Related papers: On two-dimensional tensor network group symmetries
A natural way to generalise tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product…
Spatially modulated symmetries are one of the new types of symmetries whose symmetry actions are position dependent. Yet exotic phases resulting from these spatially modulated symmetries are not fully understood and classified. In this…
Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been…
We use the Symmetry Topological Field Theory (SymTFT) to systematically characterize gapped phases in 2+1 dimensions with categorical symmetries. The SymTFTs that we consider are (3+1)d Dijkgraaf-Witten (DW) theories for finite groups $G$,…
The first part of the paper explains how to encode a one-cocycle and a two-cocycle on a group $G$ with values in its representation by networks of planar trivalent graphs with edges labelled by elements of $G$, elements of the…
We investigate the interactions of discrete zero-form and one-form global symmetries in (1+1)d theories. Focus is put on the interactions that the symmetries can have on each other, which in this low dimension result in 2-group symmetries…
Signed networks are frequently observed in real life with additional sign information associated with each edge, yet such information has been largely ignored in existing network models. This paper develops a unified embedding model for…
Tensor networks provide a useful tool to describe low-dimensional complex many-body systems. Finding efficient algorithms to use these methods for finite-temperature simulations in two dimensions is a continuing challenge. Here, we use the…
Tensor Network methods have been established as a powerful technique for simulating low dimensional strongly-correlated systems for over two decades. Employing the formalism of Matrix Product States, we investigate the phase diagram of the…
We generalize the topological response theory to detect the boundary anomalies of linear subsystem symmetries. This approach allows us to distinguish different subsystem symmetry-protected topological (SSPT) phases and uncover new ones. We…
Decoherence in realistic quantum platforms motivates a mixed-state notion of topological phases of matter, including average symmetry-protected topological (ASPT) phases. Alongside this progress, generalized symmetries--notably…
Recently a new class of quantum phases of matter: symmetry protected topological states, such as topological insulators, attracted much attention. In presence of interactions, group cohomology provides a classification of these [X. Chen et…
Classification of possible quantum spin liquid (QSL) states of interacting spin-1/2's in two dimensions has been a fascinating topic of condensed matter for decades, resulting in enormous progress in our understanding of low-dimensional…
Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the symmetry of the emergent topological…
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…
Symmetry topological field theory (SymTFT), or topological holography, posits a correspondence between symmetries in a $d$-dimensional theory and topological order in a $(d+1)$-dimensional theory. In this work, we extend this framework to…
We define and classify symmetry-protected topological (SPT) phases in mixed states based on the tensor network formulation of the density matrix. In one dimension, we introduce strong injective matrix product density operators (MPDO), which…
This thesis aims at concluding the classification results for topological phases with symmetry in 2+1 dimensions. The main result is that topological phases are classified by a triple of unitary braided fusion categories $\mathcal…
Tensor networks prepare states that share many features of states in quantum gravity. However, standard constructions are not diffeomorphism invariant and do not support an algebra of non-commuting area operators. Recently, analogues of…