Classification of spin liquids on the square lattice with strong spin-orbit coupling

2014/07/15 by Johannes Reuther, Shu-Ping Lee, Jason Alicea
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Condensed matter physics #Electron #Gapless playback #Geometry #Homogeneous space #Ising model #Lattice (music) #MAJORANA #Mathematics #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Quantum spin liquid #Rotational symmetry #Spin (aerodynamics) #Spin polarization #Spinon #Square lattice #Superconductivity #Symmetry operation #Theoretical physics #Topological Materials and Phenomena #Topology (electrical circuits) #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.90.174417

published as Phys. Rev. B 90, 174417 (2014) · 22 pages, 7 figures

arxiv created 2014/07/15 · openalex publication_date 2014/11/14 · arxiv updated 2014/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Spin liquids represent exotic types of quantum matter that evade conventional symmetry-breaking order even at zero temperature. Exhaustive classifications of spin liquids have been carried out in several systems, particularly in the presence of full SU(2) spin-rotation symmetry. Real magnetic compounds, however, generically break SU(2) spin symmetry as a result of spin-orbit coupling---which in many materials provides an ``order one'' effect. We generalize previous works by using the projective symmetry group method to classify ℤ₂ spin liquids on the square lattice when SU(2) spin symmetry is maximally lifted. We find that, counterintuitively, the lifting of spin symmetry actually results in vastly more spin-liquid phases compared to SU(2)-invariant systems. A generic feature of the SU(2)-broken case is that the spinons naturally undergo p+ip pairing; consequently, many of these ℤ₂ spin liquids feature a topologically nontrivial spinon band structure supporting gapless Majorana edge states. We study in detail several spin-liquid phases with varying numbers of gapless edge states and discuss their topological protection. The edge states are often protected by a combination of time reversal and lattice symmetries and hence resemble recently proposed topological crystalline superconductors.

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