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

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. In this talk, I introduce a newly developed finite temperature Chebyshev polynomial (FTCP) method giving 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 size and the number of Chebyshev polynomials used to approximate the eigenstates. To demonstrate the scope of this method, I apply it to the Kitaev-Heisenberg Hamiltonian, a paradigmatic model of honeycomb iridates that exhibits a rich phase diagram, including both magnetically ordered and quantum spin liquid (QSL) phases. Our results are benchmarked against the Lanczos exact diagonalization algorithm and a popular iterative method based on thermal pure quantum (TPQ) states. All methods accurately predict transitions between ferromagnetic, Néel, zigzag and stripy antiferromagnetic, and QSL phases. These benchmark tests highlight some advantages of FTCP in terms of numerical stability compared to TPQ and Lanczos.

F. B. is funded by the Engineering and Physical Sciences Research Council through a DTP studentship. A.F. acknowledges financial support from the Royal Society through a Royal Society University Research Fellowship.