Hierarchical Mean-Field Approach in Frustrated Spin and Lattice Boson Systems.

Azad E. Behzadi, Susan R. McKay

Daniel Huerga, J. Dukelsky, Nicolas Laflorencie +1 more

We study the zero-temperature phase diagram of two-dimensional hard-core bosons on a square lattice with nearest-neighbor and plaquette (ring-exchange) hoppings, at arbitrary densities, by means of a hierarchical mean-field theory. In the frustrated regime, where quantum Monte Carlo suffers from a sign problem, we find a rich phase diagram where exotic states with nonzero chirality emerge. Among them, novel insulating phases, characterized by nonzero bond-chirality and plaquette order, are found over a large region of the parameter space. In the unfrustrated regime, the hierarchical mean-field approach improves over the standard mean-field treatment as it is able to capture the transition from a superfluid to a valence bond state upon increasing the strength of the ring-exchange term, in qualitative agreement with quantum Monte Carlo results.

Ramesh V. Pai, K. Sheshadri, Rahul Anil Pandit

Леонид Исаев, Gerardo Ortíz, J. Dukelsky

We study the quantum phase diagram and excitation spectrum of the frustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying relevant degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry-preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers, and other degrees of freedom, and show that only the symmetric plaquette covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) plaquette crystal, connected with the neighboring N\'eel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the N\'eel and columnar phases. Our results suggest that the quantum phase transition between N\'eel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.

R. Allub

Stuart Pittel, Alejandro Frank