Role of the pair potential for the saturation of generalized Pauli constraints

Örs Legeza and Christian Schilling
Phys. Rev. A 97, 052105 – Published 7 May 2018

Abstract

The dependence of the (quasi-)saturation of the generalized Pauli constraints on the pair potential is studied for ground states of few-fermion systems. For this, we consider spinless fermions in one dimension which are harmonically confined and interact by pair potentials of the form |xixj|s with 1s5. We use the density matrix renormalization group approach and large orbital basis to achieve the convergence on more than ten digits of both the variational energy and the natural occupation numbers. Our results confirm that the conflict between energy minimization and fermionic exchange symmetry results in a universal and nontrivial quasisaturation of the generalized Pauli constraints (quasipinning), implying tremendous structural simplifications of the fermionic ground state for all s. Those numerically exact results are complemented by an analytical study based on a self-consistent perturbation theory which we develop for this purpose. The respective results for the weak-coupling regime eventually elucidate the singular behavior found for the specific values s=2,4,..., resulting in an extremely strong quasipinning.

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  • Received 28 November 2017

DOI:https://doi.org/10.1103/PhysRevA.97.052105

©2018 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Örs Legeza1 and Christian Schilling2,*

  • 1Wigner Research Centre for Physics, Hungarian Academy of Sciences, Konkoly-Thege Miklós út 29-33, 1121 Budapest, Hungary
  • 2Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom

  • *christian.schilling@physics.ox.ac.uk

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Vol. 97, Iss. 5 — May 2018

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