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Physical review. B, Condensed matter

Resonating-valence-bond ground state in a large-nt-Jmodel

Hal Tasaki, Mahito Kohmoto

Published Aug 1, 1990• 5 citations
Publisher

Abstract

To shed light on the roles of hole doping in strongly interacting electron systems, we study a large-n version of the t-J model. When there are holes we prove that a novel resonating-valence-bond (RVB) state, which we call the hopping-dominated RVB (hRVB) state, is the unique ground state. We conjecture the existence of a phase transition between the standard tunneling-dominated phase and the new hopping-dominated phase. By treating the hopping term in the second-order perturbation, we get an exactly solvable toy model whose ground state is the nearest-neighbor hRVB state.

DOI
10.1103/physrevb.42.2547

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Physical review. B, Condensed matter•Apr 1, 1989•16 citations
To shed light on the roles of hole doping in strongly interacting electron systems, we study a large-n version of the t-J model. When there are holes we prove that a novel resonating-valence-bond (RVB) state, which we call the hopping-dominated RVB (hRVB) state, is the unique ground state. We conjecture the existence of a phase transition between the standard tunneling-dominated phase and the new hopping-dominated phase. By treating the hopping term in the second-order perturbation, we get an exactly solvable toy model whose ground state is the nearest-neighbor hRVB state.
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 have calculated the energy of the resonating-valence-bond (RVB) state made of nearest-neighbor singlet pairs in the two-dimensional Hubbard model at half filling and the energy of holes in the RVB state near half filling. The energy of the RVB state was obtained by extrapolating the result in a 6\ifmmode\times\else\texttimes\fi{}6 square lattice with the periodic boundary condition to the infinite lattice. The energy of holes was obtained by examining the first five moments of the density of states of holes in the RVB state. We find that the holes are more stabilized in the RVB state than in the N\'eel state for J/t\ensuremath{\gtrsim}0.1, where J and t are the exchange interaction and the nearest-neighbor hopping integral, respectively. We discuss the possibility of the RVB state in the high-Tc{T}_{c}Tc​ Cu oxides.
We propose a class of ground states for doped Mott insulators in the electron second quantization representation. They are obtained from a bosonic resonating valence bond (RVB) theory of the $t\text{\penalty1000-\hskip0pt}J$ model. At half filling, the ground state describes spin correlations of the S=1∕2S=1∕2S=1∕2 Heisenberg model very accurately. Its spin degrees of freedom are characterized by RVB pairing of spins, the size of which decreases continuously as holes are doped into the system. Charge degrees of freedom emerge upon doping and are described by twisted holes in the RVB background. We show that the twisted holes exhibit an off diagonal long range order (ODLRO) in the pseudogap ground state, which has a finite pairing amplitude, but is short of phase coherence. Unpaired spins in such a pseudogap ground state behave as free vortices, preventing superconducting phase coherence. The existence of nodal quasiparticles is also ensured by such a hidden ODLRO in the ground state, which is non-Fermi liquidlike in the absence of superconducting phase coherence. Two distinct types of spin excitations can also be constructed. The superconducting instability of the pseudogap ground state is discussed and a ddd-wave superconducting ground state is obtained. This class of pseudogap and superconducting ground states unifies antiferromagnetism, pseudogap, superconductivity, and Mott physics into a new state of matter.
We propose a new exactly solvable model of strongly correlated electrons. The model is based on a d – p model of the CuO 2 plane with infinitely large repulsive interactions on Cu-sites, and it contains additional correlated-hopping, pair-hopping and charge–charge interactions of electrons. For even numbers of electrons less than or equal to 2/3-filling, we construct the exact ground states of the model, all of which have the same energy and each of which is the unique ground state for a fixed electron number. It is shown that these ground states are the resonating-valence-bond states which are also regarded as condensed states in which all electrons are in a single two-electron state. We also show that the ground states exhibit off-diagonal long-range order.
The concept of the resonating valence bond (RVB) state was originally proposed by Anderson (1987) for the ground state of the positive-U Hubbard model. However, the on-site pairing long-range order is expected to exist in the ground state of the negative-U Hubbard model and to be incompatible with the RVB order. In this article, we shall rigorously prove that, in fact, these two long-range orderings either coexist or are suppressed simultaneously in the global ground states of the doped Hubbard models.