Related papers: Geometry and Complexity of Path Integrals in Inhom…
We derive a steady-state, electromagnetic solution for collisional plasma and apply it to computing the total conductance for a vertically stratified ionosphere interrogated by a 3D signal with finite transverse wavelength, which we compare…
The embedding problem is to decide, given an ordered pair of structures, whether or not there is an injective homomorphism from the first structure to the second. We study this problem using an established perspective in parameterized…
We use the framework of $\textit{fixed-point BCFT tensor networks}$ to present a microscopic CFT derivation of the correspondence between reflected entropy (RE) and entanglement wedge cross section (EW) in AdS$_3$/CFT$_2$, for both…
In this paper, we discuss tensor network descriptions of AdS/CFT from two different viewpoints. First, we start with an Euclidean path-integral computation of ground state wave functions with a UV cut off. We consider its efficient…
An approach to approximate evaluation of the continuum Feynman path integrals is developed for the study of quantum fluctuations of particles and fields in Euclidean time-space. The paths are described by sum of Gauss functions and are…
The core of this thesis is the path-integral formulation of quantum field theory and its ability to describe strongly-coupled quantum many-body systems of finite size. Collective behaviors can be efficiently described in such systems…
For two-dimensional conformal field theories driven by evolving background space-time metrics in a closed universe, we present an operator formulation as a driven inhomogeneous CFT. The Hamiltonian of this theory is given by a background…
We study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on $\mathbb{R}^{1,d-1}$. We consider the entanglement entropy across a deformed planar or spherical entangling…
We study a quantum system in a Riemannian manifold M on which a Lie group G acts isometrically. The path integral on M is decomposed into a family of path integrals on a quotient space Q=M/G and the reduced path integrals are completely…
Motivated by the three-dimensional topological field theory / two-dimensional conformal field theory (CFT) correspondence, we study a broad class of one-dimensional quantum mechanical models, known as anyonic chains, that can give rise to…
We provide a derivation of holographic entanglement entropy for spherical entangling surfaces. Our construction relies on conformally mapping the boundary CFT to a hyperbolic geometry and observing that the vacuum state is mapped to a…
We study the problem of finding a minimum-distortion embedding of the shortest path metric of an unweighted graph into a "simpler" metric $X$. Computing such an embedding (exactly or approximately) is a non-trivial task even when $X$ is the…
For two positive integers $k$ and $\ell$, a $(k \times \ell)$-spindle is the union of $k$ pairwise internally vertex-disjoint directed paths with $\ell$ arcs between two vertices $u$ and $v$. We are interested in the (parameterized)…
We use holography in order to study the entropy of thermal CFTs on (1+1)-dimensional curved backgrounds that contain horizons. Starting from the metric of the BTZ black hole, we perform explicit coordinate transformations that set the…
We propose a codimension two holography between a gravitational theory on a $d+1$ dimensional wedge spacetime and a $d-1$ dimensional CFT which lives on the corner of the wedge. Formulating this as a generalization of AdS/CFT, we explain…
In the context of a quantum critical spin chain whose low energy physics corresponds to a conformal field theory (CFT), it was recently demonstrated [A. Milsted G. Vidal, arXiv:1805.12524] that certain classes of tensor networks used for…
We consider the form factor bootstrap approach of integrable field theories to derive matrix elements of composite branch-point twist fields associated with symmetry resolved entanglement entropies. The bootstrap equations are determined in…
Cyclomatic complexity is an incompletely specified but mathematically principled software metric that can be usefully applied to both source and binary code. We consider the application of path homology as a stronger analogue of cyclomatic…
We consider the symmetry resolution of relative entropies in the 1+1 dimensional free massless compact boson conformal field theory (CFT) which presents an internal $U(1)$ symmetry. We calculate various symmetry resolved R\'enyi relative…
Entanglement entropy~(EE) contains signatures of many universal properties of conformal field theories~(CFTs), especially in the presence of boundaries or defects. In particular, {\it topological} defects are interesting since they reflect…