Density matrix renormalization group study of a three-orbital Hubbard model with spin-orbit coupling in one dimension

TL;DR

This study uses the Density Matrix Renormalization Group method to analyze how spin-orbit coupling influences the phase diagram of a three-orbital Hubbard model in one dimension, revealing phase transitions and potential material realizations.

Contribution

It provides the first detailed DMRG analysis of a three-orbital Hubbard model with spin-orbit coupling in one dimension, complementing higher-dimensional studies.

Findings

Transition from orbital-selective Mott phase to excitonic insulator with increasing spin-orbit coupling.

Identification of a non-magnetic insulator with effective angular momentum near the excitonic phase.

Qualitative agreement with dynamical mean field theory results in higher dimensions.

Abstract

Using the Density Matrix Renormalization Group technique we study the effect of spin-orbit coupling on a three-orbital Hubbard model in the $(t_{2g})^{4}$ sector and in one dimension. Fixing the Hund coupling to a robust value compatible with some multiorbital materials, we present the phase diagram varying the Hubbard $U$ and spin-orbit coupling $\lambda$, at zero temperature. Our results are shown to be qualitatively similar to those recently reported using the Dynamical Mean Field Theory in higher dimensions, providing a robust basis to approximate many-body techniques. Among many results, we observe an interesting transition from an orbital-selective Mott phase to an excitonic insulator with increasing $\lambda$ at intermediate $U$. In the strong $U$ coupling limit, we find a non-magnetic insulator with an effective angular momentum $\langle(\textbf{J}^{eff})^{2}\rangle \ne 0$ near the excitonic phase, smoothly connected to the $\langle(\textbf{J}^{eff})^{2}\rangle = 0$ regime. We also provide a list of quasi-one dimensional materials where the physics discussed in this publication could be realized.