We develop a quantum spin-liquid theory for quantum magnets with easy-plane ferromagnetic exchange. These strongly entangled quantum states are obtained by dimer coverings of two-dimensional (2D) lattices with triplet $S=1,{m}_{z}=0$ bonds, forming a triplet resonating valence bond (tRVB) state. We discuss the conditions and the procedure to transfer well-known results from conventional singlet resonating valence bond theory to tRVB. Additionally, we present mean field theories of Abrikosov fermions on 2D triangular and square lattices, which can be controlled in an appropriate large- $N$ limit. We also incorporate the effect of charge doping which stabilizes $(p+ip)$ -wave superconductivity. Beyond the pure theoretical interest, our study may help to resolve contradictory statements on certain transition metal chalcogenides, including $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$, $1T\text{\ensuremath{-}}{\mathrm{TaSe}}_{2}$, as well as ${\mathrm{CrSiTe}}_{3}$ and ${\mathrm{CrGeTe}}_{3}$ .We develop a quantum spin-liquid theory for quantum magnets with easy-plane ferromagnetic exchange. These strongly entangled quantum states are obtained by dimer coverings of two-dimensional (2D) lattices with triplet $S=1,{m}_{z}=0$ bonds, forming a triplet resonating valence bond (tRVB) state. We discuss the conditions and the procedure to transfer well-known results from conventional singlet resonating valence bond theory to tRVB. Additionally, we present mean field theories of Abrikosov fermions on 2D triangular and square lattices, which can be controlled in an appropriate large-$N$ limit. We also incorporate the effect of charge doping which stabilizes $(p+ip)$-wave superconductivity. Beyond the pure theoretical interest, our study may help to resolve contradictory statements on certain transition metal chalcogenides, including $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$, $1T\text{\ensuremath{-}}{\mathrm{TaSe}}_{2}$, as well as ${\mathrm{CrSiTe}}_{3}$ and ${\mathrm{CrGeTe}}_{3}$.

arXiv:2109.03851Physical review. B./Physical review. BFeb 22, 20226 citations

Fermi liquid in the Hubbard Model with an electron reservoir: Normal state of cuprate superconductors

Fusayoshi J. Ohkawa

It is proved that the ground state under the supreme single-site approximation (S^3A), the dynamical mean-field theory (DMFT), or the dynamical coherent potential approximation (DCPA) is the normal Fermi liquid in the presence of an infinitesimally weak hybridization with an electron reservoir, except for the just half filling of electrons and the infinite on-site repulsion. In the strong-coupling regime, in particular, the Fermi liquid is stabilized under S^3A, DMFT, or DCPA by the Kondo effect, which stabilizes a local singlet on each unit cell, and is further stabilized beyond it by the Fock-type term of the superexchange interaction or a resonating valence bond (RVB) mechanism, which stabilizes a local singlet on each pair of nearest neighbors. The Fermi liquid is a relevant normal state to study possible lower-temperature phases or the true ground state. It is proposed that the Fermi liquid stabilized by the Kondo effect and the RVB mechanism is the normal state of cuprate high-temperature superconductors.It is proved that the ground state under the supreme single-site approximation (S^3A), the dynamical mean-field theory (DMFT), or the dynamical coherent potential approximation (DCPA) is the normal Fermi liquid in the presence of an infinitesimally weak hybridization with an electron reservoir, except for the just half filling of electrons and the infinite on-site repulsion. In the strong-coupling regime, in particular, the Fermi liquid is stabilized under S^3A, DMFT, or DCPA by the Kondo effect, which stabilizes a local singlet on each unit cell, and is further stabilized beyond it by the Fock-type term of the superexchange interaction or a resonating valence bond (RVB) mechanism, which stabilizes a local singlet on each pair of nearest neighbors. The Fermi liquid is a relevant normal state to study possible lower-temperature phases or the true ground state. It is proposed that the Fermi liquid stabilized by the Kondo effect and the RVB mechanism is the normal state of cuprate high-temperature superconductors.

arXiv:0807.0073Jul 1, 20080 citations

Resonating valence bond wave function: from lattice models to realistic systems

Michele Casula, Seiji Yunoki, Claudio Attaccalite +1 more

arXiv:cond-mat/0411745Computer Physics CommunicationsApr 16, 20059 citations

Two-leg t−J ladder: A mean-field description

Y. L. Lee, Y. W. Lee, Chung‐Yu Mou +1 more

Two-leg $t\ensuremath{-}J$ ladders are investigated in the framework of a combination of the phase string formulation and bond-operator representation. We develop a mean-field theory in the strong rung interaction regime, i.e., ${J}_{\ensuremath{\perp}}\ensuremath{\gg}J,t,$ which provides a unified description of the undoped insulating phase and the low-doping phase---the so-called $C1S0$ phase. Both of them are characterized by the resonating-valence-bond (RVB) order parameter, with gap opened up in all spin excitations. The ground state of the doped phase is intrinsically a superconductor with a d-wave symmetry, which is driven by the RVB correlations. The ground-state energy is in good agreement with numerical results. Phase separation is shown to occur beyond some critical value of $J/t$ for given doping concentration. The local structure of hole pairs as well as the spectra of various spin and charge modes are analyzed in comparison with other approaches.Two-leg $t\ensuremath{-}J$ ladders are investigated in the framework of a combination of the phase string formulation and bond-operator representation. We develop a mean-field theory in the strong rung interaction regime, i.e., ${J}_{\ensuremath{\perp}}\ensuremath{\gg}J,t,$ which provides a unified description of the undoped insulating phase and the low-doping phase---the so-called $C1S0$ phase. Both of them are characterized by the resonating-valence-bond (RVB) order parameter, with gap opened up in all spin excitations. The ground state of the doped phase is intrinsically a superconductor with a d-wave symmetry, which is driven by the RVB correlations. The ground-state energy is in good agreement with numerical results. Phase separation is shown to occur beyond some critical value of $J/t$ for given doping concentration. The local structure of hole pairs as well as the spectra of various spin and charge modes are analyzed in comparison with other approaches.

arXiv:cond-mat/9903059Physical review. B, Condensed matterNov 15, 199910 citations

S=1,{m}_{z}=0

bonds, forming a triplet resonating valence bond (tRVB) state. We discuss the conditions and the procedure to transfer well-known results from conventional singlet resonating valence bond theory to tRVB. Additionally, we present mean field theories of Abrikosov fermions on 2D triangular and square lattices, which can be controlled in an appropriate large-

N

limit. We also incorporate the effect of charge doping which stabilizes

(p+ip)

-wave superconductivity. Beyond the pure theoretical interest, our study may help to resolve contradictory statements on certain transition metal chalcogenides, including $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$, $1T\text{\ensuremath{-}}{\mathrm{TaSe}}_{2}$, as well as

{\mathrm{CrSiTe}}_{3}

and

{\mathrm{CrGeTe}}_{3}

C1S0

phase. Both of them are characterized by the resonating-valence-bond (RVB) order parameter, with gap opened up in all spin excitations. The ground state of the doped phase is intrinsically a superconductor with a d-wave symmetry, which is driven by the RVB correlations. The ground-state energy is in good agreement with numerical results. Phase separation is shown to occur beyond some critical value of

J/t

for given doping concentration. The local structure of hole pairs as well as the spectra of various spin and charge modes are analyzed in comparison with other approaches.