Cold atoms in optical lattices is the application of two formerly distinct aspects of physics: quantum gases from atomic physics and laser theory from quantum optics. Its use to simulate quantum phenomena and models in condensed matter physics is a growing field. The major goal is to use cold fermonic atoms in these superlattices for the simulations. We present here a theoretical proposal for simulating a spin ordering model using fermions. We demonstrate superexchange interaction in the double well and resonating valence bond (RVB) states in kagome lattice which is important for understanding the CuO2 plane of the superconducting cuprates and other magnetic frustrated materials.Cold atoms in optical lattices is the application of two formerly distinct aspects of physics: quantum gases from atomic physics and laser theory from quantum optics. Its use to simulate quantum phenomena and models in condensed matter physics is a growing field. The major goal is to use cold fermonic atoms in these superlattices for the simulations. We present here a theoretical proposal for simulating a spin ordering model using fermions. We demonstrate superexchange interaction in the double well and resonating valence bond (RVB) states in kagome lattice which is important for understanding the CuO2 plane of the superconducting cuprates and other magnetic frustrated materials.

arXiv:1306.0961Jun 5, 20134 citations

Triplet resonating valence bond theory and transition metal chalcogenides

Elio J. König, Yashar Komijani, Piers Coleman

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

Strong coupling Hubbard model and superconductivity

M. Noga

Czechoslovak Journal of PhysicsNov 1, 19890 citations

Fermion Pairing and Superconductivity

Philippe A. Martin, FRANÇOIS ROTHEN

Springer eBooksJan 1, 20020 citations

Low-energy physical properties of high- Tc superconducting Cu oxides: A comparison between the resonating valence bond and experiments

Kaiyu Yang, C. T. Shih, Chung-Pin Chou +4 more

In a recent review by Anderson and co-workers, it was pointed out that an early resonating valence bond (RVB) theory is able to explain a number of unusual properties of high-temperature superconducting (SC) Cu oxides. Here we extend previous calculations to study more systematically the low-energy physical properties of the plain vanilla $d$ -wave RVB state, and to compare the results with the available experiments. We use a renormalized mean-field theory combined with variational Monte Carlo and power Lanczos methods to study the RVB state of an extended $t\text{\ensuremath{-}}J$ model in a square lattice with parameters suitable for the hole-doped Cu oxides. The physical observable quantities we study include the specific heat, the linear residual thermal conductivity, the in-plane magnetic penetration depth, the quasiparticle energy at the antinode $(\ensuremath{\pi},0)$, the superconducting energy gap, the quasiparticle spectra, and the Drude weights. The traits of nodes (including ${k}_{F}$ , the Fermi velocity ${v}_{F}$ , and the velocity along Fermi surface ${v}_{2}$ ), and the SC order parameter are studied. Comparisons of the theory and the experiments in cuprates show an overall qualitative agreement, especially on their doping dependences.In a recent review by Anderson and co-workers, it was pointed out that an early resonating valence bond (RVB) theory is able to explain a number of unusual properties of high-temperature superconducting (SC) Cu oxides. Here we extend previous calculations to study more systematically the low-energy physical properties of the plain vanilla $d$-wave RVB state, and to compare the results with the available experiments. We use a renormalized mean-field theory combined with variational Monte Carlo and power Lanczos methods to study the RVB state of an extended $t\text{\ensuremath{-}}J$ model in a square lattice with parameters suitable for the hole-doped Cu oxides. The physical observable quantities we study include the specific heat, the linear residual thermal conductivity, the in-plane magnetic penetration depth, the quasiparticle energy at the antinode $(\ensuremath{\pi},0)$, the superconducting energy gap, the quasiparticle spectra, and the Drude weights. The traits of nodes (including ${k}_{F}$, the Fermi velocity ${v}_{F}$, and the velocity along Fermi surface ${v}_{2}$), and the SC order parameter are studied. Comparisons of the theory and the experiments in cuprates show an overall qualitative agreement, especially on their doping dependences.

arXiv:cond-mat/0603423Physical Review BJun 16, 200641 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}

d

-wave RVB state, and to compare the results with the available experiments. We use a renormalized mean-field theory combined with variational Monte Carlo and power Lanczos methods to study the RVB state of an extended $t\text{\ensuremath{-}}J$ model in a square lattice with parameters suitable for the hole-doped Cu oxides. The physical observable quantities we study include the specific heat, the linear residual thermal conductivity, the in-plane magnetic penetration depth, the quasiparticle energy at the antinode $(\ensuremath{\pi},0)$, the superconducting energy gap, the quasiparticle spectra, and the Drude weights. The traits of nodes (including

{k}_{F}

, the Fermi velocity

{v}_{F}

, and the velocity along Fermi surface

{v}_{2}

), and the SC order parameter are studied. Comparisons of the theory and the experiments in cuprates show an overall qualitative agreement, especially on their doping dependences.