Master equation approach to computing RVB bond amplitudes

TL;DR

This paper introduces a master equation method to analyze RVB wavefunctions, revealing how bond amplitudes evolve and indicating phase transitions in the J1-J2 antiferromagnetic Heisenberg model.

Contribution

It develops a novel master equation approach for RVB bond amplitudes and applies it to identify phase transitions and orderings in the J1-J2 model.

Findings

Bond amplitudes decay as 1/r^3 without frustration.

Signs of VBS order emerge with increased frustration.

Magnetic moment vanishes at J2/J1=0.447, indicating a phase transition.

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.