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Physica Scripta

Effective spin models and magnetic phases of an insulating bosonic ladder with unconventional synthetic flux

Zong-Zhen Pan, Shi-Jie Yang, Yi Zheng

Published Sep 18, 2024• 1 citation
Publisher

Abstract

Abstract We investigate the Mott insulating phases of a two-component bosonic lattice gas in the presence of gauge field. Such a system is described by a two-leg ladder model with an unconventional flux. The synthetic flux is generated by the spin-dependent tunneling and the site-dependent spin-flip. In the Mott regime, these two effects lead to Dzyaloshinskii-Moriya (DM) interaction and an external field that is rotating in the xy-plane. We obtain a very general XYZ model with the DM interaction, the spiral field, and the transverse field. Various interesting magnetic Hamiltonians can be covered by adjusting lattice parameters. The DM interaction or the spiral field can lead to spiral order when they appear alone. The interplay of DM coupling and spiral field leads to the emergence of a new multi-frequency spiral order between the paramagnetic phase and the spiral ferromagnetic phase. Ground state phases are investigated by focusing on order parameters, spin-spin correlation functions, and structure factors. Calculations are performed by using time evolution block decimation (TEBD) based on matrix product state (MPS).

DOI
10.1088/1402-4896/ad7c92

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Abstract We investigate the Mott insulating phases of a two-component bosonic lattice gas in the presence of gauge field. Such a system is described by a two-leg ladder model with an unconventional flux. The synthetic flux is generated by the spin-dependent tunneling and the site-dependent spin-flip. In the Mott regime, these two effects lead to Dzyaloshinskii-Moriya (DM) interaction and an external field that is rotating in the xy-plane. We obtain a very general XYZ model with the DM interaction, the spiral field, and the transverse field. Various interesting magnetic Hamiltonians can be covered by adjusting lattice parameters. The DM interaction or the spiral field can lead to spiral order when they appear alone. The interplay of DM coupling and spiral field leads to the emergence of a new multi-frequency spiral order between the paramagnetic phase and the spiral ferromagnetic phase. Ground state phases are investigated by focusing on order parameters, spin-spin correlation functions, and structure factors. Calculations are performed by using time evolution block decimation (TEBD) based on matrix product state (MPS).
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.
We study the effective spin models for a Mott insulating Bose-Hubbard model in the presence of gauge fields. We first introduce a simple method based on adiabatic elimination to determine the low-energy effective Hamiltonian. Demonstration of a two-component one-dimensional model with synthetic magnetic field is shown. We further consider a generalized Bose-Hubbard model which covers the cases where spin-orbit coupling and synthetic flux are present. The resulting XYZ model contains Dzyaloshinskii-Moriya interactions and symmetric anisotropic couplings. Under certain conditions, this model reduces to various interesting magnetic Hamiltonians. Phase diagrams for two typical situations are obtained. We investigate magnetic phase transitions by focusing on order parameters and spin-spin correlations. Results are validated by numerical calculations using tensor network algorithms.
We show that the recent experimental realization of spin-orbit coupling in ultracold atomic gases can be used to study different types of spin spiral order and resulting multiferroic effects. Spin-orbit coupling in optical lattices can give rise to the Dzyaloshinskii-Moriya (DM) spin interaction which is essential for spin spiral order. By taking into account spin-orbit coupling and an external Zeeman field, we derive an effective spin model in the Mott insulator regime at half filling and demonstrate that the DM interaction in optical lattices can be made extremely strong with realistic experimental parameters. The rich finite temperature phase diagrams of the effective spin models for fermions and bosons are obtained via classical Monte Carlo simulations.
In this paper, we provide a comprehensive study of the quantum magnetism in the Mott insulating phases of the one-dimensional (1D) Bose-Hubbard model with Abelian or non-Abelian synthetic gauge fields, using the density-matrix renormalization-group (DMRG) method. We focus on the interplay between the synthetic gauge field and the asymmetry of the interactions, which give rise to a very general effective magnetic model: an XYZ model with various Dzyaloshinskii-Moriya (DM) interactions. The properties of the different quantum magnetic phases and phases transitions of this model are investigated.
We investigate magnetic properties in the superfluid and Mott-insulating states of two-component bosons with spin-orbit (SO) coupling in two-dimensional square optical lattices. The spin-independent hopping integral ttt and SO coupled one $\ensuremath{\lambda}$ are fitted from band-structure calculations in the continuum, which exhibit oscillations with increasing SO coupling strength. The magnetic superexchange model is derived in the Mott-insulating state with one particle per site, characterized by the Dzyaloshinsky-Moriya interaction. In the limit of $|\ensuremath{\lambda}|\ensuremath{\ll}|t|$, we find a spin spiral Mott state whose pitch value is the same as that in the incommensurate superfluid state, while in the opposite limit $|t|\ensuremath{\ll}|\ensuremath{\lambda}|$, the ground state exhibits a $2\ifmmode\times\else\texttimes\fi{}2$ in-plane spin pattern.
We investigate the ground-state properties of Bose-Bose mixtures with Rashba-type spin-orbit (SO) coupling in a square lattice. The system displays rich physics from the deep Mott insulator (MI) all the way to the superfluid (SF) regime. In the deep MI regime, exotic spin-ordered phases arise due to the effective Dzyaloshinskii-Moriya type of superexchange interactions. By employing the nonperturbative bosonic dynamical mean-field theory (BDMFT), we numerically study and establish the stability of these magnetic phases against increasing hopping amplitude. We show that as hopping is increased across the MI to SF transition, exotic superfluid phases with magnetic textures emerge. In particular, we identify an exotic spin-spiral magnetic texture with spatial period 3 in the superfluid close to the MI-SF transition.