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

QuICS Special Seminar

Laurens Lootens (Ghent University)
Wednesday, July 27, 2022 - 11:00am

Recently, we presented a systematic recipe for generating duality transformations in one dimensional lattice models. Our construction is based on a detailed understanding of the most general kind of symmetry a one-dimensional lattice model can exhibit: categorical symmetries. These symmetries are conveniently described in the language of tensor networks, where they are represented as matrix product operators. For a given lattice model with such categorical symmetries, their mathematical description in terms of bimodule categories allows us to generate all possible dual models, as well as explicit matrix product operator intertwiners that implement the dualities at the level of the Hilbert space.

In this talk, I will provide an overview of these results by giving an introduction to matrix product operator symmetries, the underlying categorical structures and how they provide the right framework for studying dualities. I will discuss some well known examples to illustrate our framework, and show how the categorical approach allows us to precisely relate the various symmetry sectors of dual models to each other.

Based on arXiv:2008.11187 and arXiv:2112.09091

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