In recent years, my research group has focused on strong electron correlation, a problem that after almost 100 years of Schrodinger equation, remains pervasive and hinders many practical applications.

In this talk, I will discuss our recent efforts to tackle it using dualities that convert strongly correlated systems into more weakly correlated ones. String operators, such as those appearing in the Jordan-Wigner transformation when mapping fermions to qubits, play a central role in the theory. String operators are responsible for the algebra transmutation between fermions and spin ½ (hardcore bosons). Despite their nonlocal and many-body characteristics, matrix elements of string operators can be obtained with low polynomial computational cost in classical computers.

I will present proof of principle applications of the theory to modeling strongly correlated spin systems as fermions.