Related papers: Mixed-state TQFTs
By using quantum Teichm\"uller theory, we construct a one parameter family of TQFT's on the categroid of admissible leveled shaped 3-manifolds.
We first revisit the construction of Quinn's finite total homotopy TQFT, which depends on the choice of a homotopy finite space, $\boldsymbol{B}$. This constitutes a vast generalisation of the Dijkgraaf-Witten TQFT, with a trivial cocycle,…
We show that for every spherical category $\C$ with invertible dimension, the Turaev-Viro TQFT admits a splitting into blocks which come from an HQFT, called the Turaev-Viro HQFT. The Turaev-Viro HQFT has the classifying space $B\grad$ as…
We consider a generalization of the axioms of a TQFT, so called half-projective TQFT's, with an anomaly, $x^{\mu}$, in the composition law. $\mu$ is a coboundary on the cobordism categories with non-negative, integer values. The element $x$…
Using the numerical modular bootstrap, we constrain the space of 1+1d CFTs with a finite non-invertible global symmetry described by a fusion category $\mathcal{C}$. We derive universal and rigorous upper bounds on the lightest…
We review the main results of the effective description of the Quantum Hall fluid for the Jain fillings, nu=m/2pm+1, and the non-standard ones nu=m/pm+2 by a conformal field theory (CFT) in two dimensions. It is stressed the unifying…
Consider a d-dimensional quantum field theory (QFT) $\mathfrak{T}$, with a generalized symmetry $\mathcal{S}$, which may or may not be invertible. We study the action of $\mathcal{S}$ on generalized or $q$-charges, i.e. $q$-dimensional…
Short-range entangled topological phases of matter are closely connected to Topological Quantum Field Theory. We use this connection to classify bosonic Symmetry Protected Topological Phases in low dimensions, including the case when the…
In this paper we discuss a model of quantum computer in which a state is an operator of density matrix and gates are general quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum…
Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…
Using truncated conformal field theory (CFT), we present the formalism necessary to obtain exact matrix product state (MPS) representations for any fractional quantum hall model state which can be written as an expectation value of primary…
In the standard construction of Quantum Field Theory, a vacuum state is required. The vacuum is a vector in a separable, infinite-dimensional Hilbert space often referred to as Fock space. By definition the vacuum wavestate depends on…
The object of this paper is to define a subcategory of the category of 3-cobordisms to which invariants of rational homology 3-spheres should generalize. We specify the notion of Topological Quantum Field Theory (in the sense of Atiyah) to…
We give a presentation of the $n$-dimensional oriented cobordism category $\text{Cob}_n$ with generators corresponding to diffeomorphisms and surgeries along framed spheres, and a complete set of relations. Hence, given a functor $F$ from…
Given a not necessarily semisimple modular tensor category C, we use the corresponding 3d TFT defined in [arXiv:1912.02063] to explicitly describe a modular functor as a symmetric monoidal 2-functor from a 2-category of oriented bordisms to…
Teichm\"uller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2,R) Chern-Simons theory. To physicists, it is known in particular in the context…
We investigate the geometrical and combinatorial structures of multipartite quantum systems based on conifold and toric variety. In particular, we study the relations between resolution of conifold, toric variety, a separable state, and a…
We briefly review the advanced mathematical language of fiber bundle structures and how they can be used to classify two-level quantum systems based on the analysis of the topological properties of their sets of state vectors. The…
Modular tensor categories are generalizations of the representation categories of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFTs. Although other constructions have since been found,…
We propose a method for the realization of the two-qubit quantum Fourier transform (QFT) using a Hamiltonian which possesses the circulant symmetry. Importantly, the eigenvectors of the circulant matrices are the Fourier modes and do not…