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arXiv:cond-mat/0604122 · Physical Review B

Spectral functions and optical conductivity of spinless fermions on a checkerboard lattice

Frank Pollmann, Peter Fulde, Erich Runge

Published Mar 29, 2006• 22 citations
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Abstract

We study the dynamical properties of spinless fermions on the checkerboard lattice. Our main interest is the limit of large nearest-neighbor repulsion $V$ as compared with hopping $\ensuremath{\mid}t\ensuremath{\mid}$. The spectral functions show broad low-energy excitations which are due to the dynamics of fractionally charged excitations. Furthermore, it is shown that the fractional charges contribute to the electrical current density.

DOI
10.1103/physrevb.73.125121

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We study the dynamical properties of spinless fermions on the checkerboard lattice. Our main interest is the limit of large nearest-neighbor repulsion VVV as compared with hopping \ensuremath∣t\ensuremath∣\ensuremath{\mid}t\ensuremath{\mid}\ensuremath∣t\ensuremath∣. The spectral functions show broad low-energy excitations which are due to the dynamics of fractionally charged excitations. Furthermore, it is shown that the fractional charges contribute to the electrical current density.
Systems of strongly correlated fermions on certain geometrically frustrated lattices at particular filling factors support excitations with fractional charges ±e/2. We calculate quantum mechanical ground states, low–lying excitations and spectral functions of finite lattices by means of numerical diagonalization. The ground state of the most thorough-fully studied case, the criss-crossed checkerboard lattice, is degenerate and shows long–range order. Static fractional charges are confined by a weak linear force, most probably leading to bound states of large spatial extent. Consequently, the quasi-particle weight is reduced, which reflects the internal dynamics of the fractionally charged excitations. By using an additional parameter, we fine–tune the system to a special point at which fractional charges are manifestly deconfined—the so–called Rokhsar–Kivelson point. For a deeper understanding of the low–energy physics of these models and for numerical advantages, several conserved quantum numbers are identified.
The spectral properties of the spinless fermion model with nearest-neighbor repulsive interactions on a one-dimensional lattice are investigated using the Bethe ansatz. Although its bulk quantities are exactly the same as those of the spin-1/2 XXZ chain, the difference in the statistics of particles causes substantial effects on spectral features, such as gapless points of dispersion relations and line shapes of spectral functions. In this Letter, we clarify the origin of the differences in spectral features between fermionic and bosonic systems in terms of Bethe ansatz solutions. We also confirm that the two-string solutions have considerable spectral weights in the high-energy regime.
We address the question whether features known from quantum chromodynamics (QCD) can possibly also show up in solid-state physics. It is shown that spinless fermions of charge eee on a checkerboard lattice with nearest-neighbor repulsion provide for a simple model of confined fractional charges. After defining a proper vacuum the system supports excitations with charges ±e/2\pm e/2±e/2 attached to the ends of strings. There is a constant confining force acting between the fractional charges. It results from a reduction of vacuum fluctuations and a polarization of the vacuum in the vicinity of the connecting strings.
An analytic expression for the dynamical conductivity sigma ( omega ) of spinless fermions with local disorder and nearest-neighbour repulsion is derived on lattices with infinite coordination number Z. The model is exactly solvable in the whole parameter range assuming two possible phases: a homogeneous phase and a checkerboard charge-density wave (CDW). Away from half filling the system displays anomalous behaviour: weak particle-density fluctuations favour spontaneous symmetry breaking. First, the authors investigate the effects of this anomaly on the conductivity in the AC and DC regimes. Second, they focus on the Mott transition occurring at zero temperature at half filling. The critical exponents for the conductivity are computed for the dependence on the interaction U, the disorder gamma , the filling n, the temperature T and the frequency omega .
We study a model of strongly interacting spinless fermions on an anisotropic triangular lattice. At half-filling and the limit of strong repulsive nearest-neighbor interactions, the fermions align in stripes and form an insulating state. When a particle is doped, it either follows a one-dimensional free motion along the stripes or fractionalizes perpendicular to the stripes. The two propagations yield a dimensional tuning of the electronic state. We study the stability of this phase and derive an effective model to describe the low-energy excitations. Spectral functions are presented which can be used to experimentally detect signatures of the charge excitations.
We study ground state properties and particle excitation spectra across a commensurate charge density wave transition in a system of strongly interacting fermions, using series expansion methods and mean-field theory. We consider a 1/3-filled system of spinless fermions on a triangular lattice, with hopping parameter ttt, nearest-neighbor repulsion VVV, and a sublattice dependent chemical potential ${\ensuremath{\mu}}_{s}$. The phase transition is found to be first order for ${\ensuremath{\mu}}_{s}=0$, but becomes continuous with increasing ${\ensuremath{\mu}}_{s}$. The particle and hole excitation spectra exhibit dramatic changes in the vicinity of the phase transitions and in the charge density wave ordered phase. We discuss the relevance of this study to the pinball Fermi liquid phase postulated theoretically in earlier studies as well as to various strongly correlated triangular lattice materials.