Master equation approach to computing RVB bond amplitudes

Abstract

We describe a "master equation" analysis for the bond amplitudes h(r) of an RVB wavefunction. Starting from any initial guess, h(r) evolves (in a manner dictated by the spin hamiltonian under consideration) toward a steady-state distribution representing an approximation to the true ground state. Unknown transition coefficients in the master equation are treated as variational parameters. We illustrate the method by applying it to the J1-J2 antiferromagnetic Heisenberg model. Without frustration (J2=0), the amplitudes are radially symmetric and fall off as 1/r^3 in the bond length. As the frustration increases, there are precursor signs of columnar or plaquette VBS order: the bonds preferentially align along the axes of the square lattice and weight accrues in the nearest-neighbour bond amplitudes. The Marshall sign rule holds over a large range of couplings, J2/J1 < 0.418. It fails when the r=(2,1) bond amplitude first goes negative, a point also marked by a cusp in the ground state energy. A nonrigourous extrapolation of the staggered magnetic moment (through this point of nonanalyticity) shows it vanishing continuously at a critical value J2/J1 = 0.447. This may be preempted by a first-order transition to a state of broken translational symmetry.

8 pages, 7 figures

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Cited by in corpus (27)

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• The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• Loop updates for variational and projector quantum Monte Carlo simulations in the valence-bond basis
• Phase diagram of spin-1/2 J1-J2 Heisenberg model on honeycomb lattice
• A tensor product state approach to spin-1/2 square $J_1$-$J_2$ antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality
• Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model
• $U(1)$-symmetric infinite projected entangled-pair state study of the spin-$1/2$ square $J_1-J_2$ Heisenberg model
• Gapless spin liquid ground state of spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices
• Finite-size scaling and boundary effects in two-dimensional valence-bond-solids
• Properties of Resonating-Valence-Bond Spin Liquids and Critical Dimer Models
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• Gapped spin liquid phase in the J1-J2 Heisenberg model by a Bosonic resonating valence-bond ansatz
• Detection of symmetry-protected topological order in AKLT states by exact evaluation of the strange correlator
• Cluster functional renormalization group and absence of a bilinear spin liquid in the $J_1$-$J_2$-Heisenberg model
• Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure
• Tensor network study of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ model: incommensurate spiral order, mixed valence-bond solids, and multicritical points
• Correlated valence-bond states
• Strain-Tuned Magnetic Frustration in a Square Lattice $J_1$-$J_2$ Material
• Definitions of entanglement entropy of spin systems in the valence-bond basis
• Efficient neural-network based variational Monte Carlo scheme for direct optimization of excited energy states in frustrated quantum systems
• Slow dynamics of the Fredkin spin chain
• Phase Diagram of the Frustrated Square-Lattice Hubbard Model: Variational Cluster Approach
• Indicators of Conformal Field Theory: entanglement entropy and multiple-point correlators
• 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
• Valence bond distribution and correlation in bipartite Heisenberg antiferromagnets
• Variational wave functions for frustrated magnetic models