Theoretical Physics Seminar

Ultracold bosonic atoms in optical lattices are versatile testbeds for investigating equilibrium and out-of-equilibrium aspects of quantum many-body systems, whose behavior can be described by Bose-Hubbard-type Hamiltonians. Owing to the large local Hilbert-space dimension for bosonic atoms or mixtures of different atomic species, exact diagonalization based approaches are computationally difficult. In this context, I will discuss a computationally feasible approach by considering a family of particle number conserving ansatz states that goes beyond mean-field theory and are able to capture quantum correlations and entanglement in the ground-state via projection onto an effective low-energy manifold which grows polynomially with system size. These states have the same number of variational parameters as the well-known Gutzwiller ansatz states that are often used to describe the physical properties of such systems. Furthermore, within the framework of time-dependent variational principle, these ansatz states allow us to study the early-times relaxation dynamics of various out-of-equilibrium initial states under a sudden quench. We compare our results against exact diagonalization/ tensor-network-based approaches in the paradigmatic 1D Bose-Hubbard model in both equilibrium and out-of-equilibrium scenarios by studying the long-range phase coherence, ground-state entanglement entropy and anomalous relaxation processes such as the quantum Mpemba effect. Finally, I will discuss how these approaches can be generalized to a large class of strongly correlated systems realized in ultracold atomic setups. Reference : https://arxiv.org/pdf/2508.01692v1