Generic "Unnecessary" Quantum Critical Points with Minimal Degrees of Freedom

Abstract

We explore generic "unnecessary" quantum critical points with minimal degrees of freedom. These quantum critical points can be avoided with strong enough symmetry-allowed deformations of the Hamiltonian, but these deformations are irrelevant perturbations below certain threshold at the quantum critical point. These quantum critical points are hence unnecessary, but also unfine-tuned (generic). The previously known examples of such generic unnecessary quantum critical points involve at least eight Dirac fermions in both two and three spatial dimensions. In this work we seek for examples of generic unnecessary quantum critical points with minimal degrees of freedom. In particular, in three dimensional space, we identify two examples of such generic unnecessary quantum critical points. The first example occurs in a $3d$ interacting topological insulator, and it is described by $two$ $(3+1)d$ massless Dirac fermions in the infrared limit; the second example occurs in a $3d$ topological superconductor, and it is formally described only $one$ $(3+1)d$ massless Dirac fermion.

arXiv comment10 pages, 4 figures. In order to be self-contained, this preprint contains a review of our previous work arXiv:1906.07191 in section IIA

References in corpus (42)

• Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
• "Deconfined" quantum critical points
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Topological phases of fermions in one dimension
• Lieb-Schultz-Mattis in Higher Dimensions
• The effects of interactions on the topological classification of free fermion systems
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Nearly Flat Chern Bands in Moiré Superlattices
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Deconfined quantum critical points: symmetries and dualities
• Interacting fermionic topological insulators/superconductors in three dimensions
• Quantum criticality with two length scales
• Protected edge modes without symmetry
• Quantum valley Hall effect, orbital magnetism, and anomalous Hall effect in twisted multilayer graphene systems
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Interacting topological phases and modular invariance
• Twisted Bilayer Graphene Aligned with Hexagonal Boron Nitride: Anomalous Hall Effect and a Lattice Model
• Topological phases protected by point group symmetry
• Gate-Tunable Topological Flat Bands in Trilayer Graphene-Boron Nitride Moiré Superlattices
• Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States.
• Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator
• A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator
• Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator
• A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
• Interaction effect on topological classification of superconductors in two dimensions
• The effect of interactions on 2D fermionic symmetry-protected topological phases with Z2 symmetry
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• A new class of $(2+1)$-d topological superconductor with ${\mathbb{Z}}_8$ topological classification
• Symmetry Protected Topological States of Interacting Fermions and Bosons
• Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models
• Wave Functions of Bosonic Symmetry Protected Topological Phases
• Lieb-Schultz-Mattis Theorem and its generalizations from the Perspective of the Symmetry Protected Topological phase
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Quantum Phase Transitions Between Bosonic Symmetry Protected Topological States Without Sign Problem: Nonlinear Sigma Model with a Topological Term
• Bridging Fermionic and Bosonic Short Range Entangled States
• Free and Interacting Short-Range Entangled Phases of Fermions: Beyond the Ten-Fold Way
• Bilayer Graphene as a platform for Bosonic Symmetry Protected Topological States
• Interacting Valley Chern Insulator and its Topological Imprint on Moiré Superconductors

Cited by in corpus (9)

• Symmetry protected topological phases under decoherence
• Anomalies and symmetric mass generation for Kaehler-Dirac fermions
• Multiversality and Unnecessary Criticality in One Dimension
• Pivoting through the chiral-clock family
• Lattice Regularization of Reduced Kähler-Dirac Fermions and Connections to Chiral Fermions
• Dirac spin liquid as an "unnecessary" quantum critical point on square lattice antiferromagnets
• Charge pumps, boundary modes, and the necessity of unnecessary criticality
• Unnecessary quantum criticality in $SU(3)$ kagome magnets
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice