Annals of Physics

Global SO(3)×SO(3)×U(1) symmetry of the Hubbard model on bipartite lattices

J. M. P. Carmelo, Stellan S. Ostlund, M. J. Sampaio

Published Apr 15, 2010• 25 citations

DOI: 10.1016/j.aop.2010.03.002

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Global $SO(3)\times SO(3)\times U(1)$ symmetry of the Hubbard model on bipartite lattices

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Annals of Physics

Global SO(3)×SO(3)×U(1) symmetry of the Hubbard model on bipartite lattices

J. M. P. Carmelo, Stellan S. Ostlund, M. J. Sampaio

Published Apr 15, 2010• 25 citations

Publisher

DOI: 10.1016/j.aop.2010.03.002

Related papers

The SO(3)×SO(3)×U(1) Hubbard model on a square lattice in terms of c and αν fermions and deconfined η -spinons and spinons

J. M. P. Carmelo

arXiv:1003.4499Annals of PhysicsSep 13, 20116 citations

SO(4) Symmetry in a Hubbard Model

Chen Ning Yang

Springer proceedings in physicsJan 1, 199113 citations

Global $SO(3)\times SO(3)\times U(1)$ symmetry of the Hubbard model on bipartite latticesGlobal $SO(3)\times SO(3)\times U(1)$ symmetry of the Hubbard model on bipartite lattices

J. M. P. Carmelo, Stellan S. Ostlund, M. J. Sampaio

It is found that for on-site interaction $U\neq 0$ the local $SU(2)\times SU(2) \times U(1)$ gauge symmetry of the Hubbard model on a bipartite lattice with vanishing transfer integral $t=0$ can be lifted to a global $[SU(2)\times SU(2)\times U(1)]/Z_2^2=SO(3)\times SO(3)\times U(1)$ symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with $t>0$ . The generator of the new found hidden independent charge global U(1) symmetry is one half the rotated-electron number of singly-occupied sites operator. It is confirmed elsewhere that our results have important physical consequences concerning the further understanding of the unusual properties of the hole-doped cuprates.It is found that for on-site interaction $U\neq 0$ the local $SU(2)\times SU(2) \times U(1)$ gauge symmetry of the Hubbard model on a bipartite lattice with vanishing transfer integral $t=0$ can be lifted to a global $[SU(2)\times SU(2)\times U(1)]/Z_2^2=SO(3)\times SO(3)\times U(1)$ symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with $t>0$. The generator of the new found hidden independent charge global U(1) symmetry is one half the rotated-electron number of singly-occupied sites operator. It is confirmed elsewhere that our results have important physical consequences concerning the further understanding of the unusual properties of the hole-doped cuprates.

arXiv:0802.2146Feb 15, 20080 citations

Quantum Group Symmetry of the Hubbard Model

E. Ahmed, Ahmed Sadek Hegazi

International Journal of Theoretical PhysicsMay 1, 20001 citation

An Application of the Extended Global SO(3) × SO(3) × U(1) Symmetry of the Hubbard Model on a Square Lattice: The Spinon, η-Spinon, and c Fermion Description

J. M. P. Carmelo, M. J. Sampaio

In this paper we review recent results on the preliminary applications of the new-found extended global SO(3) × SO(3) × U(1) symmetry of the Hubbard model on a bipartite lattice. Our results refer to the particular case of the bipartite square lattice. Specifically, we review a general description for such a model with nearest-neighbor transfer integral t and on-site repulsion U on a square lattice with N2a 1 sites consistent with its extended global symmetry. It refers to three types of elementary objects whose occupancy configurations generate the state representations of the model extended global symmetry. Such objects emerge from a suitable electron-rotated-electron unitary transformation. An application to the spin spectrum of the parent compound La2CuO4 is shortly reviewed.In this paper we review recent results on the preliminary applications of the new-found extended global SO(3) × SO(3) × U(1) symmetry of the Hubbard model on a bipartite lattice. Our results refer to the particular case of the bipartite square lattice. Specifically, we review a general description for such a model with nearest-neighbor transfer integral t and on-site repulsion U on a square lattice with N2a 1 sites consistent with its extended global symmetry. It refers to three types of elementary objects whose occupancy configurations generate the state representations of the model extended global symmetry. Such objects emerge from a suitable electron-rotated-electron unitary transformation. An application to the spin spectrum of the parent compound La2CuO4 is shortly reviewed.

SymmetryDec 12, 20111 citation

A description of the Hubbard model on a square lattice consistent with its global $SO(3)\times SO(3)\times U(1)$ symmetryA description of the Hubbard model on a square lattice consistent with its global $SO(3)\times SO(3)\times U(1)$ symmetry

J. M. P. Carmelo, M. J. Sampaio

In this paper a description of the Hubbard model on the square lattice with nearest-neighbor transfer integral $t$ , on-site repulsion $U$ , and $N_a^2\gg 1$ sites consistent with its exact global $SO(3)\times SO(3)\times U(1)$ symmetry is constructed. Our studies profit from the interplay of that recently found global symmetry of the model on any bipartite lattice with the transformation laws under a suitable electron - rotated-electron unitary transformation of a well-defined set of operators and quantum objects. For $U/4t>0$ the occupancy configurations of these objects generate the energy eigenstates that span the one- and two-electron subspace. Such a subspace as defined in this paper contains nearly the whole spectral weight of the excitations generated by application onto the zero-spin-density ground state of one- and two-electron operators. Our description involves three basic objects: charge $c$ fermions, spin-1/2 spinons, and $η$ -spin-1/2 $η$ -spinons. Alike in chromodynamics the quarks have color but all quark-composite physical particles are color-neutral, the $η$ -spinon (and spinons) that are not invariant under that transformation have $η$ spin 1/2 (and spin 1/2) but are part of $η$ -spin-neutral (and spin-neutral) $2ν$ - $η$ -spinon (and $2ν$ -spinon) composite $ην$ fermions (and $sν$ fermions) where $ν=1,2,...$ is the number of $η$ -spinon (and spinon) pairs.The description introduced here is consistent with a Mott-Hubbard insulating ground state with antiferromagnetic long-range order for half filling at $x=0$ hole concentration and a ground state with short-range spin order for a well-defined range of finite hole concentrations $x>0$ .In this paper a description of the Hubbard model on the square lattice with nearest-neighbor transfer integral $t$, on-site repulsion $U$, and $N_a^2\gg 1$ sites consistent with its exact global $SO(3)\times SO(3)\times U(1)$ symmetry is constructed. Our studies profit from the interplay of that recently found global symmetry of the model on any bipartite lattice with the transformation laws under a suitable electron - rotated-electron unitary transformation of a well-defined set of operators and quantum objects. For $U/4t>0$ the occupancy configurations of these objects generate the energy eigenstates that span the one- and two-electron subspace. Such a subspace as defined in this paper contains nearly the whole spectral weight of the excitations generated by application onto the zero-spin-density ground state of one- and two-electron operators. Our description involves three basic objects: charge $c$ fermions, spin-1/2 spinons, and $η$-spin-1/2 $η$-spinons. Alike in chromodynamics the quarks have color but all quark-composite physical particles are color-neutral, the $η$-spinon (and spinons) that are not invariant under that transformation have $η$ spin 1/2 (and spin 1/2) but are part of $η$-spin-neutral (and spin-neutral) $2ν$-$η$-spinon (and $2ν$-spinon) composite $ην$ fermions (and $sν$ fermions) where $ν=1,2,...$ is the number of $η$-spinon (and spinon) pairs.The description introduced here is consistent with a Mott-Hubbard insulating ground state with antiferromagnetic long-range order for half filling at $x=0$ hole concentration and a ground state with short-range spin order for a well-defined range of finite hole concentrations $x>0$.

arXiv:0804.2358Apr 15, 20080 citations

Global

SO(3)\times SO(3)\times U(1)

symmetry of the Hubbard model on bipartite lattices

It is found that for on-site interaction

U\neq 0

the local

SU(2)\times SU(2) \times U(1)

gauge symmetry of the Hubbard model on a bipartite lattice with vanishing transfer integral

t=0

can be lifted to a global

[SU(2)\times SU(2)\times U(1)]/Z_2^2=SO(3)\times SO(3)\times U(1)

symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with

t>0

. The generator of the new found hidden independent charge global U(1) symmetry is one half the rotated-electron number of singly-occupied sites operator. It is confirmed elsewhere that our results have important physical consequences concerning the further understanding of the unusual properties of the hole-doped cuprates.

A description of the Hubbard model on a square lattice consistent with its global

SO(3)\times SO(3)\times U(1)

symmetry

In this paper a description of the Hubbard model on the square lattice with nearest-neighbor transfer integral

t

, on-site repulsion

U

, and

N_a^2\gg 1

sites consistent with its exact global

SO(3)\times SO(3)\times U(1)

symmetry is constructed. Our studies profit from the interplay of that recently found global symmetry of the model on any bipartite lattice with the transformation laws under a suitable electron - rotated-electron unitary transformation of a well-defined set of operators and quantum objects. For

U/4t>0

the occupancy configurations of these objects generate the energy eigenstates that span the one- and two-electron subspace. Such a subspace as defined in this paper contains nearly the whole spectral weight of the excitations generated by application onto the zero-spin-density ground state of one- and two-electron operators. Our description involves three basic objects: charge

c

fermions, spin-1/2 spinons, and

η

-spin-1/2

η

-spinons. Alike in chromodynamics the quarks have color but all quark-composite physical particles are color-neutral, the

η

-spinon (and spinons) that are not invariant under that transformation have

η

spin 1/2 (and spin 1/2) but are part of

η

-spin-neutral (and spin-neutral)

2ν

η

-spinon (and

2ν

-spinon) composite

ην

fermions (and

sν

fermions) where

ν=1,2,...

is the number of

η

-spinon (and spinon) pairs.The description introduced here is consistent with a Mott-Hubbard insulating ground state with antiferromagnetic long-range order for half filling at

x=0

hole concentration and a ground state with short-range spin order for a well-defined range of finite hole concentrations

x>0