Linear String Theory for the single hole-doped Quantum Dimer Model

The single hole problem in a 2d quantum antiferromagnet (AFM) attracts attention due to its relevance for high-temperature superconductivity. A microscopic justification for describing mobile holes in an AFM background as bound spinon-chargon states is provided by Linear string theory (LST). For a spin liquid, it is instead often assumed that a hole can move freely through the spin background, which however lacks definite confirmation or refutation. Here, we thus investigate the motion of a single hole through a short-ranged resonating valence bond state as described by the quantum dimer model (QDM) on a square lattice. Therefore, we construct a new model Hamiltonian for the doped QDM where longer-range singlet states are allowed configurations and which explicitly features the string tension. The corresponding potential is calculated in the framework of LST for two different dopings. First, we consider a single chargon before extending the calculation to a spinon-chargon pair. This is done by explicitly calculating the energy of the string states at the Rokhsar-Kivelson point. We find that in both cases the energy increases linearly with the string length.