• Corpus ID: 248496621

$\pi$ Flux Phase and Superconductivity for Lattice Fermions Coupled to Classical Gauge Fields

@inproceedings{Koma2022piFP,
  title={\$\pi\$ Flux Phase and Superconductivity for Lattice Fermions Coupled to Classical Gauge Fields},
  author={Tohru Koma},
  year={2022}
}
: We study superconducting lattice fermions coupled to classical gauge fields. Namely, without the gauge fields, the lattice fermions show superconducting long-range order. In the previous paper, the existence of the long-range order was proved by the present author. This paper is the continuing part of the previous one. More precisely, the interactions between fermions were assumed to be a Bardeen-Cooper-Schrieffer-type pairing which is a nearest-neighbour two-body interaction on the hypercubic… 

References

SHOWING 1-10 OF 17 REFERENCES

Infrared bounds, phase transitions and continuous symmetry breaking

We present a new method for rigorously proving the existence of phase transitions. In particular, we prove that phase transitions occur in (φ·φ)32 quantum field theories and classical, isotropic

Field Theories with ( ( Superconductor * * Solutions

S u m m a r y . T h e conditions for the existence of non-perturbative type ~ superconductor ~) solutions of field theories are examined. A non-covariant canonical transformation method is used to

Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity

Continuing the program developed in a previous paper, a "superconductive" solution describing the proton-neutron doublet is obtained from a nonlinear spinor field Lagrangian. We Gnd the pions of

Symmetry breaking in Heisenberg antiferromagnets

We extend Griffith's theorem on symmetry breaking in quantum spin systems to the situation where the order operator and the Hamiltonian do not commute with each other. The theorem establishes that

Two theorems on the Hubbard model.

  • Lieb
  • Mathematics
    Physical review letters
  • 1989
TLDR
The generalization given here yields, with ∣B∣ ≠ ∣A∣, the first provable example of itinerant electron ferromagnetism, and the theorems hold in all dimensions without even the necessity of a periodic lattice structure.

Flux phase of the half-filled band.

  • Lieb
  • Physics
    Physical review letters
  • 1994
The conjecture is verified that the optimum, energy minimizing, magnetic flux for a half-filled band of electrons hopping on a planar, bipartite graph is π per square plaquette. We require only that

Theory of Superconductivity

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is

Existence of Néel order in some spin-1/2 Heisenberg antiferromagnets

The methods of Dyson, Lieb, and Simon are extended to prove the existence of Néel order in the ground state of the 3D spin-1/2 Heisenberg antiferromagnet on the cubic lattice. We also consider the

On the flux phase conjecture at half-filling: An improved proof

We present a simplification of Lieb's proof of the flux phase conjecture for interacting fermion systems—such as the Hubbard model—at half-filling on a general class of graphs. The main ingredient is

Phase transitions in quantum spin systems with isotropic and nonisotropic interactions

We prove the existence of spontaneous magnetization at sufficiently low temperature, and hence of a phase transition, in a variety of quantum spin systems in three or more dimensions. The isotropic