Plaquette-type valence bond solid state in the𝐽1−𝐽2square-lattice Heisenberg model

Abstract

We utilize density matrix renormalization group and fully augmented matrix product states (FAMPS) methods to investigate the valence bond solid (VBS) phase in the 𝐽1−𝐽2 square lattice Heisenberg model. To differentiate between the columnar valence bond solid and plaquette valence bond solid (PVBS) phases, we introduce an anisotropy Δ𝑦 in the nearest-neighboring coupling in the 𝑦 direction, aiming at detecting the possible spontaneous rotational symmetry breaking in the VBS phase. In the calculations, we push the bond dimension to as large as 𝐷=25000 in FAMPS, simulating systems at a maximum size of 14×14. With a careful extrapolation of the truncation errors and appropriate finite-size scaling, followed by finite Δ𝑦 scaling analysis of the VBS dimer order parameters, we identify the VBS phase as a PVBS type, meaning there is no spontaneous rotational symmetry breaking in the VBS phase. This paper not only supports the presence of PVBS order in the 𝐽1−𝐽2 square lattice Heisenberg model, but also highlights the capabilities of FAMPS in the study of two-dimensional quantum many-body systems.