arXiv:1003.4499 · Annals of Physics

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

Published Sep 13, 2011• 6 citations

arXiv HTML PDF

DOI: 10.1016/j.aop.2011.09.001

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

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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

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arXiv:1003.4499 · Annals of Physics

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

Published Sep 13, 2011• 6 citations

arXiv HTML PDF

DOI: 10.1016/j.aop.2011.09.001

Related papers

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

Annals of PhysicsApr 15, 201025 citations

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

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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

The Ground State Phase Diagram of the Two-Dimensional Hubbard Model on Square Lattice

Bo-Xiao Zheng, Garnet Kin‐Lic Chan

Bulletin of the American Physical SocietyMar 6, 20150 citations

The Hubbard model on a square lattice in the one- and two-electron subspace

J. M. P. Carmelo

In this paper the spin configurations of the ground state and one- and two-electron excited states of the Hubbard model on the square lattice are studied. We profit from a general rotated-electron description, which is consistent with the model global $SO(3)\times SO(3)\times U(1)$ symmetry. For rotated electrons, doubly and single occupancy are good quantum numbers for on-site repulsion $U>0$ . The above states are within that description generated by occupancy configurations of charge $c$ fermions and spin-singlet two-spinon $s1$ bond particles. Those describe the charge and spin degrees of freedom, respectively, of the rotated electrons that singly occupy sites. While the $c$ fermions have no internal structure, that of the spin-neutral $s1$ bond-particle occupancy configurations is here described in terms of spinon occupancies of a well-defined effective spin lattice. In reference \cite{companion} it is confirmed that our results contribute to the further understanding of the role of electronic correlations in the spin spectrum of the parent compound La $_2$ CuO $_4$ . They are also of interest for studies of ultra-cold fermionic atoms on an optical lattice.In this paper the spin configurations of the ground state and one- and two-electron excited states of the Hubbard model on the square lattice are studied. We profit from a general rotated-electron description, which is consistent with the model global $SO(3)\times SO(3)\times U(1)$ symmetry. For rotated electrons, doubly and single occupancy are good quantum numbers for on-site repulsion $U>0$. The above states are within that description generated by occupancy configurations of charge $c$ fermions and spin-singlet two-spinon $s1$ bond particles. Those describe the charge and spin degrees of freedom, respectively, of the rotated electrons that singly occupy sites. While the $c$ fermions have no internal structure, that of the spin-neutral $s1$ bond-particle occupancy configurations is here described in terms of spinon occupancies of a well-defined effective spin lattice. In reference \cite{companion} it is confirmed that our results contribute to the further understanding of the role of electronic correlations in the spin spectrum of the parent compound La$_2$CuO$_4$. They are also of interest for studies of ultra-cold fermionic atoms on an optical lattice.

arXiv:0804.2379Apr 15, 20081 citation

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

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

symmetry. For rotated electrons, doubly and single occupancy are good quantum numbers for on-site repulsion

U>0

. The above states are within that description generated by occupancy configurations of charge

c

fermions and spin-singlet two-spinon

s1

bond particles. Those describe the charge and spin degrees of freedom, respectively, of the rotated electrons that singly occupy sites. While the

c

fermions have no internal structure, that of the spin-neutral

s1

bond-particle occupancy configurations is here described in terms of spinon occupancies of a well-defined effective spin lattice. In reference \cite{companion} it is confirmed that our results contribute to the further understanding of the role of electronic correlations in the spin spectrum of the parent compound La

_2

CuO

_4

. They are also of interest for studies of ultra-cold fermionic atoms on an optical lattice.