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"Self-Dual" Quantum Critical Point on the surface of $3d$ Topological Insulator
Strongly Correlated Electrons · Submitted 4 Dec 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We demonstrate that this quantum critical point has a quasi self-dual nature.
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The abstract, sentence by sentence
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: $\mathcal{L} = \bar{\psi}\gamma_\mu (\partial_\mu - i a_\mu) \psi + |(\partial_\mu - i k a_\mu)\phi|^2 + r |\phi|^2 + g |\phi|^4$, with tuning parameter $r$, arbitrary integer $k$, Dirac fermion $\psi$ and complex scalar bosonic field $\phi$ 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 $k \rightarrow + \infty$ corresponds to an ordinary $3d$ XY transition.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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). | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | In this work, rather than considering topological phases at the boundary, we will study quantum critical points driven by vortex like topological defects. | contribution 0.99 | 0.70 | 0.04 | asserted 0.71 |
| s2 | In general we will discuss a $(2+1)d$ quantum phase transition described by the following field theory: $\mathcal{L} = \bar{\psi}\gamma_\mu (\partial_\mu - i a_\mu) \psi + |(\partial_\mu - i k a_\mu)\phi|^2 + r |\phi|^2 + g |\phi|^4$, with tuning parameter $r$, arbitrary integer $k$, Dirac fermion $\psi$ and complex scalar bosonic field $\phi$ which both couple to the same $(2+1)d$ dynamical noncompact U(1) gauge field $a_\mu$. | method 0.86 | 0.37 | 0.05 | asserted 0.89 |
| s3 | The physical meaning of these quantities/fields will be explained in the text. | method 0.41 | 0.19 | 0.02 | asserted 0.53 |
| s4 | We demonstrate that this quantum critical point has a quasi self-dual nature. | result 0.98 | 0.95 | 0.65 | asserted 1.00 |
| s5 | 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 $k \rightarrow + \infty$ corresponds to an ordinary $3d$ XY transition. | result 0.53 | 0.92 | 0.30 | asserted 0.99 |
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The paper
Original 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: $\mathcal{L} = \bar{\psi}\gamma_\mu (\partial_\mu - i a_\mu) \psi + |(\partial_\mu - i k a_\mu)\phi|^2 + r |\phi|^2 + g |\phi|^4$, with tuning parameter $r$, arbitrary integer $k$, Dirac fermion $\psi$ and complex scalar bosonic field $\phi$ 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 $k \rightarrow + \infty$ corresponds to an ordinary $3d$ XY transition.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
What it cites · 3 sentences without a confident label
Uses data or values from 1 paper
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Here $Δ_xy$ is the scaling dimension of $r̃$ at the $3d$ XY universality class, which is very close to $3/2$ [ref] .
The critical behavior of magnetic systems described by Landau-Ginzburg-Wilson field theories · Introduction · 0.98
Cites as support 1 paper
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Recently a coupled wire construction of the duality further supports this idea [ref] .
Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions · Introduction · 0.99
Cites as background 3 papers
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It was demonstrated that under strong interaction the boundary of a $3d$ TI can have various topological orders that cannot be realized in a pure $2d$ system [ref] .
A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators · Introduction · 0.83
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Ref. [ref] has applied the mirror symmetry [ref] (duality between supersymmetric field theories) to the half-filled Landau level [ref] , which is a system closely related to the boundary of $3d$ TI [ref] .
Mirror symmetry and the half-filled Landau level · Introduction · 0.80
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Although it is well-known that the boundary state of a noninteracting $3d$ topological insulator (TI) is described by one or odd number of free $(2+1)d$ Dirac fermions [ref] , curiosity drives theorists to look for all possible boundary states of $3d$ TI under strong interaction.
Topological superfluids with time reversal symmetry · Introduction · 0.99
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