Disentangling Kitaev Quantum Spin Liquid

TL;DR

This paper demonstrates that Clifford circuits can significantly disentangle the Kitaev quantum spin liquid, including the gapless phase, enabling more efficient classical simulation and resource reduction for quantum state preparation.

Contribution

The study shows that a large portion of entanglement in the Kitaev QSL can be captured by Clifford circuits, extending their applicability to the gapless phase and improving simulation efficiency.

Findings

Approximately two-thirds of entanglement entropy arises from Clifford contributions.

Clifford circuits enable dramatically more efficient simulations than conventional methods.

The approach accurately determines phase boundaries in the Kitaev-Heisenberg model.

Abstract

In this work, we investigate the Kitaev honeycomb model employing the recently developed Clifford Circuits Augmented Matrix Product States (CAMPS) method. While the model in the gapped phase is known to reduce to the toric code model - whose ground state is entirely constructible from Clifford circuits - we demonstrate that the very different gapless quantum spin liquid (QSL) phase can also be significantly disentangled with Clifford circuits. Specifically, CAMPS simulations reveal that approximately two-thirds of the entanglement entropy in the isotropic point arises from Clifford-circuit contributions, enabling dramatically more efficient computations compared to conventional matrix product state (MPS) methods. Crucially, this finding implies that the Kitaev QSL state retains significant Clifford-simulatable structure, even in the gapless phase with non-abelian anyon excitations when time reversal symmetry is broken. This property not only enhances classical simulation efficiency significantly but also suggests substantial resource reduction for preparing such states on quantum devices. As an application, we leverage CAMPS to study the Kitaev-Heisenberg model and determine the most accurate phase boundary between the anti-ferromagnetic phase and the Kitaev QSL phase in the model. Our results highlight how Clifford circuits can effectively disentangle the intricate entanglement of Kitaev QSLs, opening avenues for efficiently simulating related and similar strongly correlated models.