We construct energy-optimized resonating valence bond wave functions 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-neighbor (J2) interactions. Our emphasis is not on achieving an accurate representation of the magnetically disordered intermediate phase (centered 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 labeling is fixed beforehand and another in which the worm manipulates the current labeling so as to sample various sign conventions. Our results suggest that the disordered phase evolves continuously out of the (π,π) Néel phase and largely inherits its Marshall sign structure; on the other hand, the transition from the magnetically ordered (π,0) phase is strongly first order and involves an abrupt change in the sign structure and spatial symmetry as the result of a level crossing.

@article{
  title = {Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure},
  author = {Zhang, Xiaoming and Beach, K. S. D.},
  journal = {Physical Review B},
  volume = {87},
  issue = {9},
  pages = {094420},
  numpages = {12},
  year = {2013},
  month = {Mar},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.87.094420},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.87.094420}
}