Fidelity susceptibility approach to study metastable phase separated states in the extended Bose-Hubbard ladder

Abstract

The one-dimensional extended Bose-Hubbard(EBHM) model is a well-studied problem. Depending on the interactions and hopping strength, the system can be either in a Mott insulator, supersolid, superfluid, Haldane insulator, and metastable phase-separated states. On the other hand, EBHM in a ladder setup is not well studied. The setup offers many more possibilities which can lead to novel quantum phases in the model. The system we consider is symmetric, with open boundary conditions. We restrict ourselves to unit filling fraction. Each leg has an onsite interaction, nearest neighbour interactions, and nearest neighbour hopping. An interchain hopping couples the legs. The ground state phases are identified using density wave order parameter, string correlator function, charge gap, and fidelity susceptibility. We use finite-size scaling for extrapolating to the thermodynamic limit to find the phase boundaries. We find a supersolid phase in the ladder, elusive in the one-dimensional case at unit filling fraction. The effect of interchain hopping on the phase-separated region found in the one-dimensional EBHM is also explored. We find that the interchain hopping destabilizes these metastable states to a supersolid phase. The critical points to the supersolid phase are identified using the fidelity susceptibility.