Chiral Symmetry Breaking, Deconfinement and Entanglement Monotonicity

Abstract

We employ the recent results on the generalization of the $c$-theorem to 2+1-d to derive non-perturbative results for strongly interacting quantum field theories, including QED-3 and the critical theory corresponding to certain quantum phase transitions in condensed matter systems. In particular, by demanding that the universal constant part of the entanglement entropy decreases along the renormalization group flow ("F-theorem"), we find bounds on the number of flavors of fermions required for the stability of QED-3 against chiral symmetry breaking and confinement. In this context, the exact results known for the entanglement of superconformal field theories turn out to be quite useful. Furthermore, the universal number corresponding to the ratio of the entanglement entropy of a free Dirac fermion to that of free scalar plays an interesting role in the bounds derived. Using similar ideas, we also derive strong constraints on the nature of quantum critical points in condensed matter systems with "topological order".

6 pages, 1 figure. A new section added that employs supersymmetry to derive constraints on the non-supersymmetric QED-3. Section IIA rewritten to clarify assumptions in the first version

References in corpus (16)

• Towards a derivation of holographic entanglement entropy
• Holographic c-theorems in arbitrary dimensions
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Seeing a c-theorem with holography
• On the stability of U(1) spin liquids in two dimensions
• Integer quantum Hall effect for bosons: A physical realization
• Spin-orbital quantum liquid on the honeycomb lattice
• A c-theorem for the entanglement entropy
• Quantum Phase Transition between Integer Quantum Hall States of Bosons
• Regarding confinement and dynamical chiral symmetry breaking in QED3
• Algebraic vortex liquid theory of a quantum antiferromagnet on the kagome lattice
• Disk entanglement entropy for a Maxwell field
• The Renormalization Group Studies on Four Fermion Interaction Instabilities on Algebraic Spin Liquids
• Erratum: algebraic spin liquid as the mother of many competing orders
• Chiral Symmetry breaking in Three Dimensional QED
• Entanglement sum rules in exactly solvable models

Cited by in corpus (64)

• Quantum Spin Liquids
• Entanglement entropy: holography and renormalization group
• Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model
• Entanglement entropy of electromagnetic edge modes
• A Constraint on Defect and Boundary Renormalization Group Flows
• Chiral Spin Liquid and Quantum Criticality in Extended $S=1/2$ Heisenberg Models on the Triangular Lattice
• Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions
• Coherent and dissipative dynamics at quantum phase transitions
• On the Phase Structure of Many-Flavor QED${}_3$
• Corner contributions to holographic entanglement entropy
• Corner contribution to the entanglement entropy of an O(3) quantum critical point in 2+1 dimensions
• Quantum Electrodynamics in d=3 from the epsilon-expansion
• Nonzero temperature Entanglement Negativity of quantum spin models: Area law, Linked Cluster Expansions and Sudden Death
• Symmetric Fermion Mass Generation as Deconfined Quantum Criticality
• Chiral symmetry breaking in three-dimensional quantum electrodynamics as fixed point annihilation
• From spinon band topology to the symmetry quantum numbers of monopoles in Dirac spin liquids
• Corner contribution to the entanglement entropy of strongly-interacting O(2) quantum critical systems in 2+1 dimensions
• Continuous easy-plane deconfined phase transition on the kagome lattice
• Disk entanglement entropy for a Maxwell field
• Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
• Entanglement at a Two-Dimensional Quantum Critical Point: a T=0 Projector Quantum Monte Carlo Study
• A path integral Monte Carlo method for Rényi entanglement entropies
• Bounds on corner entanglement in quantum critical states
• The F-Theorem and F-Maximization
• Detecting Goldstone Modes with Entanglement Entropy
• Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice
• Excitonic instability of three-dimensional gapless semiconductors: Large-N theory
• Emergent Multi-flavor QED3 at the Plateau Transition between Fractional Chern Insulators: Applications to graphene heterostructures
• Fermion-induced quantum critical points in two-dimensional Dirac semimetals
• Two dimensional metallic phases from disordered QED${}_3$
• Spontaneous breaking of Lorentz symmetry in $(2+\epsilon )$-dimensional QED
• Entanglement does not generally decrease under renormalization
• Transition between algebraic and ${\mathbb{Z}}_2$ quantum spin liquids at large $N$
• A series of (2+1)d Stable Self-Dual Interacting Conformal Field Theories
• Mutual information and the F-theorem
• Higher-curvature corrections to holographic entanglement entropy in geometries with hyperscaling violation
• Unusual Corrections to Scaling and Convergence of Universal Renyi Properties at Quantum Critical Points
• State-Dependent Divergences in the Entanglement Entropy
• Quantum Critical Universality and Singular Corner Entanglement Entropy of Bilayer Heisenberg-Ising model
• Breaking of the gauge symmetry in lattice gauge theories
• On the entanglement across a cubic interface in 3+1 dimensions
• Intertwining SU($N$) symmetry and frustration on a honeycomb lattice
• Topological orders of monopoles and hedgehogs: From electronic and magnetic spin-orbit coupling to quarks
• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Emergent QCD${}_3$ Quantum Phase Transitions of Fractional Chern Insulators
• Instability of Universal Terms in the Entanglement Entropy
• An analog of topological entanglement entropy for mixed states
• Twisted bilayer U(1) Dirac spin liquids
• $QC{D}_3$ Dualities and the F-Theorem
• Variational identification of a fractional Chern insulator in an extended Bose-Hubbard model
• Probing trihedral corner entanglement for Dirac fermions
• Fractionalized gapless quantum vortex liquids
• Shape dependence of two-cylinder Renyi entropies for free bosons on a lattice
• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling
• Conformal geometry from entanglement
• Pauli-Term-Induced Fixed Points in $d$-dimensional QED
• Entanglement Entropy of $(2+1)$D Quantum Critical Points with Quenched Disorder: Dimensional Reduction Approach
• Stability of $SU(N_c)$ QCD3 from the $\epsilon$-Expansion
• Monopoles in Dirac spin liquids and their symmetries from instanton calculus
• Universal divergence of the Renyi entropy of a thinly sliced torus at the Ising fixed point
• Fermionic skyrmions and bosonization for a Gross-Neveu transition
• Viewpoint: duality for fermionic vortices
• Entanglement C-functions of defects and interfaces in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• Entanglement and Excitations in Gauge/Gravity Duality