The basis of wavelets for a finite Heisenberg magnet

2015

Acta Phys. Pol. A

The one-dimensional attractive Hubbard model (U 0) is discussed for the chains of N nodes and the same number of electrons, where N − 1 of them have the same spin projection, assuming periodic boundary conditions and the half-lling case. Based on the analysis of the eigenvalue problem we provided the general analytical expression for the eigenvalues, for any number N . This formula implies the existence of two elementary particles with mutually dependent momenta on the ring with N sites the same number of electrons including N − 1 of the same spin projection.

Section: The Symmetry Of the Systemmentioning

confidence: 99%

Some Exact Results in the One-Dimensional Attractive Hubbard Model

2015

Acta Phys. Pol. A

“…Furthermore, the remaining basis for the sector with M = −1 can be obtained by replacing all pluses by minuses, and vice versa, in all electron configurations of Table 3. Table 3 contains four regular orbits , of the group C 4 , and thus consists of four elements, but Table 2, besides its eight regular orbits [22], contains two orbits which are doubly rarefied. The construction of the symmetry SU (2) (2), of elements of the group SU(2) × SU (2), which is applicable in the procedure of exact diagonalization of the one-dimensional Hubbard Hamiltonian will be used in this case.…”

Section: Diagonalizationmentioning

confidence: 99%

“…The state | denotes the element of the basis of wavelets [22], given as the appropriate Fourier transform performed on the orbit . …”

Section: Diagonalizationmentioning

confidence: 99%

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

2012

Open Physics

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. PACS

“…One can easily show, using Bethe ansatz [10], that eigenstates of the Hamiltonian (2) in this subspace are translationally covariant and represent magnon excitation, therefore we call them one-magnon spin states. These states, known in the literature as the basis of wavelets [11], have the Bloch form…”

Section: Introductionmentioning

confidence: 99%

System Size Dependence of Entanglement in Quantum One-Dimensional Models

2017

Acta Phys. Pol. A

Self Cite

We show that entanglement in one-dimensional spin and electron systems, with one excitation, depends only on the system size and has very simple form in both multipartite and bipartite case. Regarding the multipartite case, we present very simple expressions for global entanglement and N -concurrence, and show that they are mutually related. In the bipartite case, we give expressions for I-concurrence and negativity, and show that they are also dependent on each other.