Topological phase transitions in four dimensions

2020/03/31 by Nicolò Defenu, Andrea Trombettoni, Dario Zappalà · 12 citations
Mathematics · Physics and Astronomy · #Combinatorics #Condensed matter physics #Conjecture #Critical phenomena #Critical point (mathematics) #Dimension (graph theory) #Generalization #Jump #Mathematical analysis #Mathematical physics #Mathematics #Phase (matter) #Phase transition #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum many-body systems #Quantum mechanics #Quantum, superfluid, helium dynamics #Renormalization group #Superfluidity #Topology (electrical circuits) #Vortex #cond-mat.quant-gas #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2020.115295

published in Nuclear Physics B 964, 115295 (Elsevier BV) · 23 pages, 1 figure

openalex publication_date 2020/12/28 · arxiv created 2021/02/08 · arxiv updated 2021/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

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. 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 (η=1/32) and a conjecture for the universal jump of the superfluid stiffness (4/π2) presented.

Citations

• Quantum Inverse Scattering Method and Correlation Functions
• Critical exponents ofO(N)models in fractional dimensions
• Bosonization and Strongly Correlated Systems
• Continuous Quantum Phase Transitions
• Quantum Simulation of an Extra Dimension
• Criticality and scaling in 4D quantum gravity
• Exact evolution equation for the effective potential
• Renormalization of the NonlinearσModel in2+εDimensions—Application to the Heisenberg Ferromagnets
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• Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas
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• Ordering, metastability and phase transitions in two-dimensional systems
• Kosterlitz–Thouless-like deconfinement mechanism in the (2+1)-dimensional Abelian Higgs model
• Nonperturbative Functional Renormalization-Group Approach to the Sine-Gordon Model and the Lukyanov-Zamolodchikov Conjecture