Metal-insulator transition and thermal scales in $d$-wave altermagnet

Abstract

We present the first finite-temperature study of a strongly correlated $d$-wave altermagnet across the Mott insulator-metal transition using a non-perturbative numerical approach. We map out the thermal phase diagram and provide quantitative estimates of the transition scales in an interacting altermagnet. We show that altermagnetism-induced geometric frustration stabilizes a finite-temperature correlated magnetic metal and enhances the magnetic transition scale across regimes of interaction. These results establish the finite-temperature landscape of correlated altermagnets and clarify the role of strong electronic interactions in this phase.

Figures (8)

• Figure 1: Finite-temperature phase diagram in the $T-t_{am}$-plane at (a) weak $(U=t)$ and (b) strong $(U=6t)$ coupling. The thermal scales $T_{c}$ and $T_{Mott}$ quantify the loss of magnetic correlations and the collapse of the Mott gap, respectively.
• Figure 2: Temperature dependence of the (a)-(b) static magnetic structure factor ($S(q=(\pi,\pi))$) and (c)-(d) single particle DOS ($N(\omega)$) at selected $t_{am}$ for $U=t$ and $U=6t$, respectively.
• Figure 3: Spin-split spectral function $\Delta A(k, \omega) = A_{\uparrow} (k, \omega) - A_{\downarrow}(k, \omega)$ defined along the high symmetry trajectory $\Gamma - X - M$ for the representative weak $(U=t)$ and strong $(U=6t)$ coupling, at $T=0.01t$ and $T=0.20t$.
• Figure 4: (a)-(c) Real space maps (${\bf m}_{i}.{\bf m}_{j}$) representing the ALM-I, ALM-M and PM-M, respectively, at $U=t$ and $t_{am}=0.15t$, for a single Monte Carlo snapshot. Thermal evolution of the (d)-(e) local moment distribution and (f)-(g) ALM correlation ($\Delta A({\bf k})$) at $\omega \sim -3.5t$, for $U=t$ and $U=6t$, respectively, at selected $t_{am}-T$ cross sections.
• Figure S1: (a) Schematic representation of the square lattice with $L = 6 \times 6$ with reference $x-y$ axes and the corresponding anisotropic hopping $\hat{t}_x$ and $\hat{t}_y$. (b) Tight binding energy dispersion of the model along high symmetry path $[\Gamma - X - M- \Gamma - Y - M - \Gamma]$ in reciprocal space with $U = 0t \:, t = 1.0 \:, t_{am} = 1.0t \:, \mu = -2.0$. (c) corresponding Fermi-Surface contours for spin $\uparrow$ and spin $\downarrow$ sectors.