Exactly Solvable Models Hosting Altermagnetic Quantum Spin Liquids

TL;DR

This paper introduces exactly solvable spin models on specific lattices that host altermagnetic quantum spin liquids, revealing new phases with unique symmetry and topological properties.

Contribution

It constructs and analyzes new exactly solvable models hosting altermagnetic spin liquids with full symmetries and novel topological excitations.

Findings

Spin-$3/2$ model has a unique g-wave altermagnetic spin liquid ground state.

Spin-$7/2$ model exhibits multiple competing chiral and d-wave altermagnetic spin liquids.

Identified topological and non-topological excitations illustrating the phase's rich physics.

Abstract

We construct spin-$3/2$ and spin-$7/2$ models on the square-octagon and checkerboard lattices that are exactly solvable with Majorana representations. They give rise to spin-liquid phases with full spin-rotation and lattice-translational symmetries but broken time-reversal symmetry. Although non-zero on elementary plaquettes, the net orbital magnetic moment is guaranteed to vanish as a result of point symmetries; due to the analogy to long-range ordered altermagnets, these types of phases were dubbed altermagnetic spin liquids in [Phys. Rev. Research 7, 023152 (2025)]. For the spin-$3/2$ model, we find that a $g$-wave altermagnetic spin liquid emerges as the unique ground state. In contrast, the spin-7/2 model exhibits a significantly richer phase diagram, involving different types of chiral spin liquids competing with a $d$-wave altermagnetic spin liquid. Finally, we identify and characterize the topological and non-topological excitations, illustrating the rich physics of altermagnetic spin liquids resulting from the interplay of non-trivial topological and symmetry aspects of this novel phase of matter.