Tensor network approach to electromagnetic duality in (3+1)d topological gauge models

@article{Delcamp2022TensorNA,
  title={Tensor network approach to electromagnetic duality in (3+1)d topological gauge models},
  author={Clement Delcamp},
  journal={Journal of High Energy Physics},
  year={2022}
}
  • C. Delcamp
  • Published 15 December 2021
  • Mathematics
  • Journal of High Energy Physics
Abstract Given the Hamiltonian realisation of a topological (3+1)d gauge theory with finite group G, we consider a family of tensor network representations of its ground state subspace. This family is indexed by gapped boundary conditions encoded into module 2-categories over the input spherical fusion 2-category. Individual tensors are characterised by symmetry conditions with respect to non-local operators acting on entanglement degrees of freedom. In the case of Dirichlet and Neumann… 

Dualities in one-dimensional quantum lattice models: topological sectors

It has been a long-standing open problem to construct a general framework for relating the spectra of dual theories to each other. Building on ref. [arXiv:2112.09091], whereby dualities are defined

Dual Fusion 2-Categories

Given a fusion 2-category and a suitable module 2-category, the dual tensor 2-category is the associated 2-category of module 2-endofunctors. In order to study the properties of this 2-category, we

The Morita Theory of Fusion 2-Categories

We develop the Morita theory of fusion 2-categories. In order to do so, we begin by proving that the relative tensor product of modules over a separable algebra in a fusion 2-category exists. We use

A toy model for categorical charges

We consider a higher gauge topological model in three spatial dimensions whose input datum is a 2-group encoding the mixing of a 0-form Z 2 - and 1-form Z 3 -symmetry. We study the excitation content

Rigid and Separable Algebras in Fusion 2-Categories

Rigid monoidal 1-categories are ubiquitous throughout quantum algebra and low-dimensional topology. We study a generalization of this notion, namely rigid algebras in an arbitrary monoidal

Category-theoretic recipe for dualities in one-dimensional quantum lattice models

We present a systematic approach for generating duality transformations in quantum lattice models. Within our formalism, dualities are completely characterized by equivalent but distinct realizations

Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners

We present a systematic recipe for generating duality transformations in one-dimensional quantum lattice models with abelian, non-abelian or categorical symmetries. Dual models can be character-ized

References

SHOWING 1-10 OF 72 REFERENCES

Tensor Categories

  • Mathematical Surveys and Monographs
  • 2015

On tensor network representations of the (3+1)d toric code

Two dual tensor network representations of the (3+1)d toric code ground state subspace are defined, characterized by different virtual symmetries generated by string-like and membrane-like operators, respectively, and it is argued that, depending on the representation, the phase diagram of boundary entanglement degrees of freedom is naturally associated with that of a (2+1).

Algebraic higher symmetry and categorical symmetry: A holographic and entanglement view of symmetry

We introduce the notion of algebraic higher symmetry, which generalizes higher symmetry and is beyond higher group. We show that an algebraic higher symmetry in a bosonic system in $n$-dimensional

Categorical symmetry and noninvertible anomaly in symmetry-breaking and topological phase transitions

For a zero-temperature Landau symmetry breaking transition in $n$-dimensional space that completely breaks a finite symmetry $G$, the critical point at the transition has the symmetry $G$. In this

Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners

We present a systematic recipe for generating duality transformations in one-dimensional quantum lattice models with abelian, non-abelian or categorical symmetries. Dual models can be character-ized

Finite Semisimple Module 2-Categories

Let $\mathfrak{C}$ be a multifusion 2-category. We show that every finite semisimple $\mathfrak{C}$-module 2-category is canonically enriched over $\mathfrak{C}$. Using this enrichment, we prove that

Crossing with the circle in Dijkgraaf–Witten theory and applications to topological phases of matter

Given a fully extended topological quantum field theory, the “crossing with the circle” conditions establish that the dimension, or categorification thereof, of the quantum invariant assigned to a

On the stability of topological order in tensor network states

Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305, USA Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany Munich Center for

Higher-form symmetry breaking at Ising transitions

In recent years, new phases of matter that are beyond the Landau paradigm of symmetry breaking are mountaining, and to catch up with this fast development, new notions of global symmetry are

Defects in the 3-dimensional toric code model form a braided fusion 2-category

This work constructs all topological defects of codimension 2 and higher, and shows that they form a braided fusion 2-category satisfying a braiding non-degeneracy condition.
...