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.

arXiv comment12 + 11 pages (typeset with sn-jnl.cls), 4 + 1 figures; comments welcome

References in corpus (55)

• Exact evolution equation for the effective potential
• "Deconfined" quantum critical points
• The Exact Renormalisation Group and Approximate Solutions
• Aspects of the Functional Renormalisation Group
• Optimised Renormalisation Group Flows
• The nonperturbative functional renormalization group and its applications
• Conformality Lost
• Introduction to the functional RG and applications to gauge theories
• Flow Equations for N Point Functions and Bound States
• Quantum criticality with two length scales
• Walking, Weak first-order transitions, and Complex CFTs
• Competing orders, non-linear sigma models, and topological terms in quantum magnets
• Minimal Walking Technicolor: Set Up for Collider Physics
• Chiral phase structure of QCD with many flavors
• Theta-terms in nonlinear sigma-models
• 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
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• Renormalizability of gauge theories in extra dimensions
• Topological spin Hall states, charged skyrmions, and superconductivity in two dimensions
• RG Flows and Bifurcations
• Three Loop Analysis of the Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• A theory of deconfined pseudo-criticality
• On the Phase Structure of Many-Flavor QED${}_3$
• Realization of symmetry in the ERG approach to quantum field theory
• Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions
• Abelian Higgs model at four loops, fixed-point collision and deconfined criticality
• Proximate deconfined quantum critical point in SrCu2(BO3)2
• Renormalizable extra-dimensional models
• Phases of the (2+1) dimensional SO(5) non-linear sigma model with topological term
• Chiral symmetry breaking in three-dimensional quantum electrodynamics as fixed point annihilation
• 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
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• Multicritical deconfined quantum-criticality and Lifshitz point of a helical valence-bond phase
• Half-filled Landau levels: a continuum and sign-free regularization for 3D quantum critical points
• UV conformal window for asymptotic safety
• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• Critical O(N) models above four dimensions: Small-N solutions and stability
• Composite Operators in Asymptotic Safety
• Shadow of complex fixed point: Approximate conformality of Q>4 Potts model
• Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase
• Spontaneous breaking of Lorentz symmetry in $(2+\epsilon )$-dimensional QED
• Searching for continuous phase transitions in 5D SU(2) lattice gauge theory
• Functional renormalization group of the non-linear sigma model and the O(N) universality class
• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Trace anomaly and infrared cutoffs
• Tensor $O(N)$ model near six dimensions: fixed points and conformal windows from four loops
• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• Critical $O(2)$ and $O(3)$ ${\varphi }^4$ theories near six dimensions
• 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

Cited by in corpus (3)

• 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