We develop a quantum simulation-based approach for studying properties of strongly correlated magnetic materials at increasing scale. We consider a paradigmatic example of a quantum spin liquid (QSL) state hosted by the honeycomb Kitaev model and use a trainable, symmetry-guided ansatz for preparing its ground state. Applying the tools of quantum subspace expansion (QSE), Hamiltonian operator approximation, and overlap measurements, we simulate the QSL at zero temperature and finite magnetic field, thus moving outside of the symmetric subspace. Next, we implement a protocol for quantum subspace expansion-based measurement of spin-spin correlation functions. Finally, we perform QSE-based simulation of the dynamical structure factor obtained from Green's functions of the finite field Kitaev model. Our results show that quantum simulators offer an insight into quasiparticle properties of strongly correlated magnets and can become a valuable tool for studying material science.
We develop a quantum simulation-based approach for studying properties of strongly correlated magnetic materials at increasing scale. We consider a paradigmatic example of a quantum spin liquid (QSL) state hosted by the honeycomb Kitaev model and use a trainable, symmetry-guided ansatz for preparing its ground state. Applying the tools of quantum subspace expansion (QSE), Hamiltonian operator approximation, and overlap measurements, we simulate the QSL at zero temperature and finite magnetic field, thus moving outside of the symmetric subspace. Next, we implement a protocol for quantum subspace expansion-based measurement of spin-spin correlation functions. Finally, we perform QSE-based simulation of the dynamical structure factor obtained from Green's functions of the finite field Kitaev model. Our results show that quantum simulators offer an insight into quasiparticle properties of strongly correlated magnets and can become a valuable tool for studying material science.
We propose a quantum protocol that allows preparing a ground state (GS) of the honeycomb Kitaev model. Our approach efficiently uses underlying symmetries and techniques from topological error correction. It is based on the stabilization procedure, the developed centralizer ansatz, and utilizes the vortex basis description as the most advantageous for qubit-based simulations. We demonstrate the high fidelity preparation of spin liquid ground states for the original Kitaev model, getting the exact GS for N=24 spins using 230 two-qubit operations. We then extend the variational procedure to non-zero magnetic fields, studying observables and correlations that reveal the phase transition. Finally, we perform dynamical simulation, where the ground state preparation opens a route towards studies of strongly-correlated dynamics, and a potential quantum advantage.
Motivated by the appearance of Majorana fermions in a broad range of correlated and topological electronic systems, we develop a general method to compute the dynamical response of interacting Majorana fermions in the random-phase approximation (RPA). This can be applied self-consistently on top of Majorana mean-field theory backgrounds, thereby in particular providing a powerful tool to analyze behavior in the vicinity of (various heavily studied) exactly soluble models. Prime examples are quantum spin liquids (QSL) with emergent Majorana excitations, with the celebrated exact solution of Kitaev. We employ the RPA to study in considerable detail phase structure and dynamics of the extended Kitaev honeycomb K J Γ model, with and without an applied field. First, we benchmark our method with Kitaev's exactly soluble model, finding a remarkable agreement. The interactions between Majorana fermions even turn out to mimic the effect of local Z 2 flux excitations, which we explain analytically. Second, we show how small non-Kitaev couplings J and Γ induce Majorana bound states, resulting in sharp features in the dynamical structure factor in the presence of fractionalization: such “spinon excitons” naturally appear, and can coexist and interact with the broad Majorana continuum. Third, for increasing couplings or field, our theory predicts instabilities of the Kitaev QSL (KQSL) triggered by the condensation of the sharp modes. From the high-symmetry momenta of the condensation we can deduce which magnetically ordered phases surround the KQSL, in good agreement with previous finite-size numerics. We discuss implications for experiments and the broad range of applicability of our method to other QSL and Majorana systems.
The Kitaev model, renowned for its exact solvability and potential to host non-Abelian anyons, remains a focal point in the study of quantum spin liquids and topological phases. While much of the existing literature has employed Majorana fermion techniques to analyze the model, particularly at zero temperature, its finite-temperature behavior has been less thoroughly explored via alternative methods. In this paper, we investigate the finite-temperature properties of the Kitaev model using the spin Green's function formalism. This approach provides a unified framework for computing key physical quantities, such as spin correlations, magnetic susceptibility, and the dynamical spin structure factor, offering valuable insights into the system's thermal dynamics. To solve the equation of motion for the spin Green's function, we truncate the hierarchy of multispin Green's functions using the Tyablikov decoupling approximation, which is particularly accurate at high temperatures. Our results show several similarities with Majorana-based numerical simulations, though notable differences emerge. Specifically, both static and dynamical spin-spin correlation functions capture not only Z2 flux excitations but also simple spin-flip excitations, with the latter dominating the response. Additionally, without explicitly assuming fractionalization, our results for the spin susceptibility and spin relaxation rate suggest the presence of fermionic degrees of freedom at low temperatures. Unlike Majorana-based approaches, which rely on exact solvability and are inherently limited to the pure Kitaev model, the spin Green's function formalism is well-suited for studying more realistic systems. It can naturally incorporate the effects of magnetic fields, including linear-order terms, and non-Kitaev interactions, making it applicable to a broader range of materials and experimental conditions. By providing an alternative method for analyzing the finite-temperature properties of the Kitaev model, this study complements existing approaches and lays the groundwork for future investigations into real materials and extended models.
We present an augmented parton mean-field theory which (i) reproduces the exact ground state, spectrum, and dynamics of the quantum spin-liquid phase of Kitaev's honeycomb model, and (ii) is amenable to the inclusion of integrability breaking terms, allowing a perturbation theory from a controlled starting point. Thus, we exemplarily study dynamical spin correlations of the honeycomb Kitaev quantum spin liquid within the $K\ensuremath{-}J\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ model, which includes Heisenberg and symmetric-anisotropic (pseudodipolar) interactions. This allows us to trace changes of the correlations in the regime of slowly moving fluxes, where the theory captures the dominant deviations when integrability is lost. These include an asymmetric shift together with a broadening of the dominant peak in the response as a function of frequency, the generation of further-neighbor correlations and their structure in real and spin space, and a resulting loss of an approximate rotational symmetry of the structure factor in reciprocal space. We discuss the limitations of this approach and also view the neutron-scattering experiments on the putative proximate quantum spin-liquid material $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ in the light of the results from this extended parton theory.
The Kitaev model is an exactly solvable model that exhibits a quantum spin liquid as its ground state. While this model was originally proposed as an S = 1 / 2 spin model on a honeycomb lattice, extensions to higher-spin systems have recently attracted attention. In contrast to the S = 1 / 2 case, such higher- S models are not exactly solvable and remain poorly understood, particularly for spin excitations at finite temperatures. Here, we focus on the S = 1 Kitaev model, which has been proposed to host bosonic quasiparticles. We investigate this model using Schwinger boson mean-field theory, where bosonic spinons are introduced as fractional quasiparticles by extending bond operators to address anisotropic spin interactions. We determine the mean-field parameters that realize a quantum spin liquid in both ferromagnetic and antiferromagnetic Kitaev models. Based on this mean-field ansatz, we calculate the dynamical and equal-time spin structure factors. We find that, when one uses the conventional decoupling scheme based on Wick decoupling with respect to spinons to calculate spin correlations, the resultant spin structure factors exhibit a momentum dependence that is not consistent with the sign structure expected from the exchange interaction: They possess a strong spectral weight indicating ferromagnetic (antiferromagnetic) correlations in the antiferromagnetic (ferromagnetic) Kitaev model. To resolve this issue, we propose an alternative scheme for evaluating the spin correlations, which is based on decoupling with respect to the bond operators. We demonstrate that, in our scheme, this discrepancy is removed, and the momentum dependence of the spin structure factors is consistent with the sign of the exchange constant. We also calculate the temperature evolution of the dynamical spin structure factor and find that the continuum observed at zero temperature splits into two distinct structures as the temperature increases, which can be understood in terms of the bandwidth narrowing of spinons. Finally, we clarify the origin of why the two distinct decoupling schemes result in different momentum dependences of the spin structure factors and discuss their relationship to results obtained in previous studies.
Kitaev's honeycomb model is a paradigmatic exactly solvable system hosting a quantum spin liquid with non-Abelian anyons and topologically protected edge modes, offering a platform for fault-tolerant quantum computation. However, real candidate Kitaev materials invariably include complex secondary interactions that obscure the realization of spin-liquid behavior and demand novel quantum computational approaches for efficient simulation. Here we report quantum simulations of a 22-site Kitaev honeycomb lattice on a trapped-ion quantum processor, without and with non-integrable Heisenberg interactions that are present in real materials. We develop efficient quantum circuits for ground-state preparation, achieving high accuracy with energy errors equivalent to an effective temperature of 0.2 (in units of the Kitaev interactions), consistent with the experimentally relevant spin-liquid regime. Starting from these states, we apply controlled perturbations and measure time-dependent spin correlations along the system's edge. In the non-Abelian phase, we observe chiral edge dynamics consistent with a non-zero Chern number, a hallmark of topological order, which vanishes upon transition to the Abelian toric code phase. Extending to the non-integrable Kitaev-Heisenberg model, we find that weak Heisenberg interactions preserve chiral edge dynamics, while stronger couplings suppress them, signaling the breakdown of topological protection. Our work demonstrates a viable route for probing dynamical signatures of topological order in quantum spin liquids using programmable quantum hardware, opening new pathways for quantum simulation of strongly correlated materials.