相关论文: Complexity for link complement States in Chern Sim…
We study 2+1 dimensional phases with topological order, such as fractional quantum Hall states and gapped spin liquids, in the presence of global symmetries. Phases that share the same topological order can then differ depending on the…
The existence of quantum non-liquid states and fracton orders, both gapped and gapless states, challenges our understanding of phases of entangled matter. We generalize the cellular topological states to liquid or non-liquid cellular…
The perturbative expression of Chern-Simons theory for links in Euclidean 3-space is a linear combination of integrals on configuration spaces. This has successively been studied by Guadagnini, Martellini and Mintchev, Bar-Natan,…
One approach to analyzing entanglement in a gauge theory is embedding it into a factorized theory with edge modes on the entangling boundary. For topological quantum field theories (TQFT), this naturally leads to factorizing a TQFT by…
In this paper we are begining to explore the complex counterpart of the Chern-Simon-Witten theory. We define the complex analogue of the Gauss linking number for complex curves embedded in a Calabi-Yau threefold using the formal path…
A method to obtain explicit and complete topological solution of SU(2) Chern-Simons theory on $S^3$ is developed. To this effect the necessary aspects of the theory of coloured-oriented braids and duality properties of conformal blocks for…
The notion of {\em entanglement entropy} in quantum mechanical systems is an important quantity, which measures how much a physical state is entangled in a composite system. Mathematically, it measures how much the state vector is not…
We study several different $Z_2$ topological ordered states in frustrated spin systems. The effective theories for those different Z_2 topological orders all have the same form -- a Z_2 gauge theory which can also be written as a mutual…
We develop several methods that allow us to compute all-loop partition functions in perturbative Chern-Simons theory with complex gauge group G_C, sometimes in multiple ways. In the background of a non-abelian irreducible flat connection,…
We reconsider Chern-Simons gauge theory on a Seifert manifold M, which is the total space of a nontrivial circle bundle over a Riemann surface, possibly with orbifold points. As shown in previous work with Witten, the path integral…
We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4k+3 endowed with a Wu structure of degree 2k+2. After analysing the anomalies of a certain discrete symmetry, we…
We regularize compact and non-compact Abelian Chern-Simons-Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled theory with gauge fields living on a lattice and its dual lattice. The Hilbert space…
We examine the black hole solutions of dS$_3$ gravity by applying the explicit dS$_3$/CFT$_2$ correspondence. The gravity theory is described by Chern-Simons theory with complex gauge group SL$(2,\mathbb{C})$, and the complexified theory is…
We consider the link invariants defined by the quantum Chern-Simons field theory with compact gauge group U(1) in a closed oriented 3-manifold M. The relation of the abelian link invariants with the homology group of the complement of the…
Nielsen's approach to quantum state complexity relates the minimal number of quantum gates required to prepare a state to the length of geodesics computed with a certain norm on the manifold of unitary transformations. For a bipartite…
Following the method of Seifert surfaces in knot theory, we define arithmetic linking numbers and height pairings of ideals using arithmetic duality theorems, and compute them in terms of n-th power residue symbols. This formalism leads to…
Let $M$ be a compact 3--manifold with boundary a single torus. We present upper and lower complexity bounds for closed 3--manifolds obtained as even Dehn fillings of $M.$ As an application, we characterise some infinite families of even…
We investigate the topological character of lattice chiral Gaussian fermionic states in two dimensions possessing the simplest descriptions in terms of projected entangled-pair states (PEPS). They are ground states of two different kinds of…
We consider the $U(1)$ Chern-Simons gauge theory defined in a general closed oriented 3-manifold $M$; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The…
In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of the 6d $(2,0)$ theory of type $A_{N-1}$ on a 3-manifold $M$. The so-called 3d-3d correspondence is a relation between complexified Chern-Simons…