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arXiv:2504.15755 · SciPost Physics

Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers

Daniel González-Cuadra, A. Bermúdez

Published Nov 18, 2025• 0 citations
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Abstract

We investigate the emergence of bond-directional spin-spin interactions in a synthetic Fermi-Hubbard bilayer that can be realized with ultracold fermions in Raman optical lattices. The model exploits synthetic dimensions to couple two honeycomb layers, each corresponding to a different hyperfine atomic state, via Raman-assisted tunneling and, moreover, via an inter-layer Hubbard repulsion due to the cold-atom scattering. In the strong-coupling regime at half filling, we derive effective spin Hamiltonians for the kinetic exchange featuring Kitaev, Heisenberg, off-diagonal exchange ( \Gamma Γ -couplings), as well as tunable Dzyaloshinskii-Moriya interactions. We identify specific configurations that generate both ferromagnetic and antiferromagnetic Kitaev couplings with various perturbations of relevance to Kitaev materials, providing a tunable platform that can explore how quantum spin liquids emerge from itinerant fermion systems. We analyze the Fermi-liquid and Mott-insulating phases, highlighting a correspondence between Dirac and Majorana quasi-particles, with possible phase transitions thereof. In an extreme anisotropic limit, we show that the model reduces to an inter-layer ribbon in a quasi-1D ladder, allowing for a numerical study of the correlated ground state using matrix product states. We find a transition from a symmetry-protected topological insulator to a Kitaev-like regime characterized by nonlocal string order. Our results establish that cold-atom quantum simulators based on Raman optical lattices can be a playground for extended Kitaev models, bridging itinerant fermionic systems and spin-liquid physics.

DOI
10.21468/scipostphys.19.5.130

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We investigate the emergence of bond-directional spin-spin interactions in a synthetic Fermi-Hubbard bilayer that can be realized with ultracold fermions in Raman optical lattices. The model exploits synthetic dimensions to couple two honeycomb layers, each corresponding to a different hyperfine atomic state, via Raman-assisted tunneling and, moreover, via an inter-layer Hubbard repulsion due to the cold-atom scattering. In the strong-coupling regime at half filling, we derive effective spin Hamiltonians for the kinetic exchange featuring Kitaev, Heisenberg, off-diagonal exchange ( \Gamma Γ -couplings), as well as tunable Dzyaloshinskii-Moriya interactions. We identify specific configurations that generate both ferromagnetic and antiferromagnetic Kitaev couplings with various perturbations of relevance to Kitaev materials, providing a tunable platform that can explore how quantum spin liquids emerge from itinerant fermion systems. We analyze the Fermi-liquid and Mott-insulating phases, highlighting a correspondence between Dirac and Majorana quasi-particles, with possible phase transitions thereof. In an extreme anisotropic limit, we show that the model reduces to an inter-layer ribbon in a quasi-1D ladder, allowing for a numerical study of the correlated ground state using matrix product states. We find a transition from a symmetry-protected topological insulator to a Kitaev-like regime characterized by nonlocal string order. Our results establish that cold-atom quantum simulators based on Raman optical lattices can be a playground for extended Kitaev models, bridging itinerant fermionic systems and spin-liquid physics.
The Kitaev-Hubbard model of interacting fermions is defined on the honeycomb lattice and, at strong coupling, interpolates between the Heisenberg model and the Kitaev model. It is basically a Hubbard model with ordinary hopping ttt and spin-dependent hopping ${t}^{\ensuremath{'}}$. We study this model in the weak to intermediate coupling regime, at half filling, using the cellular dynamical impurity approximation (CDIA), an approach related to dynamical mean field theory but based on Potthoff's variational principle. We identify four phases in the $(U,{t}^{\ensuremath{'}})$ plane: two semimetallic phases with different numbers of Dirac points, an antiferromagnetic insulator, and an algebraic spin liquid. The last two are separated by a first-order transition. These four phases all meet at a single point and could be realized in cold atom systems.
We investigate the magnetic phases of a bilayer system of ultracold bosons in the presence of Raman-induced spin-orbit (SO) coupling and laser-assisted interlayer tunneling. We consider this bilayer system in the Mott-insulating regime where on-site two-body interactions exceed all the tunneling terms. In such a system there exists a rich set of spin textures including hetero-ferromagnetic, heterochiral magnetic, and chiral magnetic phases with interlayer antiferromagnetic. In particular, the heterochiral magnetic phase induced by SO coupling occurs extremely rarely in solid-state materials. We theoretically analyze the contribution of interlayer ferromagnetic interaction to the formation of these magnetic phases, including interactions that arise from laser-assisted tunneling, stagger ``magnetic field,'' and antisymmetric exchange, i.e., Dzyaloshinskii-Moriya interactions. Finally, we detail an experimental setup that produces the desired interactions in a system of cold alkali-metal atoms.
We study the emergence of magnetic order in localized spins that interact solely through their coupling to a Kitaev-type spin liquid. Using three toy models – the Kitaev model, the Yao–Lee model, and a square-lattice generalization of the Kitaev model – we calculate the effective exchange Hamiltonians mediated by the fractionalized excitations of these spin liquids. This setup is analogous to a Kondo lattice model, where conduction electrons are replaced by itinerant Majorana fermions. In the Kitaev model, our results show that the lowest-order perturbation theory generates short-range interactions with modified couplings and extending to sixth order introduces longer-range interactions while preserving the quantum spin-liquid ground state . Models involving more Majorana flavors on honeycomb and square lattices exhibit more complex behavior. The honeycomb Yao–Lee model with three flavors of itinerant Majorana fermions generates long-range RKKY-type interactions, leading to antiferromagnetic order and partial gapping of the Majorana fermion spectrum. In contrast, the square-lattice model produces a combination of anisotropic short- and long-range interactions, which can give rise to either a dimerized quantum paramagnetic state or an Ising antiferromagnet, depending on the parameters. These results illustrate the rich variety of magnetic orders that can be mediated by Kitaev-type spin liquids.
We study a spin model on honeycomb lattice with two types of Heisenberg exchange couplings, JJJ and J~\tilde JJ~, where JJJ is for the conventional spin and and J~\tilde JJ~ for rotated spin. When J~=0\tilde J=0J~=0, this is the conventional Heisenberg model. When J=0, the system is either in a stripy antiferromagnetic order(J~0\tilde J 0J~0, antiferromagnetic for rotated spin). The competition between two ferromagnetic orders or two antiferromagnetic orders induces Kitaev's spin liquid phase characterized by the exactly solvable Kitaev model (J=J~J=\tilde JJ=J~). Our model can be applied to layered Mott insulators A2_22​IrO3_33​ (A=Li, Na). For a monolayer of Li2_22​IrO3_33​, we show that it is possible to tune the controlling parameter into the Kitaev spin liquid regime by a link-dependent Rashba spin-orbital coupling.
We theoretically address spin chain analogs of the Kitaev quantum spin model on the honeycomb lattice. The emergent quantum spin-liquid phases or Anderson resonating valence-bond (RVB) states can be understood, as an effective model, in terms of ppp-wave superconductivity and Majorana fermions. We derive a generalized phase diagram for the two-leg ladder system with tunable interaction strengths between chains allowing us to vary the shape of the lattice (from square to honeycomb ribbon or brickwall ladder). We evaluate the winding number associated with possible emergent (topological) gapless modes at the edges. In the Az{A}_{z}Az​ phase, as a result of the emergent Z2{\mathbf{Z}}_{2}Z2​ gauge fields and $\ensuremath{\pi}$-flux ground state, one may build spin-1/2 (loop) qubit operators by analogy to the toric code. In addition, we show how the intermediate gapless BBB phase evolves in the generalized ladder model. For the brick-wall ladder, the BBB phase is reduced to one line, which is analyzed through perturbation theory in a rung tensor product states representation and bosonization. Finally, we show that doping with a few holes can result in the formation of hole pairs and leads to a mapping with the Su-Schrieffer-Heeger model in polyacetylene; a superconducting-insulating quantum phase transition for these hole pairs is accessible, as well as related topological properties.
Strongly correlated electron systems have the potential to host very exoticphases of matter. In order to have relevance to real materials, this exoticphysics often must emerge from relatively simple models. The quantumwavefunctions which describe such phases may bear little resemblance to theoriginal microscopic models. In these cases a variety of complex analytictools often must be supplemented with controlled numerical calculations tofully understand the essential behavior of these models. In this dissertation,we study such quantum phases of matter and their relationship to real materials.We focus on three main problems. First, we explore the relationship betweenstrong spin-orbit coupling and spin liquid physics by studying a very generalmodel on the triangular lattice where spin-orbit coupling leads to the presenceof highly anisotropic interactions. We use variational Monte Carlo to study bothU(1) quantum spin liquid states and ordered ones, via the Gutzwiller projectedfermion construction. We thereby obtain the ground state phase diagram in thisphase space. We furthermore consider effects beyond the Gutzwiller wavefunctionsfor the spinon Fermi surface quantum spin liquid, which are of particularimportance when spin-orbit coupling is present.Second we show that the interplay between a high density two-dimensional electrongas and localized electrons in a neighboring Mott insulator leads to kineticmagnetism unique to the Mott/band insulator interface. Our study is based upona bilayer Hubbard model at U=inftyU=\\inftyU=infty with a potential difference between thetwo layers. We combine analytic results with DMRG simulations to show thatmagnetism, and especially kinetic ferromagnetism, is greatly enhanced relative by theproximity of the two subsystems. Third we study the effect of interactions on the properties of a model 2Dtopological Kondo insulator phase. We introduce a model Hamiltonian which webelieve captures the essential physics of the different competing phases.Perhaps the most dramatic example of many-body physics in symmetry protectedtopological phases is the existence of exotic gapless edge states. We comment onthe potentially dramatic effects that interactions can have on such edge states.