Projective symmetry group classification of Abrikosov fermion mean-field ansätze on the square-octagon lattice

Abstract

We perform a projective symmetry group (PSG) classification of symmetric quantum spin liquids with different gauge groups on the square-octagon lattice. Employing the Abrikosov fermion representation for spin-$1/2$, we obtain $32$ $SU(2)$, $1808$ $U(1)$ and $384$ ${\mathbb{Z}}_2$ algebraic PSGs. Constraining ourselves to mean-field parton ansätze with short-range amplitudes, the classification reduces to a limited number, with 4 $SU(2)$, 24 $U(1)$ and 36 ${\mathbb{Z}}_2$, distinct phases. We discuss their ground state properties and spinon dispersions within a self-consistent treatment of the Heisenberg Hamiltonian with frustrating couplings.

arXiv comment28 pages, 8 figures, 5 tables

References in corpus (56)

• Quantum Spin Liquids
• Quantum Spin Liquid States
• Quantum Spin Liquids
• Quantum Orders and Symmetric Spin Liquids
• Spin-lattice coupling in frustrated antiferromagnets
• Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Spin liquid nature in the Heisenberg $J_1$-$J_2$ triangular antiferromagnet
• Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States
• Resonating Valence Bond Wave Functions for Strongly Frustrated Spin Systems
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Spin Gaps in a Frustrated Heisenberg model for CaV${}_4$O${}_9$
• Lattice symmetries and regular states in classical frustrated antiferromagnets
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• Z2 spin liquid in S=1/2 Heisenberg model on Kagome lattice: A projective symmetry group study of Schwinger-fermion mean-field states
• Phase diagram of depleted Heisenberg model for CaV4O9
• Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet
• Topological excitations and the dynamic structure factor of spin liquids on the kagome lattice
• Plaquette Resonating-Valence-Bond Ground State of CaV${}_4$O${}_9$
• Octagraphene as a Versatile Carbon Atomic Sheet for Novel Nanotubes, Unconventional Fullerenes and Hydrogen Storage
• Projective symmetry group classification of chiral spin liquids
• Valence-bond crystal in the extended kagome spin-1/2 quantum Heisenberg antiferromagnet: A variational Monte Carlo approach
• Spectral signatures of fractionalization in the frustrated Heisenberg model on the square lattice
• $Z_2$ spin liquid and chiral antiferromagnetic phase in Hubbard model on the honeycomb lattice: duality between Schwinger-fermion and Schwinger-boson representations
• Unconventional Surface Critical Behaviors Induced by Quantum Phase Transition from Two-Dimensional Affleck-Kennedy-Lieb-Tasaki Phase to Néel Order
• Spin liquids on a honeycomb lattice: Projective Symmetry Group study of Schwinger fermion mean-field theory
• Quantum s = 1/2 Antiferromagnets on Archimedean Lattices: The Route from Semiclassical Magnetic Order to Nonmagnetic Quantum States
• Critical exponents of the quantum phase transition in a planar antiferromagnet
• Spin Gap in Two-Dimensional Heisenberg Model for CaV${}_4$O${}_9$
• Symmetric $Z_2$ spin liquids and their neighboring phases on triangular lattice
• Quantum spin liquids in the absence of spin-rotation symmetry: application to Herbertsmithite
• Persistence of the gapless spin liquid in the breathing kagome Heisenberg antiferromagnet
• Pinwheel valence-bond-crystal ground state of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the $shuriken$ lattice
• Valence-bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study
• Convergent expansions for properties of the Heisenberg model for CaV${}_4$O${}_9$
• Pinch-points to half-moons and up in the stars: the kagome skymap
• Gutzwiller-projected states for the $J_1$-$J_2$ Heisenberg model on the kagome lattice: achievements and pitfalls
• The Interplay Between Lattice Topology, Frustration, and Spin Quantum Number in Quantum Antiferromagnets on Archimedean Lattices
• Interplay of non-symmorphic symmetry and spin-orbit coupling in hyperkagome spin liquids: Applications to Na${}_4$Ir${}_3$O${}_8$
• Single-orbital realization of high-temperature $s^{\pm }$ superconductivity in the square-octagon lattice
• Spin Gap of Two-Dimensional Antiferromagnet Representing CaV${}_4$O${}_9$
• Competing orders in pyrochlore magnets from a ${\mathbb{Z}}_2$ spin liquid perspective
• High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States
• Theoretical study of quantum spin liquids in $S=1/2$ hyper-hyperkagome magnets: classification, heat capacity, and dynamical spin structure factor
• High-Order Coupled Cluster Calculations Via Parallel Processing: An Illustration For CaV${}_4$O${}_9$
• Symmetric $\mathrm{U}(1)$ and ${\mathbb{Z}}_2$ spin liquids on the pyrochlore lattice
• Competing quantum spin liquids, gauge fluctuations, and anisotropic interactions in a breathing pyrochlore lattice
• Classical and quantum order in hyperkagome antiferromagnets
• On the presence of mid-gap states in CaV4O9
• Projective symmetry group classifications of quantum spin liquids on the simple cubic, body centered cubic, and face centered cubic lattices
• The Heisenberg model on the 1/5-depleted square lattice and the CaV4O9 compound
• Classification and properties of quantum spin liquids on the hyperhoneycomb lattice
• Symmetry protected gapless $Z_2$ spin liquids
• Incommensurate, helical spin ground states on the Hollandite lattice
• Competing orders in a frustrated Heisenberg model on the Fisher lattice
• Two-dimensional S=1/2 antiferromagnet on a plaquette lattice

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