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 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.

arXiv:cond-mat/0311604Nov 26, 20031 citation

Superconductivity in correlated wave functions

Claudius Gros

We describe a new method to numerically evaluate the properties of correlated superconducting wave functions. We have applied it to the resonating-valence-bond (RVB) wave function for the Hubbard model on the square lattice. For the half-filled case we find that the $d$ -wave RVB state and the antiferromagnetic ordered state have the same energy within numerical accuracy. At 10% doping we find $d$ -wave superconductivity, consistent with previous studies. We show that the superconducting order parameter is proportional to the number of holes, for small hole concentrations.We describe a new method to numerically evaluate the properties of correlated superconducting wave functions. We have applied it to the resonating-valence-bond (RVB) wave function for the Hubbard model on the square lattice. For the half-filled case we find that the $d$-wave RVB state and the antiferromagnetic ordered state have the same energy within numerical accuracy. At 10% doping we find $d$-wave superconductivity, consistent with previous studies. We show that the superconducting order parameter is proportional to the number of holes, for small hole concentrations.

Physical review. B, Condensed matterJul 1, 1988294 citations

Theory of Gossamer and resonating valence bond superconductivity

J. Y. Gan, Fu‐Chun Zhang, Zhixun Su

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 $U={U}_{c}$ , 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 $U>{U}_{c}$ to a Gossamer SC state at $U<{U}_{c}$ 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.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 $U={U}_{c}$, 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 $U>{U}_{c}$ to a Gossamer SC state at $U<{U}_{c}$ 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.

arXiv:cond-mat/0308398Physical Review BJan 13, 200527 citations

Kinetic Energy of Holes in the Hubbard Model

Pascal Lederer

This paper compares the kinetic energy of holes in the antiferromagnetic (AF) state and in an approximate singlet liquid wave function of the Resonating Valence Bond type (RVB), with only nearest neighbour singlet pairing. The atomic interaction U of the Hubbard model is taken to be large compared with the band width 8 t . In the limit 8 t / U →0, I find that the hole kinetic energy is at most as low in RVB than in AF, but there are indications that it is in fact lower in AF. At finite t / U , the comparison between AF and RVB depends on corrections of order t / U which are not known yet for RVB, but which should be of the same order as in AF. As a restult within the simplest Hubbard model with nearest neighbour hopping, it is unlikely that a small concentration of holes can stabilize RVB if the latter is less stable than AH at half band filling.This paper compares the kinetic energy of holes in the antiferromagnetic (AF) state and in an approximate singlet liquid wave function of the Resonating Valence Bond type (RVB), with only nearest neighbour singlet pairing. The atomic interaction U of the Hubbard model is taken to be large compared with the band width 8 t . In the limit 8 t / U →0, I find that the hole kinetic energy is at most as low in RVB than in AF, but there are indications that it is in fact lower in AF. At finite t / U , the comparison between AF and RVB depends on corrections of order t / U which are not known yet for RVB, but which should be of the same order as in AF. As a restult within the simplest Hubbard model with nearest neighbour hopping, it is unlikely that a small concentration of holes can stabilize RVB if the latter is less stable than AH at half band filling.

Journal of the Physical Society of JapanMay 15, 19886 citations

Hole propagation in correlated spin systems

Robert Joynt

An approximation method is presented for the calculation of the Green's function for a single hole moving in a correlated spin background. General formulas are obtained for calculating the moments of the Green's function, generalizing the Brinkman-Rice method to a general spin state. Numerical results are presented for a one-dimensional Gutzwiller resonating-valence-bond (RVB) state. In the two-dimensional case, the bandwidth is derived. The kinetic energy of a single hole in a correlated antiferromagnet or Gutzwiller RVB state is higher than in a N\'eel antiferromagnet.An approximation method is presented for the calculation of the Green's function for a single hole moving in a correlated spin background. General formulas are obtained for calculating the moments of the Green's function, generalizing the Brinkman-Rice method to a general spin state. Numerical results are presented for a one-dimensional Gutzwiller resonating-valence-bond (RVB) state. In the two-dimensional case, the bandwidth is derived. The kinetic energy of a single hole in a correlated antiferromagnet or Gutzwiller RVB state is higher than in a N\'eel antiferromagnet.

Physical review. B, Condensed matterMay 1, 198833 citations

Entanglement in doped resonating valence bond states

Ravishankar Ramanathan, Dagomir Kaszlikowski, Marcin Wieśniak +1 more

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.

arXiv:0808.3655Physical Review BDec 12, 20085 citations

d

-wave RVB state and the antiferromagnetic ordered state have the same energy within numerical accuracy. At 10% doping we find

d

-wave superconductivity, consistent with previous studies. We show that the superconducting order parameter is proportional to the number of holes, for small hole concentrations.

U

from a Gossamer superconductor at small

U

. At the critical value

U={U}_{c}

, 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>{U}_{c}

to a Gossamer SC state at

U<{U}_{c}

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.