The Nordic-walking mechanism and its explanation of deconfined pseudocriticality from Wess-Zumino-Witten theory

Abstract

The understanding of phenomena falling outside the Ginzburg-Landau paradigm of phase transitions represents a key challenge in condensed matter physics. A famous class of examples is constituted by the putative deconfined quantum critical points between two symmetry-broken phases in layered quantum magnets, such as pressurised SrCu${}_2$(BO${}_3$)${}_2$. Experiments find a weak first-order transition, which simulations of relevant microscopic models can reproduce. The origin of this behaviour has been a matter of considerable debate for several years. In this work, we demonstrate that the nature of the deconfined quantum critical point can be best understood in terms of a novel dynamical mechanism, termed Nordic walking. Nordic walking denotes a renormalisation group flow arising from a beta function that is flat over a range of couplings. This gives rise to a logarithmic flow that is faster than the well-known walking behaviour, associated with the annihilation and complexification of fixed points, but still significantly slower than the generic running of couplings. The Nordic-walking mechanism can thus explain weak first-order transitions, but may also play a role in high-energy physics, where it could solve hierarchy problems. We analyse the Wess-Zumino-Witten field theory pertinent to deconfined quantum critical points with a topological term in 2+1 dimensions. To this end, we construct an advanced functional renormalisation group approach based on higher-order regulators. We thereby calculate the beta function directly in 2+1 dimensions and provide evidence for Nordic walking.

12 + 11 pages (typeset with sn-jnl.cls), 4 + 1 figures; comments welcome

References in corpus (21)

• Exact evolution equation for the effective potential
• "Deconfined" quantum critical points
• Minimal Walking Technicolor: Set Up for Collider Physics
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Topological Mott insulator in three-dimensional systems with quadratic band touching
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• Three Loop Analysis of the Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• On the Phase Structure of Many-Flavor QED${}_3$
• Proximate deconfined quantum critical point in SrCu2(BO3)2
• Fixed Points of Nonlinear Sigma Models in d>2
• Phase diagram of electronic systems with quadratic Fermi nodes in $2<d<4$: $2+\epsilon$ expansion, $4-\epsilon$ expansion, and functional renormalization group
• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• Composite Operators in Asymptotic Safety
• Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase
• Searching for continuous phase transitions in 5D SU(2) lattice gauge theory
• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• SU(2)-Symmetric Spin-Boson Model: Quantum Criticality, Fixed-Point Annihilation, and Duality
• Hidden Critical Points in the Two-Dimensional $O(n>2)$ model: Exact Numerical Study of a Complex Conformal Field Theory
• Absence of SO(4) quantum criticality in Dirac semimetals at two-loop order
• SO(5) multicriticality in two-dimensional quantum magnets

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• Continuous order-to-order quantum phase transitions from fixed-point annihilation
• Alteration of Topology in Quantum Phase Transitions via Symmetry Enrichment
• Tunable quantum criticality and pseudocriticality across the fixed-point annihilation in the anisotropic spin-boson model