Resonating Valence Bond States and High-T c Superconductivity

C. D. Batista, Armando A. Aligia

K. P. Jain, D.K. Ray

Sudipto Singha Roy, Himadri Shekhar Dhar, Debraj Rakshit +2 more

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.

Wenjun Zheng

The stripe phase in high ${T}_{c}$ cuprates is modeled as a single stripe coupled to the resonating valence bond (RVB) spin liquid background by the single particle hopping process. In the normal state, the strong pairing correlation inherent in a RVB state is thus transferred into the Luttinger stripe and drives it toward spin-gap formation described by the Luther-Emery model. The establishment of global phase coherence in the superconducting state contributes to a more relevant coupling to Luther-Emery stripe and leads to gap opening in both spin and charge sectors. Physical consequences of the present picture are discussed.

J. González, Miguel Angel Martin-Delgado, Germán Sierra +1 more

Dmitri A. Ivanov

Gutzwiller-projected (GP) wave functions have been widely used for describing spin-liquid physics in frustrated magnets and in high-temperature superconductors. Such wave functions are known to represent states of the resonating-valence-bond (RVB) type. In the present work I discuss the RVB structure of a GP singlet superconducting state with nodes in the spectrum. The resulting state for the undoped spin system may be described in terms of a ``path integral'' over loop coverings of the lattice, thus extending the known construction for RVB states. The problem of topological order in GP states may be reformulated in terms of the statistical behavior of loops. The simple example of the projected $d$-wave state on the square lattice demonstrates that the statistical behavior of loops is renormalized in a nontrivial manner by the projection.