Interplay of magnetic and thermodynamic responses in the kagome-triangular system

TL;DR

This study probes how geometric frustration and electronic correlations compete in the kagome lattice by introducing a tunable hopping $t'/t$ to interpolate toward the triangular lattice, analyzed via determinant quantum Monte Carlo (DQMC) for the Hubbard model. It finds that increasing $t'/t$ suppresses nearest-neighbor antiferromagnetic correlations while enabling a sign change in longer-range ($r=2$) correlations around $t'/t \approx 0.3$–$0.4$, accompanied by a low-temperature peak in the specific heat that signals a spin-related energy scale. The on-site interaction $U$ strengthens magnetic correlations and shifts the crossover to larger $t'/t$, with finite-size checks supporting robustness and the sign problem constraining accessible regimes. Together, these results illuminate how frustration and correlations shape magnetic and thermodynamic responses in kagome systems and offer a framework for interpreting anomalous low-$T$ thermodynamics observed in related frustrated materials.

Abstract

Inspired by the recent experimental progress in pyrochlore derivative \ce{RE3Sb3A2O14 (A=Mg, Zn)}, we investigate the Hubbard model on the kagome lattice with an additional hopping $t'/t$, which enables continuous interpolation between the kagome and triangular lattices by using determinant quantum Monte Carlo simulations. We analyze the evolution of magnetic correlations and thermodynamic responses across different values of $t'/t$ and on-site interaction $U$. It is found that increasing $t'/t$ suppresses short-range antiferromagnetic correlations, while the next-nearest-neighbor correlations exhibit a sign change near $t'/t \approx 0.3 \text{--} 0.4$. Within this regime, the specific heat shows a pronounced low-temperature peak, indicating an emergent spin-related energy scale. Increasing $U$ enhances magnetic correlations and shifts the associated $t'/t$ crossover points to larger values. We also discuss the sign problem to clarify which parameter region of our numerical simulations is accessible and reliable. Our results uncover the competition between frustration and correlations and the interplay of magnetic and thermodynamic responses in the kagome lattice, providing insights into correlated states in frustrated materials.

Figures (6)

• Figure 1: Sketch of the kagome lattices with a set of isolated sites, which can also be viewed as introducing an infinitely repulsive single-electron potential on the $d$ sites; points $a$, $b$, and $c$ comprise the unit cell of the kagome lattice. Solid and dashed lines indicate hopping amplitudes $t$ and $t'$, respectively.
• Figure 2: (a) The spin-spin correlations $c^{bc}(r = 1)$ between the nearest-neighbor $b$ and $c$ sites and (b) the correlations $c^{cc}(r = 2)$ between the next-nearest-neighbor $c$ sites as a function of $t'/t$ for different $U$ at $L=6$ and $T=t/6$. Error bars are not shown when they are smaller than the data points.
• Figure 3: The local moment $\langle m^2 \rangle$ as a function of $t'/t$ for different interaction strength $U$ at $L=6$ and $T=t/6$. Error bars are not shown when they are smaller than the data points.
• Figure 4: (a) The spin-spin correlations $c^{bc}(r = 1)$ and (b) the correlations $c^{cc}(r = 2)$ for lattice sizes $L=6$ and $L=8$ at fixed $U=3.0t$ and $T=t/6$. Error bars are not shown when they are smaller than the data points.
• Figure 5: The specific heat $C(T)$ as a function of temperature $T$ (a) for different values of $t'/t$ at $L=6$ and $U=3.0t$ and (b) for different values of $U$ at fixed $t'/t=0.3$. The specific heat is obtained from the exponential fit and is shown in a log-linear scale.