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arXiv:0909.1622 · Physical Review B

Magnetic-flux tuning of spin chirality in Mott insulators with ring exchanges

Yi-Fei Wang, Chang-De Gong

Published Oct 27, 2010• 1 citation
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Abstract

A peculiar manifestation of the Aharonov-Bohm effect in Mott insulators, presents as a versatile scheme to manipulate the intriguing ground-state spin chirality, such as, tune the magnitude continuously, switch an abrupt jump, or even reverse its sign from a para-chiral phase to a dia-chiral phase. Such an unusual mechanism is due to the coupling between multiple-spin ring exchanges and magnetic flux, and the competition between spin chirality and magnetism, and is demonstrated explicitly in both quasi-one-dimensional ladders and two-dimensional lattices with triangles as elementary plaquettes.

DOI
10.1103/physrevb.82.132406

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A peculiar manifestation of the Aharonov-Bohm effect in Mott insulators, presents as a versatile scheme to manipulate the intriguing ground-state spin chirality, such as, tune the magnitude continuously, switch an abrupt jump, or even reverse its sign from a para-chiral phase to a dia-chiral phase. Such an unusual mechanism is due to the coupling between multiple-spin ring exchanges and magnetic flux, and the competition between spin chirality and magnetism, and is demonstrated explicitly in both quasi-one-dimensional ladders and two-dimensional lattices with triangles as elementary plaquettes.
πππ-Flux Tuning of Quantum Paramagnetism in the Triangular-Lattice Hubbard Model
We compare two time-reversal-symmetric triangular-lattice Hubbard models at half filling: the zero-flux model and a staggered πππ-flux model with zero and πππ flux through oppositely oriented triangles. Although both reduce to the same Heisenberg model at leading order in the strong-coupling limit, their distinct charge fluctuation profiles yield different quantum paramagnetic regimes. Combining a strong-coupling expansion with infinite density matrix renormalization group (iDMRG) calculations, we find that the positive ring-exchange of the zero-flux model promotes spontaneous chirality, consistent with its notion of a chiral spin liquid at intermediate coupling. In the staggered-πππ-flux model, whose noninteracting limit is a Dirac semimetal, the ring exchange changes sign and disfavors chiral order and we find no resolvable scalar chirality. This renders flux-tuned ring-exchange an efficient discriminator between chiral and non-chiral quantum paramagnets at finite coupling.
Motivated by experiments on Josephson junction arrays, and cold atoms in an optical lattice in a synthetic magnetic field, we study the ``fully frustrated'' Bose-Hubbard model with half a magnetic flux quantum per plaquette. We obtain the phase diagram of this model on a two-leg ladder at integer filling via the density matrix renormalization group approach, complemented by Monte Carlo simulations on an effective classical XYXYXY model. The ground state at intermediate correlations is consistently shown to be a chiral Mott insulator (CMI) with a gap to all excitations and staggered loop currents which spontaneously break time-reversal symmetry. We characterize the CMI state as a vortex supersolid or an indirect exciton condensate, and discuss various experimental implications.
We explore the Mott insulating phases of dual-species bosonic spinor lattice gases, emphasizing the intriguing interplay between synthetic flux and inter-species spin exchange interaction. One of the species is subjected to Raman assisted tunneling, which leads to a synthetic flux within the framework of synthetic dimensions. In the deep Mott regime, the low energy physics is governed by an unconventional and highly tunable spin model, which is characterized by two distinct spin chains. The synthetic flux serves as an effective spin-orbit coupling, inducing Dzyaloshinskii-Moriya interactions in one of the spin chains. The inter-species spin exchange interaction gives rise to the inter-chain coupling embodied as an isotropic XX interaction. Using time-evolving block decimation method for tensor network states, we compute order parameters, correlation functions and structure factors to identify the ground state magnetic phases. The DM interaction in one species, when combined with the inter-species spin-exchange interaction, can induce spiral magnetic order in the second, otherwise non-chiral species. Besides, the interplay of a transverse field applied to one spin chain and the inter-species coupling can drive both spin chains into a paramagnetic phase simultaneously. These results reveal that inter-species coupling serves as a powerful conduit for transmitting magnetic correlations, enabling exotic phases beyond the single-component perspective.
Ground-state properties of one-dimensional quantum rings with a few electrons, which interact with each other in the form of 1∕r1∕r1∕r Coulomb repulsion, are studied by exact diagonalization. For three electrons, the fully spin-polarized ground state is uniquely realized when the diameter of the ring is sufficiently large. In contrast, for four and five electrons, the fully polarized state never becomes the unique ground state, however large the diameter is. These results can be understood in terms of the multiple-spin exchange. When a perpendicular magnetic field is applied to the ring (i.e., the Aharonov-Bohm flux is introduced), the persistent current occurs, and the spin chirality is finite for a certain value of the flux. The difference between the quantum ring and the circularly arranged quantum dots is also discussed.
Magnetic exchange couplings can be tuned by coupling to periodic light, where the frequency and amplitude are typically varied: a process known as Floquet engineering. The polarization of the light is also important, and in this paper, we show how different polarizations, including several types of unpolarized light, can tune the exchange couplings in distinct ways. Using unpolarized light, for example, it is possible to tune the material without breaking either time-reversal or any lattice symmetries. To illustrate these effects generically, we consider single-band Hubbard models at half-filling on the honeycomb, square and triangular lattices. We derive the effective Heisenberg spin models to fourth order in perturbation theory for arbitrary fixed polarizations, and several types of unpolarized light that preserve time-reversal and lattice symmetries. Coupling these models to periodic light tunes first, second, and third neighbor exchange couplings, as well as ring exchange terms on the square and triangular lattices. Circularly polarized light induces chiral fields for the honeycomb and triangular lattices, which favors noncoplanar magnetism and potential chiral spin liquids. We discuss how to maximize the enhancement of the couplings without inducing heating.
We propose multi-layer moire structures in strong external magnetic fields as a novel platform for realizing highly-tunable, frustrated Hubbard physics with topological order. Identifying the layer degree of freedom as a pseudo spin, allows us to retain SU(2) symmetry while controlling ring-exchange processes and concurrently quenching the kinetic energy by large external magnetic fields. This way, a broad class of interacting Hubbard-Hofstadter states and their transitions can be studied. Remarkably, in the limit of strong interactions the system becomes Mott insulating and we find chiral pseudo spin liquid phases which are induced by the magnetic field. We find that this topologically ordered state remains exceptionally stable towards relevant perturbations. We discuss how layer pseudo-spin can be probed in near-term experiments. As the magnetic flux can be easily tuned in moire systems, our approach provides a promising route towards the experimental realization and control of topologically ordered phases of matter.