Fate of 1D Spin-Charge Separation Away from Fermi Points

We consider the dynamic response functions of interacting one dimensional spin-$\frac{1}{2}$ fermions at arbitrary momenta. We build a nonperturbative zero-temperature theory of the threshold singularities using mobile impurity Hamiltonians. The interaction induced low-energy spin-charge separation and power-law threshold singularities survive away from Fermi points. We express the threshold exponents in terms of the spinon spectrum.

Figure 1

Structure of the spectral function $A(k,\omega )$ in the $(k,\omega )$-plane (a) and along a cut for fixed $0<k<k_F$ (b),(c). (a) Shaded areas indicate the regions where $A(k,\omega )$ is nonzero. (b) Luttinger liquid (LL) results: in the vicinity of the spinon mass shell, $A(k,\omega )\propto (\omega -v_{s}k{)}^{-{\mu }_{-}^{\mathrm{LL}}}$ where ${\mu }_{-}^{\mathrm{LL}}=\frac{1}{2}-\frac{1}{4}(K_c+K_c^{-1}-2)$. (c) Schematic behavior of the spectral function beyond the LL approximation away from the Fermi points: the exponent ${\mu }_{0,-}$ is different from ${\mu }_{-}^{\mathrm{LL}}$, the charge mode is smeared out, and for $\omega >0$ the region of finite support starts from $-{ϵ}_s(k)$ with an exponent ${\mu }_{0,+}$ instead of from $-{ϵ}_c(k)$.