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Bulletin of the American Physical Society

Effects of charge doping a Mott insulator with strong spin-orbit coupling

Erick Garcia, Paola Caterina Forino, Rong Cong, Phuong Tran, Anna Tassetti, G. Allodi, Arneil P. Reyes, Patrick M. Woodward, Samuele Sanna, V. F. Mitrović

Published Mar 16, 2021• 0 citations
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We study the effects of hole doping on one-dimensional Mott insulators with orbital degrees of freedom. We describe the system in terms of a generalized $t\text{\ensuremath{-}}J$ model. At a specific point in parameter space the model becomes integrable in analogy to the one-band supersymmetric $t\text{\ensuremath{-}}J$ model. We use the Bethe ansatz to derive a set of nonlinear integral equations which allow us to study the thermodynamics exactly. Moving away from this special point in parameter space we use the density-matrix renormalization group applied to transfer matrices to study the evolution of various phases of the undoped system with doping and temperature. Finally, we study a one-dimensional version of a realistic model for cubic titanates which includes the anisotropy of the orbital sector due to Hund's coupling. We find a transition from a phase with antiferromagnetically correlated spins to a phase where the spins are fully ferromagnetically polarized, a strong tendency toward phase separation at large Hund's coupling, as well as the possibility of instability toward triplet superconductivity.
Experiments on ultracold atoms have started to explore lattice effects and thermal fluctuations for two-component bosons with spin-orbit coupling (SOC). Motivated by this, we derive and study a tJ model for lattice bosons with equal Rashba-Dresselhaus SOC and strong Hubbard repulsion in a uniform Zeeman magnetic field. Using the Gutzwiller ansatz, we find strongly correlated ground states with stripe superfluid (SF) order. We formulate a finite temperature generalization of the Gutzwiller method, and show that thermal fluctuations in the doped Mott insulator drive a two-step melting of the stripe SF, revealing a wide regime of a stripe normal fluid.