A quasiparticle description of the hole doped "short range" RVB state is developed and it is applied to study the ground state properties of the interacting many holon fluid. The model is based on the conjecture that the elementary charged excitation of the RVB state, the holon, corresponds to an quantized vortex in a condensed quantum fluid of mobile singlets. The doped RVB state is described as a two component fluid of these quasiparticles with repulsive electrostatic interparticle interactions and an effective U(1) gauge field coupling the motion of these objects to the condensed particles of the parent RVB fluid. In this model for the doped state we find: (1) Quantum commensurability effects in the doped state, similar to those encountered in the fractional quantum Hall problem, lead to phase segregation of a doped state which corresponds to a 20% dilution of the doped antiferromagnet. (2) The ground state of the interacting holon fluid at this density is found to exhibit off diagonal long range order, describing a two-dimensional pairing condensation of the holons.
The interaction between the bosonic excitations as well as between the fermionic ones in the RVB systems with the (extended) Hubbard Hamiltonian were studied by means of the slave boson technique and the perturbation theory. The corresponding effective Hamiltonians have been found. It was shown, in particular, that in the RVB system with two interpenetrating sublattices there exists the effective attraction between two holons of different kinds as well as between two spinions of different kinds in the singlet state.
The effect of gauge fields representing the fluctuations of the local constraint and those of the phases of the bond order parameters is examined for the uniform RVB state, which is a mean-field (MF) solution of the t-J model within the slave-boson formalism. It is found that the crossover temperature for the Bose condensation of holons, T BE , below which the system may be essentially considered to be a Fermi liquid, is considerably reduced as compared with that in the MF approximation. The temperature dependences of the transport relaxation rate and the electrical resistivity are also examined
The doped two-dimensional quantum dimer model is investigated by numerical techniques on the square and triangular lattices, with significantly different results. On the square lattice, at small enough doping, there is always a phase separation between an insulating valence-bond solid and a uniform superfluid phase, whereas on the triangular lattice, doping leads directly to a uniform superfluid in a large portion of the resonating-valence-bond (RVB) phase. Under an applied Aharonov-Bohm flux, the superfluid exhibits quantization in terms of half-flux quanta, consistent with Q=2e elementary charge quanta in transport properties.
We investigate the entanglement properties of resonating valence bond (RVB) states on a two-dimensional lattice in the presence of dopants that remove electrons from the lattice creating holes. The movement of the holes generated by the Hubbard Hamiltonian in the regime of strong Coulomb repulsion in this setting could be responsible for the phenomenon of high-temperature superconductivity as hypothesized by [Anderson Science 235, 1196 (1987)]. We argue that there is a particular density of dopants (holes) where the entanglement contained in the lattice attains its maximal value for the nearest-neighbor RVB liquid state. This result implies that many-body entanglement may be related to quantum phase transitions that are modeled by RVB theory.
In the ionic Hubbard model, the on-site repulsion
U, which drives a Mott insulator, and the ionic potential
V, which drives a band insulator, compete with each other to open up a window of charge fluctuations when $U\ensuremath{\sim}V$. We study this model on square and cubic lattices in the limit of large
U and
V, with $V\ensuremath{\sim}U$. Using an effective Hamiltonian and a slave-boson approach with both doublons and holons, we find that the system undergoes a phase transition as a function of
V from an antiferromagnetic Mott insulator to a paramagnetic insulator with strong singlet correlations, which is driven by a condensate of ``neutral'' doublon-holon pairs. On further increasing
V, the system undergoes another phase transition to a superconducting phase driven by condensate of ``charged'' doublons and holons. The superfluid phase, characterized by the presence of a coherent (but gapped) fermionic quasiparticle and
hc/e flux quantization, has a high ${T}_{c}\ensuremath{\sim}t$, which shows a dome-shaped behavior as a function of
V. The paramagnetic insulator phase has a deconfined U(1) gauge field and associated gapless photon excitations. We also discuss how these phases can be detected in the ultracold-atom context.