Persistence of the gapless spin liquid in the breathing kagome Heisenberg antiferromagnet

Abstract

The nature of the ground state of the spin $S=1/2$ Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e., with different superexchange couplings $J_{△}$ and $J_{▽}$ within elementary up- and down-pointing triangles) is investigated within the framework of Gutzwiller projected fermionic wave functions and Monte Carlo methods. We analyze the stability of the U(1) Dirac spin liquid with respect to the presence of fermionic pairing that leads to a gapped ${\mathbb{Z}}_2$ spin liquid. For several values of the ratio $J_{▽}/J_{△}$, the size scaling of the energy gain due to the pairing fields and the variational parameters are reported. Our results show that the energy gain of the gapped spin liquid with respect to the gapless state either vanishes for large enough system size or scales to zero in the thermodynamic limit. Similarly, the optimized pairing amplitudes (responsible for opening the spin gap) are shown to vanish in the thermodynamic limit. Our outcome is corroborated by the application of one and two Lanczos steps to the gapless and gapped wave functions, for which no energy gain of the gapped state is detected when improving the quality of the variational states. Finally, we discuss the competition with the "simplex" ${\mathbb{Z}}_2$ resonating-valence-bond spin liquid, valence-bond crystal, and nematic states in the strongly anisotropic regime, i.e., $J_{▽}\ll J_{△}$.

Published version. Main paper (9 pages, 7 figures) + Supplemental Material (4 tables)

References in corpus (24)

• Quantum Spin Liquids
• Quantum Spin Liquid States
• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Quantum magnetism in the paratacamite family: towards an ideal kagome lattice
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• Evidence for a Gapped Spin-Liquid Ground State in a Kagome Heisenberg Antiferromagnet
• 17O NMR study of the intrinsic magnetic susceptibility and spin dynamics of the quantum kagome antiferromagnet ZnCu3(OH)6Cl2
• Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• Resonating valence bond states in the PEPS formalism
• Valence-bond crystal in the extended kagome spin-1/2 quantum Heisenberg antiferromagnet: A variational Monte Carlo approach
• Magnetic behavior of volborthite Cu3V2O7(OH)2(H2O)2 determined by coupled trimers rather than frustrated chains
• Quantum Spin Liquid in a Breathing Kagome Lattice
• Quantum and Classical Spins on the Spatially Distorted Kagome Lattice: Applications to Volborthite
• Flat bands and Dirac cones in breathing lattices
• Nature of the spin liquid ground state in a breathing kagome compound studied by NMR and series expansion
• Coupled frustrated quantum spin-1/2 chains with orbital order in volborthite Cu3V2O7(OH)2(H2O)2
• Valence-bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study
• Heisenberg antiferromagnet with anisotropic exchange on the Kagome lattice: Description of the magnetic properties of volborthite
• Stability of the spin-$1/2$ kagome ground state with breathing anisotropy
• Fermionic spin liquid analysis of the paramagnetic state in Volborthite
• Lanczos steps to improve variational wave functions
• Quantum spin liquid and magnetic order in a two-dimensional non-symmorphic lattice: considering the distorted Kagome lattice of Volborthite

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