Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure

TL;DR

This paper constructs energy-optimized resonating valence bond wavefunctions to explore the phase diagram of the square-lattice quantum Heisenberg model, focusing on the Marshall sign structure's behavior near phase boundaries.

Contribution

It introduces a method to analyze static and dynamic Marshall sign structures in RVB wavefunctions, revealing how sign structures evolve across phase transitions.

Findings

Disordered phase inherits Marshall sign structure from Neel phase

Transition from (pi,pi) Neel phase is continuous with sign structure inheritance

Transition from (pi,0) phase is first order with abrupt sign change

Abstract

We construct energy-optimized resonating valence bond wavefunctions as a means to sketch out the zero-temperature phase diagram of the square-lattice quantum Heisenberg model with competing nearest- (J1) and next-nearest-neighbour (J2) interactions. Our emphasis is not on achieving an accurate representation of the magnetically disordered intermediate phase (centred on a relative coupling g = J2/J1 ~ 1/2 and whose exact nature is still controversial) but on exploring whether and how the Marshall sign structure breaks down in the vicinity of the phase boundaries. Numerical evaluation of two- and four-spin correlation functions is carried out stochastically using a worm algorithm that has been modified to operate in either of two modes: one in which the sublattice labelling is fixed beforehand and another in which the worm manipulates the current labelling so as to sample various sign conventions. Our results suggest that the disordered phase evolves continuously out of the (pi,pi) Neel phase and largely inherits its Marshall sign structure; on the other hand, the transition from the magnetically ordered (pi,0) phase is strongly first order and involves an abrupt change in the sign structure and spatial symmetry as the results of a level crossing.