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

Cheianov, Vadim V.; Zvonarev, M. B.

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

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Description

In this Letter we present a calculation of the one-particle irreducible density matrix $ρ(x)$ 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 $ρ(x)$ we derive analytical expressions for both large and small $x$ at an arbitrary filling factor $0<\varrho<1/2.$ The large $x$ asymptotics of $ρ(x)$ is found to be remarkably accurate starting from $x\sin(2π\varrho)\sim 1.$ We find that the one-particle momentum distribution function $ρ(k)$ is a smooth function of $k$ peaked at $k=2k_F,$ thus violating the Luttinger theorem.
4 pages, 3 figures