The resonant valence bond (RVB) state is a quantum spin liquid that initiated a transformative shift in modern physics, influencing a broad spectrum of fields, from high-temperature superconductors to quantum computing, and gave birth to key concepts in physics, such as emergent gauge symmetries, topological order, and fractionalisation. Despite extensive efforts over the past fifty years to demonstrate the existence of an RVB phase, a definitive realisation has proven elusive.
Recently, it was, however, shown that the RVB state can be induced in certain magnetic systems through doping as a consequence of frustration of the kinetic energy of the spins. In particular, the so-called t-J model on both the pyrochlore and checkerboard lattices shows an RVB ground state when t is dominant and the doping concentration is sufficiently low.
This project aims to investigate the stability of the RVB state on the checkerboard lattice when the coupling strength is different on the diagonal and non-diagonal bonds. Understanding this will be important to guide experimentalists towards an experimental realisation of the long-sought-after RVB state.
The project will employ numerical methods such as exact diagonalisation.