Exploring instantons with spin-lattice systems

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 non-topological instantons using Monte Carlo methods on lattices of interacting spins. As a proof of principle, we systematically construct instanton solutions in $O(3)$ non-linear 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 non-trivial field configurations in these theories. In particular, by means of simulated annealing, we demonstrate how to obtain domain walls, merons and critical instanton solutions.

arXiv comment11 pages, 5 figures. v2: minor modifications and references added

References in corpus (40)

• Skyrmion Lattice in a Chiral Magnet
• Spontaneous Skyrmion Ground States in Magnetic Metals
• Knots and Particles
• Solving the 3D Ising Model with the Conformal Bootstrap
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Skyrmions and Anomalous Hall Effect in a Dzyloshinskii-Moriya Spiral Magnet
• Electric field driven switching of individual magnetic skyrmions
• To be or knot to be?
• Hidden symmetry and knot solitons in a charged two-condensate Bose system
• Creation and confirmation of Hopfions in magnetic multilayer systems
• Skyrmion Lattice in Two-Dimensional Chiral Magnet
• The skyrmion lattice phase in three dimensional chiral magnets from Monte Carlo simulations
• Solitons, Links and Knots
• Faddeev-Hopf knots: Dynamics of linked un-knots
• Skyrmion knots in frustrated magnets
• Binding a Hopfion in Chiral Magnet Nanodisk
• Hopfions in chiral magnets
• Static Hopf Solitons and Knotted Emergent Fields in Solid-State Noncentrosymmetric Magnetic Nanostructures
• Chiral Magnetic Skyrmions with Arbitrary Topological Charge ("skyrmionic sacks")
• Theory of helical spin crystals: phases, textures and properties
• Magnetic skyrmions, chiral kinks and holomorphic functions
• Asymmetric isolated skyrmions in polar magnets with easy-plane anisotropy
• Instantons in Quantum Mechanics and Resurgent Expansions
• Instanton constituents in the O(3) model at finite temperature
• Instanton constituents and fermionic zero modes in twisted CP(n) models
• Skyrmion-Skyrmion Interaction in a Magnetic Film
• Quantum Computing for Quantum Tunnelling
• Magnetic skyrmion interactions in the micromagnetic framework
• A Performance Study of the 2D Ising Model on GPUs
• Decomposing Instantons in Two Dimensions
• Skyrmion interactions and lattices in chiral magnets: analytical results
• Instantons in Chiral Magnets
• Toroidal Confugurations As Stable Solitons
• Conformal symmetry of the critical 3D Ising model inside a sphere
• The Monte Carlo method in quantum field theory
• Kelvin knots in superconducting state
• A structural test for the conformal invariance of the critical 3d Ising model
• Observing the fate of the false vacuum with a quantum laboratory
• Complex instantons in sigma models with chemical potential
• The Emergence of Electroweak Skyrmions through Higgs Bosons

Cited by in corpus (4)

• Quantum Optimisation of Complex Systems with a Quantum Annealer
• Elvet -- a neural network-based differential equation and variational problem solver
• Towards a Quantum Simulation of Nonlinear Sigma Models with a Topological Term
• Simulating magnetic antiskyrmions on the lattice