe-Universität, 60438 Frankfurt/Main, Germany

^*torbati@itp.uni-frankfurt.de
^†hofstett@physik.uni-frankfurt.de

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 100, Iss. 3 — 15 July 2019

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Schematic representation of the Hamiltonian Eq. (1) on the triangular lattice. The three sublattices $A, B$ , and $C$ acquire different on-site energies due to the staggered potential $Δ_{r}$ . (b) The phase diagram of the model Eq. (1) at $1 / 3$ filling for the inverse temperature $β = 20 / t$ in the $U − Δ$ plane with energies given in units of the hopping parameter $t$ , computed using dynamical mean-field theory method. The continuous and dashed lines denote, respectively, the second- and the first-order phase transitions. (c) Schematic representation of the different phases: band insulator (BI), where mainly the sublattice $A$ is occupied, charge-ordered magnetic insulator (COMI), where the sublattice $A$ is occupied by two fermionic components and the third component occupies the sublattice $B$ , and magnetic Mott insulator (MMI) where each component occupies one of the three sublattices.
Reuse & Permissions
Figure 2
Local density at the different sublattices $A, B$ , and $C$ and for the different components 0, 1, and 2 plotted versus the Hubbard interaction $U$ at the staggered potentials $Δ = 3 t$ (a), $Δ = 7 t$ (b), and $Δ = 10 t$ (c). The different phases band insulator (BI), paramagnetic metal (PM), three-sublattice magnetic Mott insulator (MMI), charge-ordered magnetic insulator (COMI), and charge-ordered magnetic metal (COMM) are distinguished. The results shown are obtained for four bath sites of the impurity solver.
Reuse & Permissions
Figure 3
Local moment on sublattice $A$ plotted versus the staggered potential $Δ$ for different values of the Hubbard interaction $U$ . The local moment is shifted for clarity by $(16 t - U) \times 0.05$ along the vertical axis. We have used BI for band insulator, PM for paramagnetic metal, and COMI for charge-ordered magnetic insulator. The results are for five bath sites of the impurity solver.
Reuse & Permissions
Figure 4
The spectral function $A (ω)$ plotted versus energy $ω$ in the paramagnetic (a) and magnetically ordered phases (b)–(d). For the paramagnetic metal (PM) and the band insulator (BI), the spectral function is independent than the internal component $α$ . For the three-sublattice magnetic Mott insulator (MMI), the spectral functions of all the three internal components $α = 0, 1, 2$ are represented. For the charge-ordered magnetic insulator (COMI) and the charge-ordered magnetic metal (COMM), the spectral functions of components $α = 0$ and $α = 2$ are the same due to the symmetry. In each panel, we have distinguished the spectral functions of the different sublattices $A, B$ , and $C$ by the different colors blue, green, and red, respectively. The results are for five bath sites in the Anderson impurity problem.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics