Order by disorder decision making via Berry flux

Benjamin O. Sung and Michael J. Lawler
Phys. Rev. B 94, 144438 – Published 25 October 2016

Abstract

Order by disorder is a decision making process for frustrated systems but often leads to simple answers. We study order by disorder in the kagome Kondo model known for its complexity seeking rich decision making capabilities. At half-filling and large Kondo coupling to hopping ratio JK/t, the full manifold of 120 kagome ground states are degenerate at second order in t/JK. We show this degeneracy lifts at sixth order when a fermion can hop around a hexagon and feel the Berry flux induced by a given spin texture. Using the Monte Carlo method, we then seek the ground state of this sixth-order Hamiltonian and find in a 4×4 unit cell system that a coplanar 12-site unit cell order is selected over the 3×3,q=0 and cuboc1 states, a result that survives even in the thermodynamic limit. This state is selected for its SU(2) flux properties induced by the spin texture. Given the existence of numerous quantum Hall plateaus for electrons in a magnetic field, the existence of this 12-site unit cell state suggests that complex decision making is possible on the manifold of 120 states and achievable in different kagome Kondo models.

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  • Received 3 June 2016
  • Revised 18 August 2016

DOI:https://doi.org/10.1103/PhysRevB.94.144438

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Benjamin O. Sung1 and Michael J. Lawler2,1

  • 1Department of Physics, Cornell University, Ithaca, New York 14853, USA
  • 2Department of Physics, Applied Physics and Astronomy, Binghamton University, Vestal, New York 13850, USA

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Issue

Vol. 94, Iss. 14 — 1 October 2016

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