Commensurate flux phase of the Heisenberg model and anyonic superconductivity

We show using bosonization methods that extended Hubbard-Heisenberg models on two types of two leg ladders (without flux and with flux $\ensuremath{\pi}$ per plaquette) have commensurate pair-density-wave (PDW) phases. In the case of the conventional (flux-less) ladder, the PDW arises when certain filling fractions for which commensurability conditions are met. For the flux $\ensuremath{\pi}$ ladder, the PDW phase is generally present. The PDW phase is characterized by a finite spin gap and a superconducting order parameter with a finite (commensurate in this case) wave vector and power-law superconducting correlations. In this phase, the uniform superconducting order parameter, the $2{k}_{F}$ charge-density-wave (CDW) order parameter and the spin-density-wave N\'eel order parameter exhibit short range (exponentially decaying) correlations. We discuss in detail the case in which the bonding band of the ladder is half filled for which the PDW phase appears even at weak coupling. The PDW phase is shown to be dual to a uniform superconducting (SC) phase with quasi-long-range order. By making use of bosonization and the renormalization group, we determine the phase diagram of the spin-gapped regime and study the quantum phase transition. The phase boundary between PDW and the uniform SC ordered phases is found to be in the Ising universality class. We generalize the analysis to the case of other commensurate fillings of the bonding band, where we find higher-order commensurate PDW states for which we determine the form of the effective bosonized field theory and discuss the phase diagram. We compare our results with recent findings in the Kondo-Heisenberg chain. We show that the formation of PDW order in the ladder embodies the notion of intertwined orders.We show using bosonization methods that extended Hubbard-Heisenberg models on two types of two leg ladders (without flux and with flux $\ensuremath{\pi}$ per plaquette) have commensurate pair-density-wave (PDW) phases. In the case of the conventional (flux-less) ladder, the PDW arises when certain filling fractions for which commensurability conditions are met. For the flux $\ensuremath{\pi}$ ladder, the PDW phase is generally present. The PDW phase is characterized by a finite spin gap and a superconducting order parameter with a finite (commensurate in this case) wave vector and power-law superconducting correlations. In this phase, the uniform superconducting order parameter, the $2{k}_{F}$ charge-density-wave (CDW) order parameter and the spin-density-wave N\'eel order parameter exhibit short range (exponentially decaying) correlations. We discuss in detail the case in which the bonding band of the ladder is half filled for which the PDW phase appears even at weak coupling. The PDW phase is shown to be dual to a uniform superconducting (SC) phase with quasi-long-range order. By making use of bosonization and the renormalization group, we determine the phase diagram of the spin-gapped regime and study the quantum phase transition. The phase boundary between PDW and the uniform SC ordered phases is found to be in the Ising universality class. We generalize the analysis to the case of other commensurate fillings of the bonding band, where we find higher-order commensurate PDW states for which we determine the form of the effective bosonized field theory and discuss the phase diagram. We compare our results with recent findings in the Kondo-Heisenberg chain. We show that the formation of PDW order in the ladder embodies the notion of intertwined orders.

arXiv:1111.6320Physical Review BJan 9, 201269 citations

The Hubbard Model and Anyon Superconductivity

A. P. Balachandran, E. Ercolessi, G. Morandi +1 more

World Scientific lecture notes in physicsJan 1, 199023 citations

Anyonic superconductivity in a modified large-UHubbard model

Asim Gangopadhyaya, Prasanta Kumar Panigrahi

A modified large-U Hubbard model at half filling is analyzed by a mean-field approach. Preserving a local U(1) symmetry of the action, the fluctuations about half filling are studied in the spirit of the commensurate-flux-phase condition. The fluctuations then contribute a Chern-Simons term to the tree-level Lagrangian with a coefficient appropriate to that of a half fermion. With the Coulomb repulsion term, we study the low-energy excitations of the model and show the existence of superconductivity in the presence of a four-Fermi interaction term.A modified large-U Hubbard model at half filling is analyzed by a mean-field approach. Preserving a local U(1) symmetry of the action, the fluctuations about half filling are studied in the spirit of the commensurate-flux-phase condition. The fluctuations then contribute a Chern-Simons term to the tree-level Lagrangian with a coefficient appropriate to that of a half fermion. With the Coulomb repulsion term, we study the low-energy excitations of the model and show the existence of superconductivity in the presence of a four-Fermi interaction term.

Physical review. B, Condensed matterNov 1, 19912 citations

Anyon quarks and superconductivity

A.M. Din

Physics Letters BNov 1, 19893 citations

Superconductivity from commensurate flux phases

Pascal Lederer, Didier Poilblanc, Thomas Maurice Rice

We use a renormalized mean-field theory of the t-J model to show that flux states closely related to those recently proposed by Anderson, Shastry, and Hristopoulos are stabilized, at values of J/t\ensuremath{\gtrsim}1, when the flux per plaquette is commensurate with the electron density in a way similar to that found recently for noninteracting electrons. These states (in the interacting t-J model) are characterized by a collective gauge variable which leads to superconductivity. At not too small values of J/t the state with half a flux quantum per plaquette is stable at low doping.We use a renormalized mean-field theory of the t-J model to show that flux states closely related to those recently proposed by Anderson, Shastry, and Hristopoulos are stabilized, at values of J/t\ensuremath{\gtrsim}1, when the flux per plaquette is commensurate with the electron density in a way similar to that found recently for noninteracting electrons. These states (in the interacting t-J model) are characterized by a collective gauge variable which leads to superconductivity. At not too small values of J/t the state with half a flux quantum per plaquette is stable at low doping.

Physical Review LettersOct 2, 1989191 citations

Boson-Fermion model of superconductivity

Richard M. Friedberg, T.D. Lee

Physics Letters AJul 1, 198980 citations

2{k}_{F}

charge-density-wave (CDW) order parameter and the spin-density-wave N\'eel order parameter exhibit short range (exponentially decaying) correlations. We discuss in detail the case in which the bonding band of the ladder is half filled for which the PDW phase appears even at weak coupling. The PDW phase is shown to be dual to a uniform superconducting (SC) phase with quasi-long-range order. By making use of bosonization and the renormalization group, we determine the phase diagram of the spin-gapped regime and study the quantum phase transition. The phase boundary between PDW and the uniform SC ordered phases is found to be in the Ising universality class. We generalize the analysis to the case of other commensurate fillings of the bonding band, where we find higher-order commensurate PDW states for which we determine the form of the effective bosonized field theory and discuss the phase diagram. We compare our results with recent findings in the Kondo-Heisenberg chain. We show that the formation of PDW order in the ladder embodies the notion of intertwined orders.