Band structure of a simple 1D chain with hopping parameter \(t\)
and repulsive Hubbard-type interaction of strength \(U/t=5.0\). The band structure
was obtained by means of Cluster Perturbation Theory (CPT) with a cluster size of \(M_C = 18\)
lattice sites.
The band structure features a Mott gap and the separation of the dispersing features into
spin and charge excitations.#
Effective 1D model of a Transpolyacetylene with Hubbard-type interactions#
Band structure of an effective lattice model for Transpolyacetylene molecules.
This effective model is also known as the Su-Schrieffer-Heeger chain.
Here we plot the band structure of the non-interacting model (\(U/t=0\)) derived
from CPT with cluster size \(M_C=8\).
The band structure displays two bands, the binding one, with energies below the Fermi energy
\(E_F=0\) and the non-binding one.#
Here we plot the band structure of the Transpolyacetylene model with interaction strength
\(U/t=1.0\) derived from CPT with cluster size \(M_C=8\).
The impact of the artificial broadening \(\eta\) of the
self-energy has been reduced via an approach employing equations of motion.#
Band structure of the Transpolyacetylene model with interaction strength
\(U/t=5.0\) derived from CPT with cluster size \(M_C=8\). We observe significant
broadening of the spectral weight around the \(\Gamma\) point as well as a shift of the
lower band to energies above the Fermi energy.#
Band structure of a one-dimensional diamond chain calculated with CPT using a cluster of
\(M_C=6\) lattice sites. The chain features three orbitals per single
unit cell. The resulting band structure at interaction strength \(U/t=0.0\) consists of two dispersing bands enclosing a flat band located at
the Fermi surface with a threefold degeneracy at the \(X\) symmetry points.#
The band structure at interaction strength \(U/t=1.0\) still consists of two dispersing bands enclosing a flat band located at
the Fermi surface with a threefold degeneracy at the \(X\) symmetry points, albeit with slightly increased broadening.#
Band structure for interaction strength \(U/t=5.0\). We observe a significant broadening
of the dispersive bands. The flat band appears to have split into two bands of reduced spectral
weight symmetrically above and below the Fermi energy. The degeneracy at the symmetry points
\(X\) has been lifted.#
Band structure of a one-dimensional Lieb chain calculated with CPT using a cluster of
\(M_C=6\) lattice sites. The chain features three orbitals per single
unit cell. The resulting band structure at interaction strengths \(U/t=0\) and \(U/t=1.0\) consists of two dispersing bands enclosing
a flat band located at the Fermi surface.#
The band structure at interaction strength \(U/t=1.0\) still consists of two dispersing bands enclosing a flat band located at
the Fermi surface with a threefold degeneracy at the \(X\) symmetry points, albeit with slightly increased broadening.#
Band structure for interaction strength \(U/t=5.0\). We observe a significant broadening
of the dispersive bands. The flat band appears to have split into two sections of significantly broadened spectral
weight symmetrically above and below the Fermi energy.#
Band structure of the non-interacting dimensional square lattice. The band structure was calculated
with CPT using a \(M_C = 2\times 2\) cluster.
The impact of the artificial broadening of the
self-energy has been reduced via an approach equations of motion approach.
The band structure features cosine bands in \(x\)- and \(y\)-direction.#
Band structure for repulsive interaction \(U/t = 1.0\). We observe slight broadening over
the entire Brillouin zone and extensive broadening around the symmetry points \(X\) and
half-way between the symmetry points \(M\) and \(\Gamma\).#
Band structure for strong repulsive interaction \(U/t = 5.0\).
A Mott gap has developed at the symmetry points \(X\) and on the k-point path between \(M\)
and \(\Gamma\).#
Band structure of the non-interacting honeycomb lattice of Graphene with Graphene specific hopping parameters \(t=2.6\) eV.
At the symmetry points \(K (H)\) we observe the well-known Dirac-cone.#
Band structure of the honeycomb lattice of Graphene with a Hubbard-type interaction of
strength \(U/t=1.o\) and Graphene specific hopping parameters \(t=2.6\) eV.
At the symmetry points \(K (H)\) we observe the well-known Dirac-cone.#
Band structure of the honeycomb lattice of Graphene with a Hubbard-type interaction of
strength \(U/t=4.0\) and Graphene specific hopping parameters \(t=2.6\) eV.
The Dirac-cone has given way to a gap.#
Band structure of the Lieb lattice without interaction and cluster size \(M_C=12\). This lattice features three sites per single unitcell
at \((0,0)\), \((0, 0.5)\), \((0.5, 0)\).
The band structure exhibits the characteristic
flat-band crossing the cone formed by the two dispersing bands at the \(S\) symmetry points.#
Band structure of the Lieb lattice with a repulsive Hubbard-type interaction of strength \(U/t=5.0\).
The crossing of the dispersing bands has been replaced by a Mott gap at the symmetry points \(S\) and the flat band has split
into two significantly broadened regions of spectral weight above and below the Fermi energy.#
Band structure of the non-interacting Kagome lattice. This lattice features three sites per single unitcell at
\((0,0)\), \((0.5, 0.0)\), \((0.25, 0.433)\). The band structure features two crossing
dispersing bands and a flat band above the higher dispersing band.#
Band structure of the Kagome lattice with Hubbard-type interaction of strength \(U/t=1.0\) and cluster size \(M_C=12\).
We observe increased broadening for the flat band and the lower dispersing band.#
Band structure of the Kagome lattice with Hubbard-type interaction of strength \(U/t=5.0\) and cluster size \(M_C=12\).
We observe very strong broadening across the entire spectrum, but particularly for the flat band.#
Band structure of the Dice lattice with Hubbard-type interaction of strength \(U/t=0.0\) and cluster size \(M_C=12\).
We find a flat band at the Fermi energy.#
Band structure of the Dice lattice with Hubbard-type interaction of strength \(U/t=1.0\) and cluster size \(M_C=12\).
The spectral weight of the flat band is now significantly broadened.#
Band structure of the Dice lattice with Hubbard-type interaction of strength \(U/t=5.0\) and cluster size \(M_C=12\).
There is broadening also for the dispersing bands, while the flat band has split into two regions of spectral weight.#
