Locality of Spontaneous Symmetry Breaking and Universal Spacing Distribution of Topological Defects Formed Across a Phase Transition

• URL: http://arxiv.org/abs/2202.11731v2
• Date: Thu, 13 Oct 2022 14:20:27 GMT
• Title: Locality of Spontaneous Symmetry Breaking and Universal Spacing Distribution of Topological Defects Formed Across a Phase Transition
• Authors: Adolfo del Campo, Fernando Javier G\'omez-Ruiz, and Hai-Qing Zhang
• Abstract summary: A continuous phase transition results in the formation of topological defects with a density predicted by the Kibble-Zurek mechanism (KZM) We characterize the spatial distribution of point-like topological defects in the resulting nonequilibrium state and model it using a Poisson point process in arbitrary spatial dimension with KZM density.
• Score: 62.997667081978825
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The crossing of a continuous phase transition results in the formation of topological defects with a density predicted by the Kibble-Zurek mechanism (KZM). We characterize the spatial distribution of point-like topological defects in the resulting nonequilibrium state and model it using a Poisson point process in arbitrary spatial dimension with KZM density. Numerical simulations in a one-dimensional $\phi^4$ theory unveil short-distance defect-defect corrections stemming from the kink excluded volume, while in two spatial dimensions, our model accurately describes the vortex spacing distribution in a strongly-coupled superconductor indicating the suppression of defect-defect spatial correlations.

Related papers

• Universal Vortex Statistics and Stochastic Geometry of Bose-Einstein Condensation [0.0]
  vortex statistics are described by a homogeneous point process (PPP) with a density dictated by the Kibble-Zurek mechanism (KZM) We validate this model using numerical simulations of the two-dimensional Gross-Pitaevskii equation (SGPE) for both a homogeneous and a hard-wall condensate.
  arXiv  Detail & Related papers  (2024-01-17T19:00:00Z)
• Large Deviations Beyond the Kibble-Zurek Mechanism [2.4020585213586387]
  We study the universality of fluctuations beyond the KZM. We report the exact form of the rate function in the transverse-field quantum Ising model.
  arXiv  Detail & Related papers  (2023-07-05T18:00:00Z)
• Structural phase transition and its critical dynamics from holography [0.0]
  We introduce a gravitational lattice theory defined in an AdS$_3$ black hole background that provides a holographic dual description of the linear-to-zigzag structural phase transition. The transition from the high-symmetry linear phase to the broken-symmetry doubly-degenerate phase can be driven by quenching the coupling between adjacent sites through the critical point. An analysis of the equilibrium correlation length and relaxation time reveals mean-field critical exponents.
  arXiv  Detail & Related papers  (2023-02-22T19:00:17Z)
• Shape And Structure Preserving Differential Privacy [70.08490462870144]
  We show how the gradient of the squared distance function offers better control over sensitivity than the Laplace mechanism. We also show how using the gradient of the squared distance function offers better control over sensitivity than the Laplace mechanism.
  arXiv  Detail & Related papers  (2022-09-21T18:14:38Z)
• Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition [62.997667081978825]
  We analyze the role of boundary conditions in the statistics of topological defects. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate.
  arXiv  Detail & Related papers  (2022-07-08T09:55:05Z)
• Simultaneous Transport Evolution for Minimax Equilibria on Measures [48.82838283786807]
  Min-max optimization problems arise in several key machine learning setups, including adversarial learning and generative modeling. In this work we focus instead in finding mixed equilibria, and consider the associated lifted problem in the space of probability measures. By adding entropic regularization, our main result establishes global convergence towards the global equilibrium.
  arXiv  Detail & Related papers  (2022-02-14T02:23:16Z)
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model [62.997667081978825]
  We study the ground state properties of the one-dimensional extended Hubbard model at half-filling. In particular, in the superconducting region, we obtain that the entanglement spectrum signals a transition between a dominant singlet (SS) to triplet (TS) pairing ordering in the system.
  arXiv  Detail & Related papers  (2021-10-29T21:02:24Z)
• Topology of anti-parity-time-symmetric non-Hermitian Su-Schrieffer-Heeger model [0.0]
  We show that the large non-Hermiticity constructively creates nontrivial topology and greatly expands the topological phase. Our findings can be verified through introducing dissipations in every another two sites of the standard SSH model even in its trivial phase.
  arXiv  Detail & Related papers  (2021-05-08T11:17:08Z)
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach [51.819912248960804]
  We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system.
  arXiv  Detail & Related papers  (2021-03-12T13:16:18Z)
• Disorder-free localization in an interacting two-dimensional lattice gauge theory [0.0]
  Disorder-free localization has been recently introduced as a mechanism for ergodicity breaking in low-dimensional homogeneous lattice gauge theories. We show that genuinely interacting systems in two spatial dimensions can become nonergodic as a consequence of this mechanism.
  arXiv  Detail & Related papers  (2020-03-10T18:00:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.