"Self-Dual" Quantum Critical Point on the surface of $3d$ Topological Insulator

Abstract

In the last few years a lot of exotic and anomalous topological phases were constructed by proliferating the vortex like topological defects on the surface of the $3d$ topological insulator (TI). In this work, rather than considering topological phases at the boundary, we will study quantum critical points driven by vortex like topological defects. In general we will discuss a $(2+1)d$ quantum phase transition described by the following field theory: $\mathcal{L}=\bar{\psi }{\gamma }_{\mu }({\partial }_{\mu }-i{a}_{\mu })\psi +|({\partial }_{\mu }-ik{a}_{\mu })\varphi {|}^2+r|\varphi {|}^2+g|\varphi {|}^4$, with tuning parameter $r$, arbitrary integer $k$, Dirac fermion $\psi$ and complex scalar bosonic field $\varphi$ which both couple to the same $(2+1)d$ dynamical noncompact U(1) gauge field $a_{\mu }$. The physical meaning of these quantities/fields will be explained in the text. We demonstrate that this quantum critical point has a quasi self-dual nature. And at this quantum critical point, various universal quantities such as the electrical conductivity, and scaling dimension of gauge invariant operators can be calculated systematically through a $1/k^2$ expansion, based on the observation that the limit $k\to +\infty$ corresponds to an ordinary $3d$ XY transition.

5 pages, 2 figures

References in corpus (9)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• "Deconfined" quantum critical points
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Algebraic spin liquid as the mother of many competing orders
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography
• Self-dual Quantum Electrodynamics as Boundary State of the three dimensional Bosonic Topological Insulator
• A square lattice algebraic spin liquid with SO(5) symmetry

Cited by in corpus (1)

• Realizing topological surface states in a lower-dimensional flat band