Spin, charge and $\eta$-spin separation in one-dimensional photo-doped Mott insulators

TL;DR

This paper demonstrates that in one-dimensional photo-doped Mott insulators, spin, charge, and $$-spin degrees of freedom are effectively separated, with wave functions analogous to Ogata-Shiba states, revealing detailed correlation properties.

Contribution

It introduces an analytical wave function framework for photo-doped Mott insulators showing spin, charge, and $$-spin separation, extending Ogata-Shiba states to non-equilibrium conditions.

Findings

Wave functions factorize into charge, spin, and $$-spin parts.

Metastable $$-pairing and CDW states correspond to gapless and gapful XXZ states.

Central charges for $$-pairing and CDW states are 3 and 2, respectively.

Abstract

We show that effectively cold metastable states in one-dimensional photo-doped Mott insulators described by the extended Hubbard model exhibit spin, charge and $\eta$-spin separation. Namely, their wave functions in the large on-site Coulomb interaction limit can be expressed as $|\Psi\rangle =|\Psi_{\rm charge}\rangle|\Psi_{\rm spin}\rangle |\Psi_{\rm \eta-spin}\rangle$, which is analogous to the Ogata-Shiba states of the doped Hubbard model in equilibrium. Here $\eta$-spin represents the type of the photo-generated pseudeparticles (doublon or holon). $|\Psi_{\rm charge}\rangle$ is determined by spinless free fermions, $|\Psi_{\rm spin}\rangle$ by the isotropic Heisenberg model in the squeezed spin space, and $|\Psi_{\rm \eta-spin}\rangle$ by the XXZ model in the squeezed $\eta$-spin space. In particular, the metastable $\eta$-pairing and charge-density-wave (CDW) states correspond to the gapless and gapful states of the XXZ model. The specific form of the wave function allows us to accurately determine the exponents of correlation functions. The form also suggests that the central charge of the $\eta$-pairing state is 3 and that of the CDW phase is 2, which we numerically confirm. Our study provides analytic and intuitive insights into the correlations between active degrees of freedom in photo-doped strongly correlated systems.