A hole injected into a Mott insulator will gain an internal structure as recently identified by exact numerics, which is characterized by a nontrivial quantum number whose nature is of central importance in understanding the Mott physics. In this work, we show that a spin texture associated with such an internal degree of freedom can explicitly manifest after the spin degeneracy is lifted by a weak Rashba spin-orbit coupling (SOC). It is described by an emergent angular momentum ${J}_{z}=\ifmmode\pm\else\textpm\fi{}\frac{3}{2}$ as shown by both exact diagonalization and variational Monte Carlo calculations, which are in good agreement with each other at a finite size. In particular, as the internal structure such a spin texture is generally present in the hole composite even at high excited energies, such that a corresponding texture in momentum space, extending deep inside the Brillouin zone, can be directly probed by the spin-polarized angle-resolved photoemission spectroscopy (ARPES). This is in contrast to a Landau quasiparticle under the SOC, in which the spin texture induced by SOC will not be protected once the excited energy is larger than the weak SOC coupling strength, away from the Fermi energy. We point out that the spin texture due to the SOC should be monotonically enhanced with reducing spin-spin correlation length in the superconducting-pseudogap phase at finite doping. A brief discussion of a recent experiment of the spin-polarized ARPES will be made.
The recent experimental observations of loop current in
Sr2IrO4, YBa2Cu3O7, and
Sr14Cu24O41 have inspired a theoretical study that broadly redefines loop current as a manifestation of quantum liquid crystals. Using the density-matrix renormalization group method, we investigate the emergence of spin loop-current (sLC) textures in carrier-doped (i) excitonic insulators, (ii) orbital-selective Mott insulators, and (iii) two-dimensional Mott insulators, modeled by a two-orbital Hubbard model on a ladder lattice in (i) and (ii) and a single-orbital Hubbard model on a square lattice in (iii). Calculating the spatial distribution of spin current around a bond to which a pinning field is applied, we find conditions for longer-ranged sLC correlations. In system (i), when using the model parameters employed to describe the excitonic condensation, we find that a sLC texture appears near half-filling, associated with an excitonic condensation in a spin channel. In system (ii), using typical sets of model parameters for
BaFe2Se3, we find that a sLC texture appears at electron fillings where a block-type antiferromagnetism develops. In system (iii), introducing a next-nearest-neighbor hopping ${t}^{\ensuremath{'}}\ensuremath{\sim}\ensuremath{-}0.25$ (in units of the nearest-neighbor hopping) suggested for high-
Tc cuprates, we find that an axial-sLC texture emerges at hole-carrier density $\ensuremath{\delta}=0.125$, where the charge stripe simultaneously appears.
We study the Mott phase of three-component bosons, with one particle per site, in an optical lattice by mapping it onto an SU(3) spin model. In the simplest case of full SU(3) symmetry, one obtains a ferromagnetic Heisenberg model. Introducing an SU(3) analog of spin-orbit coupling, additional spin-spin interactions are generated. We first consider the scenario of spin-dependent hopping phases, leading to Dzyaloshinskii-Moriya-type interactions. They result in the formation of spiral spin textures, which in one dimension can be understood by a local unitary transformation. Applying classical Monte Carlo simulations, we extend our study to two-dimensional systems, and systems with ``true'' spin-orbit coupling, involving spin-changing hoppings.