Extended Crossover from a Fermi Liquid to a Quasiantiferromagnet in the Half-Filled 2D Hubbard Model

The ground state of the Hubbard model with nearest-neighbor hopping on the square lattice at half filling is known to be that of an antiferromagnetic (AFM) band insulator for any on-site repulsion. At finite temperature, the absence of long-range order makes the question of how the interaction-driven insulator is realized nontrivial. We address this problem with controlled accuracy in the thermodynamic limit using self-energy diagrammatic determinant Monte Carlo and dynamical cluster approximation methods and show that development of long-range AFM correlations drives an extended crossover from Fermi liquid to insulating behavior in the parameter regime that precludes a metal-to-insulator transition. The intermediate crossover state is best described as a non-Fermi liquid with a partially gapped Fermi surface.

Figure 1

Crossover lines between the Fermi-liquid (FL, red), non-Fermi-liquid (nFL, gray), and quasi-AFM insulator (I, blue) regimes of the half-filled 2D Hubbard model (1) on the square lattice in the $U\text{−}T$ plane obtained by $\mathrm{\Sigma }\mathrm{DDMC}$. The solid lines fit data by the functions $T_{\mathrm{an}}=a\exp (-b/\sqrt{U})$ and $T_{\mathrm{n}}=a^{\prime }\exp (-b^{\prime }/\sqrt{U})$ with $\{a,b,a^{\prime },b^{\prime }\}=\{6.99,6.51,4.7,6.08\}$. It follows that below $U=2.5t$ the low-temperature physics is of the mean-field character, while beyond $U=4t$ the low-temperature behavior is expected to resemble that of the Heisenberg model.

Figure 2

Illustration of the FL-to-insulator crossover at $T/t=0.1$: evolution of the self-energy (imaginary part) at the two lowest Matsubara frequencies ${\omega }_0$ and ${\omega }_1$ at the momentum ${\mathbf{k}}_{\mathrm{an}}=(\pi ,0)$ (left panel) and ${\mathbf{k}}_n=(\pi /2,\pi /2)$ (right panel) with increasing $U$. Colors correspond to FL, nFL, and quasi-AFM insulator regions of Fig. 1.

Figure 3

Imaginary part of the self-energy obtained by DCA and compared to $\mathrm{\Sigma }\mathrm{DDMC}$ at ${\mathbf{k}}_n$ (left) and ${\mathbf{k}}_{\mathrm{an}}$ (right) in the insulating regime, $U/t=3$, $T/t=0.12$ (cluster sizes are $N_c=16$, 64, 72, 128, 144).

Figure 4

(Quasi)momentum distribution $n(\mathbf{k})$ (top row), $\mathrm{Im}{\mathrm{\Sigma }}_{\mathbf{k}}(i{\omega }_0)$ (middle row), and $\mathrm{\Delta }{\mathrm{\Sigma }}_{\mathbf{k}}$ (bottom row) in the Brillouin zone at $T=0.2t$ and different values of $U$ (columns).