We consider RVB state as a variational estimate for the ground state of Heisenberg antiferromagnet in square lattice. We present numerical calculation of energy, spin-spin correlation function and spin excitation spectrum. We show, that the quantum flactuations reduce of magnetization respect to Neel order. Our results are in good agreement with other methods such as spin-wave calculation and series expansions.

Iranian Journal of Physics ResearchSep 15, 20090 citations

arXiv:cond-mat/0311604

A renormalised hamiltonian approach for a resonant valence bond wavefunction

F. C. Zhang, Claudius Gros, Thomas Maurice Rice, Hiroyuki Shiba

Published Nov 26, 2003• 1 citation

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.cond-mat/0311604

Related papers

A renormalised Hamiltonian approach to a resonant valence bond wavefunction

Fu‐Chun Zhang, Claudius Gros, Thomas Maurice Rice +1 more

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(1) invariance leads to a redundancy in the representation. The introduction of holes removes these local invariances and the authors 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(1) invariance leads to a redundancy in the representation. The introduction of holes removes these local invariances and the authors 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.

Superconductor Science and TechnologyJun 1, 1988560 citations

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

TWO-DIMENSIONAL ANTIFERROMAGNETIC HEISENBERG MODEL: EXACT AND RVB STATES

Didier Poilblanc

The exact many-body states of a 10-site square cluster with periodic boundary conditions of a S = 1/2 antiferromagnetic Heisenberg lattice model are investigated. A general form of a Resonating Valence Bond wavefunction (RVB), written in fermion representation is examined. It is shown that the optimum variational wavefunction has complex singlet bond distribution amplitudes of s+id symmetry . It has a very large overlap with the groundstate, belongs to the same space group representation and its energy functional has a minimum very close to the ground-state energy. On the other hand, if the amplitudes are restricted to real numbers, the local minimum has slightly higher energy and d-wave symmetry.The exact many-body states of a 10-site square cluster with periodic boundary conditions of a S = 1/2 antiferromagnetic Heisenberg lattice model are investigated. A general form of a Resonating Valence Bond wavefunction (RVB), written in fermion representation is examined. It is shown that the optimum variational wavefunction has complex singlet bond distribution amplitudes of s+id symmetry . It has a very large overlap with the groundstate, belongs to the same space group representation and its energy functional has a minimum very close to the ground-state energy. On the other hand, if the amplitudes are restricted to real numbers, the local minimum has slightly higher energy and d-wave symmetry.

International Journal of Modern Physics BOct 1, 19881 citation

Optimized resonating valence bond state in square lattice: correlations & excitations

Zahra Nourbakhsh, Farhad Shahbazi, Sayed Akbar Jafari

Iranian Journal of Physics ResearchSep 15, 20090 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.