Entanglement entropy and spectrum across superfluid-insulator transitions with different symmetry breaking

We study the entanglement properties across superfluid-Mott insulator transitions with different types of symmetry breaking. In a previous work [1] about the paradigmatic Bose- Hubbard model on a square lattice, the value of entanglement entropy (EE) at the U(1) transition point at integer filling, where Goldstone and Higgs modes become gapless, is the highest in the phase diagram. In order to expand the discussion of the relationship between EE and symmetry breaking, we consider the Bose-Hubbard model in which the sign of the nearest-neighbor hopping J is inverted on a triangular lattice. In this model, frustration induces a 120-degree phase structure in the superfluid phase, which breaks Z₂ chirality symmetry, in addition to U(1). We also consider the case of anisotropic triangular lattice with frustrated hoppings J, J’. By changing the ratio J’/J we can interpolate between various interesting limits (1D chain, triangular lattice, square lattice) and investigate the properties of EE and entanglement spectrum(ES), including the singular points between different lattice shapes. In this presentation, we discuss superfluid-Mott insulator transition in different types of symmetry breaking from the perspectives of EE and ES.