Breakdown of the Luttinger sum rule within the Mott-Hubbard insulator

The validity of the Luttinger sum rule is investigated within the prototype tight-binding model of interacting fermions in one dimension, i.e., the $t\text{−}V$ model including the next-nearest-neighbor hopping $t^{\prime }$, in order to break the particle-hole symmetry. Scaling analysis of finite-system results at half filling reveals evident breakdown of the sum rule in the large gap regime at $V⪢t$ while the sum rule appears to recover together with vanishing of the Mott-Hubbard gap.

Figure 1

(Color online) Scaled gap ${\Delta }_0$ for nonsymmetric case $t^{\prime }=0.4t$ (points), and exact Bethe ansatz results for $t^{\prime }=0$ (line).

Figure 2

(Color online) Evolution of $\text{Re}G\left(k,0\right)$ with increasing interaction $V$ for $t^{\prime }/t=0.4$ and for half-filled system of $N=26$ sites with allowed wave vectors (points), and indications of $k_F=\pi /2$ (dashed line) and $k_L$ (full line). Points are connected with straight lines.

Figure 3

(Color online) Scaling of $\overline{G}\left(N\right)$ for two values of $V/t$ and $t^{\prime }=0.4t$.

Figure 4

(Color online) Scaling of $\Delta G\left(N\right)$ for two values of $V/t$ and $t^{\prime }=0.4t$.

Figure 5

(Color online) Calculated Luttinger momentum $k_L$ vs $V/t$ for two values of $t^{\prime }/t$.