Electric field control of a quantum spin liquid in weak Mott insulators

TL;DR

Applying a DC electric field to the triangular lattice Hubbard model can tune the system into a chiral spin liquid phase by enhancing ring exchange interactions, offering a new method for experimental control of quantum spin liquids.

Contribution

The paper derives how electric fields modify exchange interactions and demonstrates, via DMRG, that electric fields can induce a chiral spin liquid phase in the model.

Findings

Electric field enhances ring exchange interactions relative to Heisenberg interactions.

Electric field shifts the phase boundary, favoring the spin liquid phase.

Electric field can drive a transition from magnetic order to spin liquid.

Abstract

The triangular lattice Hubbard model at strong coupling, whose effective spin model contains both Heisenberg and ring exchange interactions, exhibits a rich phase diagram as the ratio of the hopping $t$ to onsite Coulomb repulsion $U$ is tuned. This includes a chiral spin liquid (CSL) phase. Nevertheless, this exotic phase remains challenging to realize experimentally because a given material has a fixed value of $t/U$ that can difficultly be tuned with external stimuli. One approach to address this problem is applying a DC electric field, which renormalizes the exchange interactions as electrons undergo virtual hopping processes; in addition to creating virtual doubly occupied sites, electrons must overcome electric potential energy differences. Performing a small $t/U$ expansion to fourth order, we derive the ring exchange model in the presence of an electric field and find that it not only introduces spatial anisotropy but also tends to enhance the ring exchange term compared to the dominant nearest-neighbor Heisenberg interaction. Thus, increasing the electric field serves as a way to increase the importance of the ring exchange at constant $t/U$. Through density matrix renormalization group calculations, we compute the ground state phase diagram of the ring exchange model for two different electric field directions. In both cases, we find that the electric field shifts the phase boundary of the CSL towards a smaller ratio of $t/U$. Therefore, the electric field can drive a magnetically ordered state into the CSL. This explicit demonstration opens the door to tuning other quantum spin systems into spin liquid phases via the application of an electric field.