Simulation of Quantum Spin-Liquid Phases with Spectral Methods*

In this work, we combine accurate Chebyshev polynomial expansions [1-3] and thermal pure quantum states (TPQ) [4] to simulate quantum spin models with highly entangled ground states. We use this hybrid framework to map out in a numerically exact fashion the phase diagram of the Kitaev-Heisenberg model on the honeycomb lattice [5]. Energy, magnetization and spin correlations are calculated with spectral accuracy in large systems with up to 24 spins. Our method can be easily extended to realistic spin models accommodating impurities, defects
and external perturbations. Our results suggest that the hybrid spectral-TPQ approach can provide advantages over pure TPQ and other state-of-the-art methods in probing complex spin systems.

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[2] A. Braun, P. Schmitteckert, Phys. Rev. B 90, 165112 (2014)
[3] S. M. Joao et al., Royal Society Open Science, 7, 2 (2020)
[4] S. Sugiura and A. Shimizu, Phys. Rev. Lett. 108, 240401 (2012)
[5] J. Chaloupka, G. Jackeli, and G. Khaliullin, Phys. Rev. Lett. 105, 027204 (2010)