Chiral spin liquid and quantum phase diagram of spin-$1/2$ $J_1$-$J_2$-$J_{\chi }$ model on the square lattice

Abstract

We study the spin-$1/2$ Heisenberg model on the square lattice with the first and second nearest-neighbor antiferromagnetic couplings $J_1$, $J_2$, as well as the three-spin scalar chiral coupling $J_{\chi }$. Using density matrix renormalization group calculations, we obtain a quantum phase diagram of this system for $0\le J_2/J_1\le 1.0$ and $0\le J_{\chi }/J_1\le 1.5$. We identify the Néel and stripe magnetic order phase at small $J_{\chi }$ coupling. With growing $J_{\chi }$, we identify the emergent chiral spin liquid (CSL) phase characterized by the quantized spin Chern number $C=1/2$ and entanglement spectrum with the quasidegenerate group of levels agreeing with chiral SU(2)${}_1$ conformal field theory, which is an analog of the $\nu =1/2$ Laughlin state in spin system. In the vicinity of the Néel and CSL phase boundary, our numerical results do not find evidence to support the phase coexistence of Néel order and topological order that was conjectured by mean-field calculations. In the larger $J_2$ and $J_{\chi }$ coupling regime, the entanglement spectrum of the ground state also exhibits the chiral quasidegeneracy consistent with a CSL, but the adiabatic flux insertion simulations fail to obtain the quantized Chern number. By analyzing the finite-size scaling of magnetic order parameter, we find the vanished magnetic order suggesting a magnetic disorder phase, whose nature needs further studies. Different from the spin-$1$ $J_1$-$J_2$-$J_{\chi }$ model, we do not find the coexistent stripe magnetic order and topological order. We also investigate the $J_{\chi }$ dominant regime and find a strong tendency of the system to develop a dimer order rather than the chiral spin magnetic order observed in the spin-$1$ model.

16 pages, 17 figures

References in corpus (28)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Identifying Topological Order by Entanglement Entropy
• Characterizing topological order by studying the ground states of an infinite cylinder
• Giant thermal Hall conductivity from neutral excitations in the pseudogap phase of cuprates
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model
• Four-Spin Terms and the Origin of the Chiral Spin Liquid in Mott Insulators on the Triangular Lattice
• Variational Monte Carlo study of chiral spin liquid in the extended Heisenberg model on the Kagome lattice
• Thermal Hall conductivity in the cuprate Mott insulators Nd${}_2$CuO${}_4$ and Sr${}_2$CuO${}_2$Cl${}_2$
• Phase diagram of the anisotropic triangular lattice Hubbard model
• Quantum Spin Liquid with Emergent Chiral Order in the Triangular-lattice Hubbard Model
• Emergence of Chiral Spin Liquids via Quantum Melting of Non-Coplanar Magnetic Orders
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• Charged Defects and Phonon Hall Effects in Ionic Crystals
• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• Quantum Phase Diagram and Spontaneously Emergent Topological Chiral Superconductivity in Doped Triangular-Lattice Mott Insulators
• Topological chiral and nematic superconductivity by doping Mott insulators on triangular lattice
• Consideration of Thermal Hall Effect in Undoped Cuprates
• Extrinsic phonon thermal Hall transport from Hall viscosity
• Phonon Thermal Hall Conductivity from Scattering with Collective Fluctuations
• 50 years of quantum spin liquids
• Large extrinsic phonon thermal Hall effect from resonant scattering
• Thermal Hall conductivity of electron-doped cuprates
• Phonon Hall viscosity from phonon-spinon interactions
• Thermal Conductivity and Theory of Inelastic Scattering of Phonons by Collective Fluctuations
• Coexistence of non-Abelian chiral spin liquid and magnetic order in a spin-1 antiferromagnet
• Majorana chiral spin liquid in Mott insulating cuprates

Cited by in corpus (7)

• Above room temperature multiferroic tunnel junction with the altermagnetic metal CrSb
• Quantum state preparation of topological chiral spin liquids via Floquet engineering
• Frustration and chirality in three-dimensional trillium lattices: Insights and Perspectives
• Coexistence of anomalous spin dynamics and weak magnetic order in a chiral trillium lattice K2FeSn(PO4)3
• Quantum Hall to Chiral Spin Liquid transition in a Triangular Lattice Hofstadter-Hubbard Model
• Chiral vortex-line liquid of three-dimensional interacting Bose systems with moat dispersion
• Chiral Edge States Emerging on Anyon-Net