Simulating a two-dimensional frustrated spin system with fermionic resonating-valence-bond states

Abstract

The frustrated Heisenberg $J_1-J_2$ model on a square lattice is numerically investigated by variational Monte Carlo simulations. We propose a antiferromagnetic fermion resonating-valence-bond (AF-fRVB) state that has ability to examine the entire phase diagram in the $J_1-J_2$ model. Two phase transition points, the second order around $J_2/J_1=0.45$ and the first order around $J_2/J_1=0.6$, can be extracted more clearly than the conventional bosonic RVB state. At the maximally frustrated point ($J_2/J_1=0.5$), the AF-fRVB state shows the variational ground-state energy in the thermodynamic limit very close to the one estimated by the projected entangled pair state at the largest bond dimension available. On the other hand, in the frustrated regime $0.4\lesssim J_2/J_1\le 0.5$, AF-fRVB states with $s_{+-}$ (using the terminology in the field of iron-based superconductors) and $d_{xy}$ pairing symmetries are degenerate in the thermodynamic limit, implying the existence of gapless Dirac excitations in the spinon spectrum.

5 pages, 4 figures

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• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the $J_1$--$J_2$--$J_1^{\perp }$ model
• Cluster functional renormalization group and absence of a bilinear spin liquid in the $J_1$-$J_2$-Heisenberg model
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• Thermal Hall conductivity of a valence bond solid phase in the square lattice $J_1$-$J_2$ antiferromagnet Heisenberg model with a Dzyaloshinskii-Moriya interaction
• 2D excitation information by MPS method on infinite helixes
• Gapped paramagnetic state in a frustrated spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the cross-striped square lattice
• Hidden $SU(2)$ Symmetries, the Symmetry Hierarchy and the Emergent Eight-Fold Way in Spin-1 Quantum Magnets
• Field-induced states and thermodynamics of the frustrated Heisenberg antiferromagnet on a square lattice