The Low-Energy TQFT of the Generalized Double Semion Model

@article{Debray2018TheLT,
  title={The Low-Energy TQFT of the Generalized Double Semion Model},
  author={Arun Debray},
  journal={Communications in Mathematical Physics},
  year={2018},
  volume={375},
  pages={1079-1115}
}
  • A. Debray
  • Published 8 November 2018
  • Mathematics
  • Communications in Mathematical Physics
The generalized double semion (GDS) model, introduced by Freedman and Hastings, is a lattice system similar to the toric code, with a gapped Hamiltonian whose definition depends on a triangulation of the ambient manifold M , but whose space of ground states does not depend on the triangulation, but only on the underlying manifold. In this paper, we use topological quantum field theory (TQFT) to investigate the low-energy limit of the GDS model. We define and study a functorial TQFT $$Z_{\mathrm… 

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References

SHOWING 1-10 OF 65 REFERENCES

Double Semions in Arbitrary Dimension

We present a generalization of the double semion topological quantum field theory to higher dimensions, as a theory of $${d-1}$$d-1 dimensional surfaces in a d dimensional ambient space. We construct

Cohomological twisting of 2-linearization and extended TQFT

In this paper, we describe a relation between a categorical quantization construction, called “2-linearization”, and extended topological quantum field theory (ETQFT). We then describe an extension

Construction of bosonic symmetry-protected-trivial states and their topological invariants viaG×SO(∞)nonlinearσmodels

It has been shown that the L-type bosonic symmetry-protected-trivial (SPT) phases with pure gauge anomalous boundary can all be realized via non-linear $\sigma$-models (NL$\sigma$Ms) of the symmetry

Invertible Topological Field Theories

A $d$-dimensional invertible topological field theory is a functor from the symmetric monoidal $(\infty,n)$-category of $d$-bordisms (embedded into $\mathbb{R}^\infty$ and equipped with a tangential

Topological Order from a Cohomological and Higher Gauge Theory perspective

In recent years, attempts to generalize lattice gauge theories to model topological order have been carried out through the so called $2$-gauge theories. These have opened the door to interesting new

Three-dimensional topological lattice models with surface anyons

We study a class of three dimensional exactly solvable models of topological matter first put forward by Walker and Wang [arXiv:1104.2632v2]. While these are not models of interacting fermions, they

Topological gauge theories and group cohomology

We show that three dimensional Chern-Simons gauge theories with a compact gauge groupG (not necessarily connected or simply connected) can be classified by the integer cohomology groupH4(BG,Z). In a

The cobordism category and Waldhausen's K-theory

This paper examines the category C^k_{d,n} whose morphisms are d-dimensional smooth manifolds that are properly embedded in the product of a k-dimensional cube with an (d+n-k)-dimensional Euclidean

Homotopy Quantum Field Theory

Homotopy Quantum Field Theory (HQFT) is a branch of Topological Quantum Field Theory founded by E. Witten and M. Atiyah. It applies ideas from theoretical physics to study principal bundles over
...