Related papers: On two-dimensional tensor network group symmetries
The 1-form symmetries in two-dimensional topological systems are ``shadowed'' as global symmetries in their one-dimensional quantum transfer matrices. In this work, we introduce a distinct shadow effect arising from the pair-creation of…
Symmetry topological field theory (SymTFT) gives a holographic correspondence between systems with a global symmetry and a higher-dimensional topological field theory. In this framework, classification of gapped phases of matter in…
We discuss physical constructions, and the boundary properties of various symmetry protected topological phases that involve 1-form symmetries, from one spatial dimension (1d) to four spatial dimensions (4d). For example, the prototype 3d…
The intuitiveness of the tensor network graphical language is becoming well known through its use in numerical simulations using methods from tensor network algorithms. Recent times have also seen rapid progress in developing equations of…
We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states (cMPS) to spatial dimensions $d\geq 2$. By construction, they are Euclidean…
We construct a tensor network representation of the 3d toric code ground state that is stable to a generating set of uniform local tensor perturbations, including those that do not map to local operators on the physical Hilbert space. The…
The analysis of 3D symmetric second-order tensor fields often relies on topological features such as degenerate tensor lines, neutral surfaces, and their generalization to mode surfaces, which reveal important structural insights into the…
Topological order has been proposed to go beyond Landau symmetry breaking theory for more than twenty years. But it is still a challenging problem to generally detect it in a generic many-body state. In this paper, we will introduce a…
Symmetry acting on a (2+1)$D$ topological order can be anomalous in the sense that they possess an obstruction to being realized as a purely (2+1)$D$ on-site symmetry. In this paper, we develop a (3+1)$D$ topological quantum field theory to…
Fusion category symmetries are finite symmetries in 1+1 dimensions described by unitary fusion categories. We classify 1+1d time-reversal invariant bosonic symmetry protected topological (SPT) phases with fusion category symmetry by using…
We construct fixed point lattice models for group supercohomology symmetry protected topological (SPT) phases of fermions in 2+1D. A key feature of our approach is to construct finite depth circuits of local unitaries that explicitly build…
We discuss the geometry of a class of tensor network states, called projected entangled pair states in the Physics literature. We provide initial results towards a question of Verstraete and Rizzi regarding the tensor network state of an $M…
Two global symmetries are holo-equivalent if their algebras of local symmetric operators are isomorphic. Holo-equivalent classes of global symmetries are classified by gappable-boundary topological orders (TO) in one higher dimension…
The 2+1D topological order can be characterized by the mapping-class-group representations for Riemann surfaces of genus-1, genus-2, etc. In this paper, we use those representations to determine the possible gapped boundaries of a 2+1D…
Gauging introduces gauge fields in order to localize an existing global symmetry, resulting in a dual global symmetry on the gauge fields that can be gauged again. By iterating the gauging process on spin chains with Abelian group…
Tensor network states are capable of describing many-body systems with complex quantum entanglement, including systems with non-trivial topological order. In this paper, we study methods to calculate the topological properties of a tensor…
We discuss physical properties of `integer' topological phases of bosons in D=3+1 dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke interactions in a fundamental way but do not…
In this work, we introduce a new type of topological order which is protected by subsystem symmetries which act on lower dimensional subsets of lattice many-body system, e.g. along lines or planes in a three dimensional system. The symmetry…
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…
Tensor networks provide discrete representations of quantum many-body systems, yet their precise connection to continuum field theories remains relatively poorly understood. Invoking a notion of typicality, we develop a continuum…