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The action of the nearest neighbor Coulomb repulsion on the homogeneity in the high concentration domain for itinerant systems

Zsolt Gulacsi

Abstract

Exact results are presented for itinerant systems demonstrating that the nearest neighbor Coulomb repulsion (V) destroys the homogeneity in the high concentration regime, this property being not present in the low concentration domain. Since the effects of V often seems contradictory, and the number of phases in which it could appear is extremely large, this result underlines that the action of the nearest neighbor repulsion is not necessarily routed in the characteristics of phases on which it acts, but could be intimately related to V itself. The $V > 0$ case usually means non-integrability, hence the deduced exact ground states are related to non-integrable systems, the technique being based on positive semidefinite operator properties.

The action of the nearest neighbor Coulomb repulsion on the homogeneity in the high concentration domain for itinerant systems

Abstract

Exact results are presented for itinerant systems demonstrating that the nearest neighbor Coulomb repulsion (V) destroys the homogeneity in the high concentration regime, this property being not present in the low concentration domain. Since the effects of V often seems contradictory, and the number of phases in which it could appear is extremely large, this result underlines that the action of the nearest neighbor repulsion is not necessarily routed in the characteristics of phases on which it acts, but could be intimately related to V itself. The case usually means non-integrability, hence the deduced exact ground states are related to non-integrable systems, the technique being based on positive semidefinite operator properties.

Paper Structure

This paper contains 13 sections, 35 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The Hamiltonian used in the high concentration region.
  3. The interaction energy terms.
  4. The kinetic energy term.
  5. The case of the diamond chain
  6. The Hamiltonian
  7. The V=0 ground state
  8. The $V > 0$ ground state
  9. The case of the two bands 2D square lattice with spin-orbit interactions
  10. The Hamiltonian
  11. The ground state at $V=0$
  12. The ground state at $V > 0.$
  13. Summary and Discussions

Figures (3)

  • Figure 1: The diamond chain. ${\bf i}$ denotes the lattice site (and the cell origin), ${\bf a}$ is the lattice constant, $t$ and $t_{\alpha}$ with $\alpha$ denoting the parallel and perpendicular components are hopping matrix elements, $\epsilon$ represents on-site one particle potential, ${\bf r}_1,{\bf r}_2$, and ${\bf r}_3=0$ are the three on-cell positions.
  • Figure 2: Unit cell at lattice site ${\bf i}$, with in cell notation of sites $n=1,2,3,4$, the Bravais vectors being denoted by ${\bf x}_1$, ${\bf x}_2$.
  • Figure 3: Division of the system in two sublattices: A (open dots), and B (black dots).