Quantum subspace expansion approach for simulating dynamical response functions of Kitaev spin liquids

TL;DR

This work tackles the challenge of simulating dynamical properties of strongly correlated magnets, focusing on the Kitaev honeycomb model under a finite magnetic field. It develops a quantum subspace expansion (QSE) workflow that combines symmetry-guided ground-state preparation with a Krylov-based subspace to access symmetry-broken regimes and to compute Green's functions, spectral functions, and the dynamical structure factor. The authors demonstrate near-exact ground-state energies and dynamical observables by comparing QSE results against exact diagonalization for modest system sizes, showing robustness to Trotter errors and feasibility on near-term quantum hardware. The approach provides a scalable quantum simulation toolbox for quasiparticle properties in Kitaev spin liquids and can be extended to generalized Kitaev models and related strongly correlated materials.

Abstract

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 to quasiparticle properties of strongly correlated magnets and can become a valuable tool for studying material science.

Figures (6)

• Figure 1: Sketch of workflow for quantum subspace expansion-based approach for studying properties of Kitaev materials. First, material physics is mapped into a strongly-correlated spin model that can host a spin liquid (here represented by the honeycomb lattice Kitaev model for spin-1/2). Next, the spin Hamiltonian is mapped into a quantum simulator with the same coupling topology, representing a quantum digital twin. Then, we perform a state preparation and dynamical evolution with the system Hamiltonian, followed overlap measurements (via Hadamard test, reference state comparison, or equivalent). Finally, the measured overlaps are post-processed to distill the information about off-diagonal Green's functions for spin-spin correlations, dynamical structure factor (DSF), and quasiparticle response functions.
• Figure 2: Infidelity (a) and energy distance (b) between symmetry-aware variational ground state and exact Kitaev model GS, shown as a function of varying number of ansatz layers $d$. We consider $J=-1.0$, $h^z=0$ and $N=8$ and $N=12$. Variational ansatz was trained for 500 epochs and same performance is observed over various initialization of parameters (random uniform).
• Figure 3: Energy distance between GS prepared by QSE and exact Kitaev model GS for $N=8$, $J=-1.0$, $h^z=0.1$, as a function of $n_l$, for QSE with exact time evolution (a) and Trotterized time evolution with $r=1$ step (b).
• Figure 4: (a) Energy distance between GS prepared by QSE with exact time evolution and exact Kitaev model GS as a function of number of basis states. (b) Energy distance between GS prepared by QSE with Trotterized time evolution and exact Kitaev model GS as a function of number of Trotter steps. For all calculations, the magnetic field was set as $h^z=0.1$. For the Trotterized QSE, we set $n_k=n_l=3$.
• Figure 5: Real part of the retarded Green's function $G_{12}$ (a) and the corresponding spectral function $\mathrm{SF}_{12}$ (b) of the Kitaev model for $N=8$, $J=-1$, $h^z=0.1$. We calculate both quantities on the spins $(1,2)$, i.e. $\hat{c}_\alpha = \hat{Z}_1$ and $\hat{c}^\dagger_\beta = \hat{Z}_2$. We use the same basis size as for the ground state preparation, i.e. $n_k=n_l=\Tilde{n}_k = \Tilde{n}_l=3$.