Variational-Correlations Approach to Quantum Many-Body Physics

I will present a variational method for studying the ground state of a quantum many-body Hamiltonian, which treats the correlation functions as variational parameters. This numerical approach is based on approximating the positivity of the density matrix in a controlled manner, and allows for obtaining the (approximate) ground state in polynomial time. Unlike the conventional variational principle which provides an upper bound on the ground-state energy, in this approach one obtains a lower bound on the ground-state energy. I will demonstrate the method on several one-dimensional spin 1/2 Hamiltonians. Possible extensions of the method will be discussed.