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Exploring instantons in nonlinear sigma models with spin-lattice systems

Schenk, Sebastian and Spannowsky, Michael (2021) 'Exploring instantons in nonlinear sigma models with spin-lattice systems.', Physical review B., 103 (14). p. 144436.

Abstract

Instanton processes are present in a variety of quantum field theories relevant to high energy as well as condensed matter physics. While they have led to important theoretical insights and physical applications, their underlying features often remain elusive due to the complicated computational treatment. Here, we address this problem by studying topological as well as nontopological instantons using Monte Carlo methods on lattices of interacting spins. As a proof of principle, we systematically construct instanton solutions in O ( 3 ) nonlinear sigma models with a Dzyaloshinskii-Moriya interaction in ( 1 + 1 ) and ( 1 + 2 ) dimensions, thereby resembling an example of a chiral magnet. We demonstrate that, due to their close correspondence, Monte Carlo techniques in spin-lattice systems are well suited to describe topologically nontrivial field configurations in these theories. In particular, by means of simulated annealing, we demonstrate how to obtain domain walls, merons, and critical instanton solutions.

Item Type:Article
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1103/PhysRevB.103.144436
Publisher statement:Reprinted with permission from the American Physical Society: Schenk, Sebastian & Spannowsky, Michael (2021). Exploring instantons in nonlinear sigma models with spin-lattice systems. Physical Review B 103(14): 144436. © (2021) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.
Date accepted:19 April 2021
Date deposited:30 September 2021
Date of first online publication:30 April 2021
Date first made open access:30 September 2021

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