Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Physical Society of Japan

Four-Point Hubbard Model and Conserved Quantities

C. M. Villet, W.‐H. Steeb

Published Feb 15, 1990• 10 citations
Publisher

Abstract

The spectrum of the half-filled four point Hubbard model with cyclic boundary conditions is calculated in Wannier and Bloch representation. The total number operator and total spin operator are conserved and spin-reversal symmetry exists. In Wannier representation we have additionally the C 4 v symmetry and in Bloch representation we have the total momentum operator wich is conserved. After group-theoretical reduction with respect to these symmetries, it is found that degeneracy still exists in some subspaces. From the theorem of von Neumann and Wigner we conjecture that there is a hidden symmetry. Since there is a Lax representation for the one-dimensional Hubbard model we conjecture that the hidden symmetry can be found from the Lax pair.

DOI
10.1143/jpsj.59.393

Related papers

The spin reversal symmetry of the ground state of the half-filled Hubbard model

Z. Song, H Shen

Using a method based on Lieb's theorems and SU(2) symmetry for the half-filled Hubbard model on a bipartite lattice with mod A mod = mod B mod =N (where mod A mod ( mod B mod ) is the number of sites in the A (B) sublattice), we show that the ground-state wave function has even (odd) symmetry with respect to the spin reversal operator when N is even (odd) for both U>0 and U<0 cases. These rigorous results hold in all dimensions without the necessity for a periodic boundary condition.

Journal of Physics Condensed Matter•Feb 14, 1994•0 citations

On the SU(2)×SU(2) symmetry in the Hubbard model

Dorota Jakubczyk, Paweł Jakubczyk

Abstract We discuss the one-dimensional Hubbard model, on finite sites spin chain, in context of the action of the direct product of two unitary groups SU(2)×SU(2). The symmetry revealed by this group is applicable in the procedure of exact diagonalization of the Hubbard Hamiltonian. This result combined with the translational symmetry, given as the basis of wavelets of the appropriate Fourier transforms, provides, besides the energy, additional conserved quantities, which are presented in the case of a half-filled, four sites spin chain. Since we are dealing with four elementary excitations, two quasiparticles called “spinons”, which carry spin, and two other called “holon” and “antyholon”, which carry charge, the usual spin-SU(2) algebra for spinons and the so called pseudospin-SU(2) algebra for holons and antiholons, provide four additional quantum numbers.

Open Physics•May 30, 2012•7 citations

Pseudo-spin symmetry in the Hubbard model

J. P. Wallington, James F. Annett

We present a hidden SU(2) ‘pseudo-spin’ symmetry of the half-filled Hubbard model, relating superconducting and charge orderings. Using an appropriate functional integral representation, we show the consequences of this symmetry for the quasiparticle excitation spectrum.

Philosophical Magazine B•Nov 1, 1997•3 citations

Antiferromagnetism of the two-dimensional Hubbard model at half-filling: the analytic ground state for weak coupling

Michele Cini, Gianluca Stefanucci

We introduce a local formalism to deal with the Hubbard model on an N × N square lattice (for even N ) in terms of eigenstates of number operators, having well defined point symmetry. For U →0, the low-lying shells of the kinetic energy are filled in the ground state. At half-filling, using the 2 N -2 one-body states of the partially occupied shell hf , we build a set of degenerate unperturbed ground states with S z = 0 which are then resolved by the Hubbard interaction Ŵ = U ∑ r r ↑ r ↓ . We study the many-body eigenstates in hf of the kinetic energy with vanishing eigenvalue of the Hubbard repulsion ( W = 0 states). In the S z = 0 sector, this is an N -times-degenerate multiplet. From the singlet component one obtains the ground state of the Hubbard model for U = 0 + , which is unique, in agreement with a theorem of Lieb. The wave function demonstrates an antiferromagnetic order, a lattice step translation being equivalent to a spin flip. We show that the total momentum vanishes, while the point symmetry is s or d for even or odd N /2, respectively.

arXiv:cond-mat/0009058•Journal of Physics Condensed Matter•Jan 25, 2001•2 citations

Scattering matrix and excitation spectrum of the Hubbard model

Fabian H.L. Eβler, V. E. Korepin

We consider the one-dimensional Hubbard model at half filling. We show that both excitation spectrum and S matrix are determined by the SO(4) symmetry of the model. The complete set of excitations is given by the scattering states of four elementary excitations, which form the fundamental representation of SU(2)\ifmmode\times\else\texttimes\fi{}SU(2). We evaluate the exact S matrix, which satisfies the Yang-Baxter relation. The results for the repulsive and attractive Hubbard model are related by an interchange of spin and charge degrees of freedom.

arXiv:cond-mat/9308004•Physical Review Letters•Feb 7, 1994•60 citations

Theory of electrons with orbital degeneracy

You‐Quan Li, Ulrich Eckern

The Hubbard model for electrons with orbital degeneracy is shown to have an underlying ${\mathrm{SU}}_{d}(4)$ symmetry of spin-orbital double. A hidden charge ${\mathrm{SU}}_{c}(4)$ symmetry is exposed and an extended Lieb-Mattis transformation, which maps these two symmetries into each other, is given. On the basis of elementary degenerate perturbative theory, it is shown that the system with strong repulsive coupling is equivalent to a $\mathrm{SO}(6)$ Heisenberg magnet at half-filling and a $\mathrm{SU}(4)$ one at quarter-filling. The band is half-filled at all temperature for $\ensuremath{\mu}=3U/2.$ The features of ground-state and low-lying excitations in one dimension are indicated according to exact solutions.

arXiv:cond-mat/9911192•Physical review. B, Condensed matter•Dec 15, 2000•5 citations
The spectrum of the half-filled four point Hubbard model with cyclic boundary conditions is calculated in Wannier and Bloch representation. The total number operator and total spin operator are conserved and spin-reversal symmetry exists. In Wannier representation we have additionally the C 4 v symmetry and in Bloch representation we have the total momentum operator wich is conserved. After group-theoretical reduction with respect to these symmetries, it is found that degeneracy still exists in some subspaces. From the theorem of von Neumann and Wigner we conjecture that there is a hidden symmetry. Since there is a Lax representation for the one-dimensional Hubbard model we conjecture that the hidden symmetry can be found from the Lax pair.
Abstract We discuss the one-dimensional Hubbard model, on finite sites spin chain, in context of the action of the direct product of two unitary groups SU(2)×SU(2). The symmetry revealed by this group is applicable in the procedure of exact diagonalization of the Hubbard Hamiltonian. This result combined with the translational symmetry, given as the basis of wavelets of the appropriate Fourier transforms, provides, besides the energy, additional conserved quantities, which are presented in the case of a half-filled, four sites spin chain. Since we are dealing with four elementary excitations, two quasiparticles called “spinons”, which carry spin, and two other called “holon” and “antyholon”, which carry charge, the usual spin-SU(2) algebra for spinons and the so called pseudospin-SU(2) algebra for holons and antiholons, provide four additional quantum numbers.
We introduce a local formalism to deal with the Hubbard model on an N × N square lattice (for even N ) in terms of eigenstates of number operators, having well defined point symmetry. For U →0, the low-lying shells of the kinetic energy are filled in the ground state. At half-filling, using the 2 N -2 one-body states of the partially occupied shell hf , we build a set of degenerate unperturbed ground states with S z = 0 which are then resolved by the Hubbard interaction Ŵ = U ∑ r r ↑ r ↓ . We study the many-body eigenstates in hf of the kinetic energy with vanishing eigenvalue of the Hubbard repulsion ( W = 0 states). In the S z = 0 sector, this is an N -times-degenerate multiplet. From the singlet component one obtains the ground state of the Hubbard model for U = 0 + , which is unique, in agreement with a theorem of Lieb. The wave function demonstrates an antiferromagnetic order, a lattice step translation being equivalent to a spin flip. We show that the total momentum vanishes, while the point symmetry is s or d for even or odd N /2, respectively.
We consider the one-dimensional Hubbard model at half filling. We show that both excitation spectrum and S matrix are determined by the SO(4) symmetry of the model. The complete set of excitations is given by the scattering states of four elementary excitations, which form the fundamental representation of SU(2)\ifmmode\times\else\texttimes\fi{}SU(2). We evaluate the exact S matrix, which satisfies the Yang-Baxter relation. The results for the repulsive and attractive Hubbard model are related by an interchange of spin and charge degrees of freedom.
The Hubbard model for electrons with orbital degeneracy is shown to have an underlying SUd(4){\mathrm{SU}}_{d}(4)SUd​(4) symmetry of spin-orbital double. A hidden charge SUc(4){\mathrm{SU}}_{c}(4)SUc​(4) symmetry is exposed and an extended Lieb-Mattis transformation, which maps these two symmetries into each other, is given. On the basis of elementary degenerate perturbative theory, it is shown that the system with strong repulsive coupling is equivalent to a SO(6)\mathrm{SO}(6)SO(6) Heisenberg magnet at half-filling and a SU(4)\mathrm{SU}(4)SU(4) one at quarter-filling. The band is half-filled at all temperature for $\ensuremath{\mu}=3U/2.$ The features of ground-state and low-lying excitations in one dimension are indicated according to exact solutions.