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arXiv:cond-mat/9512150

Quantum melting on a lattice and a delocalization transition

E. V. Tsiper, F. G. Pikus, Alexei L. Efros

Published Dec 22, 1995• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.cond-mat/9512150

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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 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 $\ensuremath{\nu}=1/2$ 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.
Using a few electrons interacting via a U/r Coulomb repulsion on two dimensional L ×L square lattices with periodic boundary conditions and nearest neighbor hopping t, I review on results of systematic exact finite size numerical studies of the ground state as a function of the Coulomb energy to kinetic energy ratio rs=UL/(2t√πN). Studies of the persistent currents, of the magnetization, of the inter-particle spacing distributions, of a simple analytical ansatz converge towards the same conclusion: there is a new regime for intermediate values rs, where delocalized electrons co-exist with a solid Wigner molecule. The study of this new regime, first done in the presence of random potentials, is extended to the clean lattice limit. The results are consistent, for a finite size lattice, with a possibility proposed by Andreev and Lifshitz for the continuous thermodynamic limit: a quantum crystal may have delocalized defects without melting, the number of sites of the crystalline array being smaller than the total number of particles.
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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 consider a one-dimensional lattice model with the nearest-neighbour interaction and the next-nearest-neighbour interaction with filling factor 1/2 at zero temperature. The particles are assumed to be spinless fermions or hard-core bosons. Using very simple assumptions we are able to predict the basic structure of the insulator - metal phase diagram for this model. Computations of the flux sensitivity support the main features of the proposed diagram and show that the system maintains metallic properties at arbitrarily large values of and along the line , where J is the hopping amplitude, and . We think that close to this line the system is a `weak' metal in the sense that the flux sensitivity decreases with the size of the system not exponentially but as with .
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