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.
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.
We investigate the trends of genuine multipartite entanglement of high-temperature superconducting states, usually described by doping the Mott insulator. We begin by analyzing the ground states of a Hubbard model with large onsite interactions obtained by exact diagonalization in regimes where the superconducting phase is observed for relatively high doping. The ground states are observed to be genuine multipartite entangled, with the maximum value achieved close to the superconducting phase boundary. Subsequently, for finite hole doping, the short-range resonating valence bond (RVB) state is considered to be the ground state of the Hubbard model. We prove that doped RVB ladder states are always genuine multipartite entangled. We then formulate an analytical recursion method for the wave function, which allows us to efficiently estimate the entanglement as well as other physical quantities in large doped RVB ladders. The maximum genuine multipartite entanglement in these RVB states is observed at doping corresponding to the superconducting phase of the Hubbard model.
We use an effective Hamiltonian for two-dimensional Hubbard model including an antiferromagnetic spin-spin coupling term to study recently proposed Gossamer superconductivity. We apply a renormalized mean field theory to approximately take into account the strong correlation effect in partially projected Gutzwiller wave functions. At the half-filling, there is a first order phase transition to separate a Mott insulator at large Coulomb repulsion U from a Gossamer superconductor at small U. At the critical value U=Uc, the charge carrier density and the superconducting (SC) order parameter change discontinuously from zero in the Mott insulating phase to finite values in the Gossamer SC phase. The first order transition is due to the interplay of the kinetic and spin exchange energies. As the electron density changes away from half-filling, the Gossamer SC state changes smoothly, while the Mott insulator is evolved into a resonating valence bond (RVB) SC state. The Gossamer and RVB SC states have the same pairing symmetry. The SC order parameter changes smoothly from a RVB SC state at U>Uc to a Gossamer SC state at U<Uc at a fixed nonhalf-filled electron density. We argue that the RVB SC state is smoothly connected to the Gossamer SC state, hence to the BCS state.
Resonating valence bond (RVB) states are fundamental for understanding quantum spin liquids in two-dimensional (2D) systems. The RVB state is a collective phenomenon in which spins are uncoupled. 2D lattices such as triangular, honeycomb, and dice lattices were investigated using the Hubbard model and exact diagonalization method. We analyzed the total spin, spin-spin correlation functions, local magnetic moments, and spin and charge gaps as a function of on-site Coulomb repulsion, electron concentration, and electronic hopping parameters. Phase diagrams showed that RVB states can live in half-filled and hole-doped anisotropic triangular lattices. We found two types of RVB states: one in the honeycomb sublattice and the other in the centered hexagons in the triangular lattices. Owing to the novel discovery of exotic magnetic ordering in triangular moiré patterns in twisted bilayer graphene and transition metal dichalcogenide systems, our results provide physical insights into the onset of magnetism and possible spin liquid states in these layered materials.
The effective Hamiltonian of strongly correlated electrons on a square lattice is replaced by a renormalised Hamiltonian and the factors that renormalise the kinetic energy of holes and the Heisenberg spin-spin coupling are calculated using a Gutzwiller approximation scheme. The accuracy of this renormalisation procedure is tested numerically and found to be qualitatively excellent. Within the scheme a resonant valence bond (RVB) wavefunction is found at half-filling to be lower in energy than the antiferromagnetic state. If the wavefunction is expressed in fermion operators, local SU(2) and U(l) invariance leads to a redundancy in the representation. The introduction of holes removes these local invariances and we find that a d-wave RVB state is lowest in energy. This state has a superconducting order parameter whose amplitude is linear in the density of holes.
The Hubbard model in D dimensions, with the on-site repulsion U and the transfer integral between nearest neighbors −t/D, is studied on the basis of the Kondo-lattice theory. If U/∣t∣≫1, ∣n−1∣≲∣t∣/(DU), where n is the number of electrons per unit cell, and D is so small that ∣J∣/D≫kBTc, where J=−4t2/U and Tc is 0K for D=1 and is the highest critical temperature among possible ones for D≥2, a low-T phase where Tc<T≪∣J∣/(kBD) is a frustrated electron liquid. Since the liquid is stabilized by the Kondo effect in conjunction with the resonating-valence-bond (RVB) mechanism, it is simply the RVB electron liquid; in one dimension, it is also the Tomonaga-Luttinger liquid. The Kondo energy of the RVB liquid is kBTK=O(∣J∣/D); its effective Fermi energy is O(kBTK). A midband appears on the chemical potential between the upper and lower Hubbard bands; the Hubbard gap is a pseudogap. As regards the density of states per unit cell of the midband, its bandwidth is O(kBTK) or O(∣J∣/D), its peak height is O(1/U), and its spectral weight is O[t2/(DU2)]. Since the midband almost disappears in the Heisenberg limit, the RVB electron liquid in the Heisenberg limit is simply the RVB spin liquid. The RVB electron and spin liquids adiabatically continue to each other. Since local moments form in a high-T phase where T≳TK, the high-T phase is simply the Mott insulator.
In a recent Letter [Phys. Rev. Lett. 99, 170502 (2007); quant-ph/0703227], Chandran and coworkers study the entanglement properties of valence bond (VB) states. Their main result is that VB states do not contain (or only an insignificant amount of) two-site entanglement, whereas they possess multi-body entanglement. Two examples ("RVB gas and liquid") are given to illustrate this claim, which essentially comes from a lower bound derived for spin correlators in VB states. We show in this Comment that (i) for the "RVB liquid" on the square lattice, the calculations and conclusions of Chandran et al. are incorrect. (ii) A simple analytical calculation gives the exact value of the correlator for the "RVB gas", showing that the bound found by Chandran et al. is tight. (iii) The lower bound for spin correlators in VB states is equivalent to a celebrated result of Anderson dating from more than 50 years ago.