Beyond Gutzwiller: Exploring correlated excitations with perturbative tensor networks

The Mott insulator–superfluid transition in the one-dimensional Bose–Hubbard model is a paradigmatic example of a second-order quantum phase transition. While mean-field approaches capture the transition itself, they fail to accurately describe correlated excitations in the Mott phase. We introduce a perturbative tensor network ansatz based on the Bogoliubov–de Gennes (BdG) equations that overcomes this limitation. Our results demonstrate that BdG excitations provide both conceptual insight and quantitative accuracy for correlated excitations in the Mott phase. Moreover, we establish a connection between these excitations and tangent vectors on the tensor network variety.