Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition

Abstract

In a scenario of spontaneous symmetry breaking in finite time, topological defects are generated at a density that scale with the driving time according to the Kibble-Zurek mechanism (KZM). Signatures of universality beyond the KZM have recently been unveiled: The number distribution of topological defects has been shown to follow a binomial distribution, in which all cumulants inherit the universal power-law scaling with the quench rate, with cumulant rations being constant. In this work, we analyze the role of boundary conditions in the statistics of topological defects. In particular, we consider a lattice system with nearest-neighbor interactions subject to soft anti-periodic, open, and periodic boundary conditions implemented by an energy penalty term. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate that is independent of the boundary conditions except by an additive term, that becomes prominent in the limit of slow quenches, leading to the breaking of power-law behavior. We test our theoretical predictions with a one-dimensional scalar theory on a lattice.

9 Pages, 5 Figures

References in corpus (12)

• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Universal adiabatic dynamics across a quantum critical point
• Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum Ising model
• Structural defects in ion crystals by quenching the external potential: the inhomogeneous Kibble-Zurek mechanism
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond
• Spontaneous nucleation of structural defects in inhomogeneous ion chains
• Full Counting Statistics of Topological Defects After Crossing a Phase Transition
• Twisted boundary condition and Lieb-Schultz-Mattis ingappability for discrete symmetries
• Universal Statistics of Vortices in a Newborn Holographic Superconductor: Beyond the Kibble-Zurek Mechanism
• Distribution of Kinks in an Ising Ferromagnet After Annealing and the Generalized Kibble-Zurek Mechanism
• Adiabatic dynamics of an inhomogeneous quantum phase transition: the case of z > 1 dynamical exponent
• Planar Josephson Tunnel Junctions in an Asymmetric Magnetic Field

Cited by in corpus (9)

• Large Deviations Beyond the Kibble-Zurek Mechanism
• Universal Vortex Statistics and Stochastic Geometry of Bose-Einstein Condensation
• Structural phase transition and its critical dynamics from holography
• Out-of-equilibrium scaling behavior arising during round-trip protocols across a quantum first-order transition
• Apparent delay of the Kibble-Zurek mechanism in quenched open systems
• Kibble-Zurek Mechanism and Beyond: Lessons from a Holographic Superfluid Disk
• Annealing Dynamics of Regular Rotor Networks: Universality and Its Breakdown
• Topologically Protected Metastable States in Classical Dynamics
• Anomalous Dynamical Scaling at Topological Quantum Criticality