Discriminating antiferromagnetic signatures in systems of ultracold fermions by tunable geometric frustration

Recently, it has become possible to tune optical lattices continuously between square and triangular geometries. We compute thermodynamics and spin correlations in the corresponding Hubbard model using a determinant quantum Monte Carlo technique and show that the frustration effects induced by the variable hopping terms can be clearly separated from concomitant bandwidth changes by a proper rescaling of the interaction. An enhancement of the double occupancy by geometric frustration signals the destruction of nontrivial antiferromagnetic correlations at weak coupling and entropy $s\lesssim \ln \left(2\right)$ (and restores Pomeranchuk cooling at strong frustration), paving the way to the long-sought experimental detection of antiferromagnetism in ultracold fermions on optical lattices.

Figure 1

(a) Double occupancy $D$ versus entropy $s$ at scaled interaction $U=4t_{\alpha }$ and variable frustration $\alpha =t^{\prime }/t$. Solid line: DMFT estimate of $D\left(s\right)$ at $\alpha =0$. Inset: At unscaled $U=4t$, $D\left(s\right)$ does not collapse. (b) Short-range spin-correlation functions $C_{(1,0)}$ and $C_{(1,1)}$ (equivalent in triangular limit $\alpha =1$) at $U=4t_{\alpha }$. Inset: Square lattice geometry used in simulations and topologically equivalent anisotropic triangular lattice. (c) Longer-range spin correlation $C_{(2,0)}$. (d) $D\left(s\right)$ at density $n=0.9$ and frustration $\alpha$ at $U/t_{\alpha }=4$. Vertical dotted lines indicate $s^{*}\equiv \ln \left(2\right)$.

Figure 2

Double occupancy $D$ versus entropy $s$ (left column) and temperature $T/t_{\alpha }$ (right column) at strong coupling $U=12.25t_{\alpha }$ (top) and $U=8t_{\alpha }$ (bottom).

Figure 3

Short-range spin-correlation functions $C_{(1,0)}$ and $C_{(1,1)}$ at $U=8t_{\alpha }$. The vertical dotted line indicates $s^{*}\equiv \ln \left(2\right)$. Inset: spin-correlation function $C_{(2,0)}$.

Figure 4

Entropy $s$ versus temperature $T/t_{\alpha }$ at various interactions $U/t_{\alpha }$. Data at frustration $\alpha >0$ is offset vertically (by $2.5\alpha$); black solid lines represent $U=0$ results for the square lattice as a common reference. Horizontal bars indicate the effect of adiabatic cooling at entropy $s=0.6$, which increases roughly linearly with $\alpha$.

Figure 5

The effect of finite Trotter discretization $\Delta \tau$ on DQMC estimates of the double occupancy $D$ at weak coupling $U=4t_{\alpha }$ and variable frustration $\alpha$. Colored lines show least-squares fits linear in ${\left(\Delta \tau \right)}^2$. The thin vertical line marks the value of $\Delta \tau t_{\alpha }=0.04$ used in the main paper. Thin horizontal lines correspond to extrapolated values of $D$.

Figure 6

The effect of finite Trotter discretization $\Delta \tau$ on DQMC estimates of the double occupancy $D$ at weak coupling $U=4t_{\alpha }$ and variable frustration $\alpha$. The data at $\Delta \tau t_{\alpha }=0.04$ (thin gray symbols) are compared with corresponding $\Delta \tau$ extrapolations (bold colored symbols).

Figure 7

The effect of finite Trotter discretization $\Delta \tau$ on DQMC estimates of double occupancy $D$ (main panel) and entropy per particle $s$ (inset) at strong coupling $U=12.25t_{\alpha }$ for the square lattice ($\alpha =0$). The data for $\Delta \tau t_{\alpha }=0.04$ (thin dashed lines) are compared with corresponding $\Delta \tau$ extrapolations (Ref. 20) (bold solid lines).

Figure 8

Finite-size effects on the DQMC estimates of double occupancy $D$ and spin-spin correlations $C_{(1,0)}$ and $C_{(1,1)}$ at weak coupling $U=4t_{\alpha }$ for a square lattice ($\alpha =0$) for a set of thermal parameters: $\beta t=5.0$, $s=0.25\pm 0.02$ (open squares and solid lines), $\beta t=3.6$, $s=0.4\pm 0.02$ (filled squares and dashed lines), $\beta t=3.0$, $s=0.46\pm 0.02$ (open circles and short-dashed lines). Colored lines show linear least-squares fits with respect to $L^{-2}$. Thin vertical line marks the value of $L=8$ used in the main paper. Thin horizontal lines correspond to the extrapolated values of observables.