Magic of Kitaev spin liquids

Quantum spin liquids (QSLs) are phases of matter characterized by long-range entanglement and fractionalized excitations. While entanglement is a well-studied diagnostic of quantum complexity, it does not fully capture the classical simulation difficulty of a quantum state. This paper investigates magic—also known as nonstabilizerness—as a complementary diagnostic of many-body complexity in the Kitaev honeycomb model (KHM).

The authors compute the stabilizer Rényi entropy (SRE), a standard measure of magic, for the KHM ground state. They derive a mapping between physical Pauli strings and itinerant Majorana operators, which allows them to treat the KHM as a fermionic Gaussian state. This mapping enables the use of an optimized sampling algorithm that reduces computational complexity from O(N^4) to O(N^3), allowing for simulations on systems with up to 4,600 spins.

The study reveals that magic is most prominent in the gapless phase of the KHM, with a maximum at the isotropic point. In the gapped phases, magic decreases and eventually vanishes in the limit of decoupled dimers. The authors demonstrate that subleading volume-law corrections to the SRE vanish in the gapped phase but remain finite in the gapless phase, suggesting the presence of non-local magic. Furthermore, the SRE exhibits universal scaling at the topological phase transition, with critical exponents consistent with the semi-Dirac universality class.

This work establishes the SRE as a sensitive probe for phase transitions between different types of quantum spin liquids. By showing that magic can detect topological order and critical behavior, the authors provide a new tool for researchers to distinguish between quantum phases that might otherwise appear similar under standard entanglement measures. The optimized algorithm also provides a high-performance framework for studying nonstabilizerness in a wide range of other free-fermion systems.