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Abstract We consider the stability of the circular Fermi surface of a two-dimensional electron gas system against an elliptical deformation induced by an anisotropic Coulomb interaction potential. We use the jellium approximation for the neutralizing background and treat the electrons as fully spin-polarized (spinless) particles with a constant isotropic (effective) mass. The anisotropic Coulomb interaction potential considered in this work is inspired from studies of two-dimensional electron gas systems in the quantum Hall regime. We use a Hartree–Fock procedure to obtain analytical results for two special Fermi liquid quantum electronic phases. The first one corresponds to a system with circular Fermi surface while the second one corresponds to a liquid anisotropic phase with a specific elliptical deformation of the Fermi surface that gives rise to the lowest possible potential energy of the system. The results obtained suggest that, for the most general situations, neither of these two Fermi liquid phases represent the lowest energy state of the system within the framework of the family of states considered in this work. The lowest energy phase is one with an optimal elliptical deformation whose specific value is determined by a complex interplay of many factors including the density of the system.
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Sampling the reciprocal Coulomb potential in finite anisotropic cells
We present a robust strategy to numerically sample the Coulomb potential in reciprocal space for periodic Born–von Karman cells of general shape. Our approach tackles two common issues of plane-wave based implementations of Coulomb integrals under periodic boundary conditions: the treatment of the singularity at the Brillouin-zone center and discretization errors, which can cause severe convergence problems in anisotropic cells, necessary for the calculation of low-dimensional systems. We apply our strategy to the Hartree–Fock and coupled cluster (CC) theories and discuss the consequences of different sampling strategies on different theories. We show that sampling the Coulomb potential via the widely used probe-charge Ewald method is unsuitable for CC calculations in anisotropic cells. To demonstrate the applicability of our developed approach, we study two representative, low-dimensional use cases: the infinite carbon chain, for which we report the first periodic CCSD(T) potential energy surface, and a surface slab of lithium hydride, for which we demonstrate the impact of different sampling strategies for calculating surface energies. We find that our Coulomb sampling strategy serves as a vital solution, addressing the critical need for improved accuracy in plane-wave based CC calculations for low-dimensional systems.
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- Award ID(s):
- 2045046
- PAR ID:
- 10593650
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 160
- Issue:
- 5
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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