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arXiv:cond-mat/9708150 · Physical review. B, Condensed matter

Structural and insulator-metal quantum phase transitions on a lattice

E. V. Tsiper, Alexei L. Efros

Published Mar 15, 1998• 9 citations
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Abstract

We consider a two-dimensional gas of spinless fermions with Coulomb and short-range interactions on a square lattice at $T=0$. Using the exact-diagonalization technique we study finite clusters up to 16 particles at filling factors $\ensuremath{\nu}=1/2$ and 1/6. By increasing the hopping amplitude we obtain the low-energy spectrum of the system in a wide range from the classical Wigner crystal to an almost free gas of fermions. Particular effort is made to study the mechanism of the structural and insulator-metal transitions. We show that both transitions are determined by the energy band of the defect with the lowest energy in the Wigner crystal.

DOI
10.1103/physrevb.57.6949

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We consider a two-dimensional gas of spinless fermions with Coulomb and short-range interactions on a square lattice at T=0T=0T=0. Using the exact-diagonalization technique we study finite clusters up to 16 particles at filling factors \ensuremathν=1/2\ensuremath{\nu}=1/2\ensuremathν=1/2 and 1/6. By increasing the hopping amplitude we obtain the low-energy spectrum of the system in a wide range from the classical Wigner crystal to an almost free gas of fermions. Particular effort is made to study the mechanism of the structural and insulator-metal transitions. We show that both transitions are determined by the energy band of the defect with the lowest energy in the Wigner crystal.
We consider 2d gas of spinless fermions with the Coulomb interaction on a lattice at T=0 and at different values of the hopping amplitude J. At small J electrons form a periodic structure. At filling factor ν=1/6 this structure melts at J as low as 0.02--0.03 in units of the nearest-neighbor Coulomb energy. We argue that this transition is connected to the dielectric-metal and dielectric-superconductor transitions. To demonstrate this point we perform computer modeling of the systems 6x6 with 6 and 7 electrons and 6x12 with 12 electrons. By sweeping J we compute simultaneously persistent current and structural characteristics of the electron distribution.
We study the level spacing statistics P(s)P(s)P(s) and eigenstate properties of spinless fermions with Coulomb interaction on a two-dimensional lattice at constant filling factor and various disorder strengths. For the noninteracting localized phase in the limit of large lattice size, Coulomb interaction induces a transition of P(s)P(s)P(s) from the Poisson to the Wigner-Dyson distribution, at a critical total energy independent of the number of fermions. This implies the emergence of quantum ergodicity induced by interaction and delocalization in the Hilbert space at zero temperature inside the one-particle insulating phase.
We discuss the metal-insulator transition of the spinless fermion model on the Kagomé lattice at 1/3-filling. The system is analyzed using exact diagonalization, the density-matrix renormalization group methods and the random phase approximation. In the strong-coupling region, the charge-ordered ground state is consistent with the predictions of the effective model with a plaquette order. We find that the qualitative properties of the metal-insulator transition are totally different depending on the sign of the hopping integrals, reflecting the difference of band structure at the Fermi level.
We discuss the metal-insulator transition of the spinless fermion model on a kagome lattice at 1/3 filling. The system is analyzed by using exact diagonalization, density-matrix renormalization group methods, and random-phase approximation. In the strong-coupling region, the charge-ordered ground state is consistent with the predictions of an effective model, i.e., plaquette order. We find that the qualitative properties of the metal-insulator transition are totally different depending on the sign of the hopping matrix elements, reflecting the difference in the band structure near the Fermi level.
The cluster perturbation theory is presented in the 2D Hubbard model constructed using X operators in the Hubbard-I approximation. The short-range magnetic order is taken into account by dividing the entire lattice into individual 2 × 2 clusters and solving the eigenvalue problem in an individual cluster using exact diagonalization taking into account all excited levels. The case of half-filling taking into account jumps between nearest neighbors is considered. As a result of numerical solution, a shadow zone is discovered in the quasiparticle spectrum. It is also found that a gap in the density of states in the quasiparticle spectrum at zero temperature exists for indefinitely small values of Coulomb repulsion parameter U and increases with this parameter. It is found that the presence of this gap in the spectrum is due to the formation of a short-range antiferromagnetic order. An analysis of the temperature evolution of the density of states shows that the metal-insulator transition occurs continuously. The existence of two characteristic energy scales at finite temperatures is demonstrated, the larger scale is associated with the formation of a pseudogap in the vicinity of the Fermi level, and the smaller scale is associated with the metal-insulator transition temperature. A peak in the density of states at the Fermi level, which is predicted in the dynamic mean field theory in the vicinity of the metal-insulator transition, is not observed.