Tensor network projection variational Monte Carlo approach to many-body quantum lattice systems

Quantum materials exhibit highly cooperative many-body phenomena such as Mott- insulating behaviour, high-Tc superconductivity and colossal magnetoresistance. These effects descend from strong interactions between charge carriers and make such materials very sensitive to small external perturbations. The key scientific question in this theory project is 'does intense THz frequency mode-selective driving of quantum materials coerce them into exhibiting a superconducting phase at higher temperatures than it would under equilibrium conditions?'. By modelling these systems our aim is to guide experiments trying to optimise and control the responses. Extending these effects to room temperature could have a potentially enormous impact on their technological applications. This key approach of this work is to implement dynamical stabilisation. The so-called Kapitza pendulum is an archetypal example. By rapidly vibrating the pivot point of a simple pendulum the usually unstable inverted state can be made stable. Analogously, a series of ground- breaking experiments have recently shown that when a crystal lattice is shaken, modulated or distorted in the right way, then an otherwise unstable or hidden many-body phase can be dynamically stabilised. Application of this idea to condensed matter has now become possible because of two significant experimental advances. The first is the development of high-field coherent optical methods at THz frequencies, which has opened up some of the most important excitations in solids, like optical phonons, superconductor gaps, and Josephson plasma resonances, for interrogation and driving. The second is the substantial progress in fabricating, with atomic precision, complex transition metal oxide heterostructures that induce novel properties at interfaces. Together highly selective strong dynamical distortions and static microscopic tuning promise to deliver new pathways for engineering and stabilising desired forms of order in quantum materials. Motivated by these developments this project will focus on a new and potentially very powerful computational approach, called tensor network projection, for computing the dynamical behaviour of driven strongly-correlated systems. This ansatz contains within it many different variants of commonly used wave functions in variational Monte Carlo. A software package handling all of these in a unified framework will be developed. Extensions to dynamics via the time-dependent variational principle will be implemented. The resulting codes will then be applied directly to the driven Hubbard model to ascertain the emergence of novel correlations, such as superconductivity.