Stable Interacting (2 + 1)d Conformal Field Theories at the Boundary of a class of (3 + 1)d Symmetry Protected Topological Phases
Stable Interacting (2 + 1)d Conformal Field Theories at the Boundary of a class of (3 + 1)d Symmetry Protected Topological Phases
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一类 (3 1)d 对称保护拓扑相边界处的稳定相互作用 (2 1)d 共形场论
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发表时间：
2016
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通讯作者：
Cenke Xu
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作者：
Zhen Bi;Alex Rasmussen;Yoni BenTov;Cenke Xu
受对称保护拓扑(SPT)相的最新研究的启发，我们探索了定义在Grassman流形上的$(2+1)d$非线性sigma模型中可能存在的无间隙量子无序相，该模型定义在Grassman流形$frac{U(N)}{U(N)imes U(N-n)}$上，其中WZW项位于$k$能级，这是某些$(3+1)d$SPT态边界的有效低能场理论。当$k=0$时，该模型有一个很好控制的大-$N$极限，即它的重整化群方程可以用大-$N$精确地计算。然而，对于WZW项，仅有大$N$和大$k$限制并不足以可靠地研究量子无序相的性质。我们证明了通过大N元、大K元和ε元相结合的推广，量子无序相中的稳定不动点可以可靠地定位在大元-N元极限和引导级的元-ε-元展开中，这对应于一个$(2+1)d$强相互作用共形场理论。
Motivated by recent studies of symmetry protected topological (SPT) phases, we explore the possible gapless quantum disordered phases in the $(2+1)d$ nonlinear sigma model defined on the Grassmannian manifold $frac{U(N)}{U(n) imes U(N - n)}$ with a Wess-Zumino-Witten (WZW) term at level $k$, which is the effective low energy field theory of the boundary of certain $(3+1)d$ SPT states. With $k = 0$, this model has a well-controlled large-$N$ limit, $i.e.$ its renormalization group equations can be computed exactly with large-$N$. However, with the WZW term, the large-$N$ and large-$k$ limit alone is not sufficient for a reliable study of the nature of the quantum disordered phase. We demonstrate that through a combined large-$N$, large-$k$ and $epsilon-$generalization, a stable fixed point in the quantum disordered phase can be reliably located in the large$-N$ limit and leading order $epsilon-$expansion, which corresponds to a $(2+1)d$ strongly interacting conformal field theory.