Real-space spectral simulation of quantum spin models: Application to the Kitaev-Heisenberg model

Abstract

The proliferation of quantum fluctuations and long-range entanglement presents an outstanding challenge for the numerical simulation of interacting spin systems with exotic ground states. Here, we present a Chebyshev iterative method that gives access to the thermodynamic properties and critical behavior of frustrated quantum spin models with good accuracy. The computational complexity scales linearly with the Hilbert space dimension and the number of Chebyshev iterations used to approximate the eigenstates. Using this approach, we calculate the spin correlations of the Kitaev-Heisenberg model, a paradigmatic model of honeycomb iridates that exhibits a rich phase diagram including a quantum spin liquid phase. Our results are benchmarked against exact diagonalization and a popular iterative method based on thermal pure quantum (TPQ) states. All methods accurately predict a transition to a stripy (spin-liquid) phase for the critical value of the Kitaev coupling J K ≈ −1.3J H (J K ≈ −8.0J H ) for honeycomb layers with ferromagnetic Heisenberg interactions (J H > 0). Our findings suggest that a hybrid Chebyshev-TPQ approach could open the door to previously unattainable studies of quantum spin models in two dimensions.