One-particle irreducible density matrix for the spin disordered infinite $U$ Hubbard chain

In this Letter we present a calculation of the one-particle irreducible density matrix $\rho(x)$ for the one-dimensional (1D) Hubbard model in the infinite $U$ limit. We consider the zero temperature spin disordered regime, which is obtained by first taking the limit $U\to \infty$ and then the limit $T\to 0.$ Using the determinant representation for $\rho(x)$ we derive analytical expressions for both large and small $x$ at an arbitrary filling factor $0<\varrho<1/2.$ The large $x$ asymptotics of $\rho(x)$ is found to be remarkably accurate starting from $x\sin(2\pi\varrho)\sim 1.$ We find that the one-particle momentum distribution function $\rho(k)$ is a smooth function of $k$ peaked at $k=2k_F,$ thus violating the Luttinger theorem.