Geometric Frustration Assisted Kinetic Ferromagnetism in Doped Mott Insulators

TL;DR

This work identifies a microscopic route to itinerant ferromagnetism in doped Mott insulators on a geometrically frustrated triangular lattice. Using large-scale DMRG and unrestricted Hartree-Fock, it shows ferromagnetism emerges at intermediate to strong coupling near $δ=1/2$, driven predominantly by doublon-singlon exchange among several hopping channels, with clear particle-hole asymmetry favoring electron-doping. The authors show a minimal $t_{QQ}-U$ model is sufficient to realize itinerant FM, map the magnetic phase diagram, and demonstrate robustness to magnetic anisotropy via RPA and DMRG analyses, including a finite-spin-wave gap $\,Δ=2zJ_3$ when $J_3>0$. These findings shed light on kinetic-energy–driven ferromagnetism in doped frustrated Mott systems and have relevance for triangular-lattice moiré materials and quantum simulators, highlighting the role of lattice geometry and hopping structure in stabilizing ferromagnetism at intermediate coupling. $U/t$ and $δ$-dependent FM stability persists alongside experimentally observed spin correlations, suggesting a route to tunable ferromagnetic states in correlated oxide and moiré platforms.

Abstract

Understanding ferromagnetism mechanism in doped Mott insulators on frustrated lattices remains challenging at intermediate coupling and finite doping. Here, we study the itinerant ferromagnetism and propose its mechanism in doped Mott insulators on a geometrically frustrated triangular lattice. Using large-scale density matrix renormalization group (DMRG) and unrestricted Hartree-Fock mean-field methods, we reveal that itinerant ferromagnetism appears at intermediate coupling ($10\lesssim U\ll\infty$) near 50% electron doping in the triangular-lattice Hubbard model. By analyzing all microscopic hopping processes, we find that doublon-singlon exchange alone drives the fully polarized ferromagnetism and uncovers the particle-hole asymmetry. We also establish the magnetic phase diagram and compare local spin correlations with recent experiments. Random phase approximation and DMRG calculations consistently confirm that the ferromagnetism persists when $SU(2)$ symmetry is explicitly broken by magnetic anisotropy. These results clarify a microscopic route to itinerant ferromagnetism at intermediate coupling and finite doping in doped Mott insulators.

Figures (13)

• Figure 1: $\vert$ The static spin structure factor $\boldsymbol{ S(\mathbf{q})}$ as a function of coupling strength $\boldsymbol{U/t}$ at electron doping $\boldsymbol{\delta=1/2}$. (a)-(b) The contour plot of $S(\mathbf{q})$ for cylinders at $U/t=10$ (a), and $U/t=24$ (b). The black dots represent the accessible momenta in the Brillouin zone (denoted as a white hexagon), and interpolation has been applied in the contour plot. We remark that the cylindrical geometry adopted in the density matrix renormalization group (DMRG) simulation breaks the lattice's rotational symmetry. (c) Schematic of the evolution of the $\mathbf{q}_0$ with increasing $U/t$, indicated by the color gradient from light to dark along the black dashed arrows. Here, $\mathbf{q}_0$ denotes the momenta where $S(\mathbf{q})$ reaches its maximum, within the Brillouin zone represented by a hexagon. Rotational symmetry of triangular lattices is assumed in this schematic for clarity. (d) Ferromagnetic squared order parameter $m_s^2(\mathbf{\Gamma})$ as a function of $U/t$. For larger $U/t$, the peak of $S(\mathbf{q})$ stabilizes at momentum $\mathbf{\Gamma}$ with a size-independent saturation value, indicating the fully polarized ferromagnetism. (e) Line-cut plot of $S(\mathbf{q})$ along the momentum path passing through the $\mathbf{\Gamma}$ point in (c), depicted as a white dashed line in (b). (f) Squared order parameter $m_s^2(\mathbf{\Gamma})$ from unrestricted Hartree-Fock calculations with periodic boundary conditions.
• Figure 2: $\vert$ The single-particle propagator $\boldsymbol{ C(r)}$ at separation $\boldsymbol{r}$ and electron momentum distribution $\boldsymbol{ n(\mathbf{k})}$ at electron doping $\boldsymbol{\delta=1/2}$. (a) Single-particle propagator $|C(r)|$ for different $U/t$, where $U$ is the on-site Hubbard interaction, and $t$ is the nearest-neighbor hopping amplitude. For comparison, the dashed and solid gray lines correspond to $|C(r)|\sim r^{-2}$ and $|C(r)|\sim r^{-1}$, respectively. (b) Line-cut plot of electron momentum distribution $n(\mathbf{k})$ along a specific momentum path that traverses the momentum $\mathbf{\Gamma}$, depicted as a blue dashed line in its inset. The inset shows the contour plot of $n(\mathbf{k})$, the white hexagon denotes the first Brillouin zone, and the colour bar encodes $n(\mathbf{k})$.
• Figure 3: $\vert$ Microscopic hopping processes in the Hubbard model and their kinetic energy contributions for intermediate coupling $\boldsymbol{ U/t}$. (a)-(c) Schematic illustration of nearest-neighbor hopping processes described in Eq. \ref{['eq:SepHoppingHt']}. (d) Schematic illustration of ring-exchange coupling. (e),(f) The kinetic energies (in blue) of different microscopic hopping processes as functions of $U/t$ for lattice width $L_y=4$ in (e) and $L_y=6$ in (f). Ferromagnetic squared order parameter $m_s^2(\mathbf{\Gamma})$ (in orange) is plotted for comparison.
• Figure 4: $\vert$ Impact of the microscopic hopping processes on itinerant ferromagnetism in the Hubbard model. (a)-(f) Static spin structure factor $S(\mathbf{q})$ ((a)-(c)) and the momentum distribution $n(\mathbf{k})$ ((d)-(f)) obtained by independently turning off each hopping process: (a),(d) $t_\mathrm{PQ}=0$, (b),(e), $t_\mathrm{PP}=0$, (c),(f), $t_\mathrm{QQ}=0$. Other hopping terms in Eq. \ref{['eq:SepHoppingHt']} are set to $t$. The white hexagon indicates the first Brillouin zone; interpolation is applied to contours. Here, we fix the system size as $8\times 4$ cylinders, the electron doping $\delta=1/2$, and the interaction strength $U=10$.
• Figure 5: $\vert$ Magnetic phase diagram and stability. (a) Renormalized ferromagnetic order parameter $m_s^2(\mathbf{\Gamma})/m_{s,\mathrm{F}}^2(\mathbf{\Gamma})$ for the Hubbard model \ref{['eq:model']} as a function of electron doping $\delta$ and $U/t$, where $U$ is the on-site Hubbard interaction, and $t$ is the nearest-neighbor (NN) hopping amplitude. Here, $m_{s,\mathrm{F}}^2(\mathbf{\Gamma})\equiv[(1-\delta)/2]^2$ is full polarization value of $m_s^2(\mathbf{\Gamma})$. Circles denote the data obtained numerically. (b) Average NN spin correlations $\bar{S}(r=1)$ as a function of doping $\delta$ on cylinders of width $L_y=4,6$, resembling cold-atom quantum simulator findings MuqingXu2023 for the same model. (c) Static structure factor $S(\mathbf{q})$ at the $\boldsymbol{\Gamma}$ point as a function of $J_3$, for the Hubbard model with additional term $\delta H =-J_{3}\sum_{\langle\mathbf{i}\mathbf{j}\rangle} S_{\mathbf{i}}^{z}S_{\text{$\mathbf{j}$}}^{z}$ at $U=10$ and $8\times4$ cylinder. The ferromagnetism persists for $J_3 > 0$. Inset: $S(\mathbf{q})$ for $J_3=3$.