Topological phase transitions in four dimensions

Abstract

We show that four-dimensional systems may exhibit a topological phase transition analogous to the well-known Berezinskii-Kosterlitz-Thouless vortex unbinding transition in two-dimensional systems. The realisation of an engineered quantum system, where the predicted phase transition shall occur, is also presented. We study a suitable generalization of the sine-Gordon model in four dimensions and the renormalization group flow equation of its couplings, showing that the critical value of the frequency is the square of the corresponding value in $2D$. The value of the anomalous dimension at the critical point is determined ($\eta =1/32$) and a conjecture for the universal jump of the superfluid stiffness ($4/{\pi }^2$) presented.

23 pages, 1 figure

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Cited by in corpus (8)

• Long-range interacting quantum systems
• $BKT$ transitions in classical and quantum long-range systems
• Anomalous scaling at non-thermal fixed points of the sine-Gordon model
• Stability of the Fulde-Ferrell-Larkin-Ovchinnikov states in anisotropic systems and critical behavior at thermal $m$-axial Lifshitz points
• Villain model with long-range couplings
• Lorentz symmetry violating Lifshitz-type field theories
• Berezinskii-Kosterlitz-Thouless phase transitions with long-range couplings
• Higher-derivative four-dimensional sine-Gordon model