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arXiv:2605.30061 · Physical review. B./Physical review. B

Slave-rotor theory of correlated altermagnets on the Lieb lattice

Vanuildo S. de Carvalho, Hermann Freire, Rodrigo G. Pereira

Published Oct 8, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate the metal-insulator transition driven by the onsite repulsive interaction $U$ in an altermagnetic Hubbard model defined on a Lieb lattice. Using the slave-rotor approach at half-filling, we find that the system exhibits a cascade of interaction-driven phase transitions. As $U$ increases, the system evolves from a normal metal to an altermagnetic metal, then to an altermagnetic insulator, and eventually to an altermagnetic Mott insulator characterized by the complete suppression of the quasiparticle weight. These phases are supported by the calculation of the electronic spectral function, which features spin-split bands in both the metallic and insulating regimes. However, the spin splitting becomes substantially suppressed in the Mott-insulating phase. Our results suggest that the observation of spin splitting in the spectral function of $d$-wave altermagnets with a Lieb-lattice-like structure may be limited to the weak-to-moderate correlation regime.

DOI
10.1103/wkx4-mr24

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We investigate the metal-insulator transition driven by the onsite repulsive interaction UUU in an altermagnetic Hubbard model defined on a Lieb lattice. Using the slave-rotor approach at half-filling, we find that the system exhibits a cascade of interaction-driven phase transitions. As UUU increases, the system evolves from a normal metal to an altermagnetic metal, then to an altermagnetic insulator, and eventually to an altermagnetic Mott insulator characterized by the complete suppression of the quasiparticle weight. These phases are supported by the calculation of the electronic spectral function, which features spin-split bands in both the metallic and insulating regimes. However, the spin splitting becomes substantially suppressed in the Mott-insulating phase. Our results suggest that the observation of spin splitting in the spectral function of ddd-wave altermagnets with a Lieb-lattice-like structure may be limited to the weak-to-moderate correlation regime.
Altermagnetism is an unconventional form of magnetic order characterized by spin-split electronic bands and zero net magnetization. Here, the authors utilize a variational Monte Carlo approach to reveal the emergence of ddd-wave altermagnetism in the Hubbard model on the Shastry-Sutherland lattice and demonstrate how strong electronic correlations manifest in the metal-insulator transition. The calculation of photoemission spectral functions highlights the presence of altermagnetic Zeeman splitting, also in the Mott insulating phase (and upon doping).
We study the emergence of altermagnetism from repulsive interactions for electrons on the Lieb lattice as a model of quasi-2D oxychalcogenides with the so-called "anti-CuO_{2}" lattice structure. A comprehensive study of the Lieb lattice Hubbard model, using unrestricted Hartree-Fock and exact diagonalization techniques, establishes the presence of a spin-1/2 altermagnetic Mott insulating ground state for average electron densities of 2 and 4 per unit cell. Both phases show the characteristic spin splitting in the electron bands as well as in the magnon bands, as indicated by solutions of an effective spin-1/2 Heisenberg model that we construct. We also provide evidence for altermagnetic metal formation in the electron- and hole-doped Mott state, giving rise to Fermi surfaces with d_{x^{2}-y^{2}}-wave spin splitting and quasi-one-dimensional characteristics.
The Lieb lattice possesses three bands and, with intrinsic spin-orbit coupling $\ensuremath{\lambda}$, supports topologically nontrivial band insulating phases. At half filling the lower band is fully filled, while the upper band is empty. The chemical potential lies in the flat band (FB) located at the middle of the spectrum, thereby stabilizing a flat band insulator. At this filling, we introduce on-site Hubbard interaction UUU on all sites. Within a slave rotor mean-field theory we show that, in spite of the singular effect of interaction on the FB, the three bands remain stable up to a fairly large critical correlation strength (Ucrit{U}_{\text{crit}}Ucrit​), creating a correlated flat band insulator. Beyond Ucrit{U}_{\text{crit}}Ucrit​, there is a sudden transition to a Mott insulating state, where the FB is destroyed due to complete transfer of spectral weight from the FB to the upper and lower bands. We show that all the correlation driven insulating phases host edge modes with linearly dispersing bands along with a FB passing through the Dirac point, exhibiting that the topological nature of the bulk band structure remains intact in the presence of strong correlation. Furthermore, in the limiting case of UUU introduced only on one sublattice where $\ensuremath{\lambda}=0$, we show that the Lieb lattice can support mixed edge modes containing contributions from both spinons and electrons, in contrast to purely spinon edge modes arising in the topological Mott insulator.
The Lieb lattice possesses three bands and with intrinsic spin orbit coupling λ\lambdaλ, supports topologically non-trivial band insulating phases. At half filling the lower band is fully filled, while the upper band is empty. The chemical potential lies in the flat band (FB) located at the middle of the spectrum, thereby stabilizing a flat band insulator. At this filling, we introduce on-site Hubbard interaction UUU on all sites. Within a slave rotor mean field theory we show that, in spite of the singular effect of interaction on the FB, the three bands remain stable up to a fairly large critical correlation strength (UcritU_{crit}Ucrit​), creating a correlated flat band insulator. Beyond UcritU_{crit}Ucrit​, there is a sudden transition to a Mott insulating state, where the FB is destroyed due to complete transfer of spectral weight from the FB to the upper and lower bands. We show that all the correlation driven insulating phases host edge modes with linearly dispersing bands along with a FB passing through the Dirac point, exhibiting that the topological nature of the bulk band structure remains intact in presence of strong correlation. Furthermore, in the limiting case of UUU introduced only on one sublattice where λ=0\lambda=0λ=0, we show that the Lieb lattice can support mixed edge modes containing contributions from both spinons and electrons, in contrast to purely spinon edge modes arising in the topological Mott insulator.
Using the determinant quantum Monte Carlo method, we investigate the metal-insulator transition in the interacting disordered Hubbard model of a Lieb lattice in which the system characterizes the flat band centered at the Fermi level. By choosing suitable electron densities, we ensure the weak interaction sign problem to improve the reliability of our results. It is found that disorder and on-site Coulomb repulsive interaction produce interesting effects that induce the metal-insulator transition which is impossible in the half-filled case. The density of states at the Fermi energy is still finite in the thermodynamic limit, suggesting that the system is an Anderson insulator rather than a Mott insulator. Moreover, this doping system is paramagnetic, unlike the half-filled system which is ferrimagnetic.
We study the magnetic field-driven metal-to-insulator transition in half-filled Hubbard model on the Bethe lattice, using the dynamical mean-field theory by solving the quantum impurity problem with density-matrix renormalization group algorithm. The method enables us to obtain a high-resolution spectral densities in the presence of a magnetic field. It is found that the Kondo resonance at the Fermi level splits at relatively high magnetic field: the spin-up and -down components move away from the Fermi level and finally form a spin-polarized band insulator. By calculating the magnetization and spin susceptibility, we clarify that an applied magnetic field drives a transition from a paramagnetic metallic phase to a band insulating phase. In the weak interaction regime, the nature of the transition is continuous and captured by the Stoner's description, while in the strong interaction regime the transition is very likely to be metamagnetic, evidenced by the hysteresis curve. Furthermore, we determine the phase boundary by tracking the kink in the magnetic susceptibility, and the steplike change of the entanglement entropy and the entanglement gap closing. Interestingly, the phase boundaries determined from these two different ways are largely consistent with each other.