Related papers: Tensor networks as path integral geometry
In this paper we study maps (curved flats) into symmetric spaces which are tangent at each point to a flat of the symmetric space. Important examples of such maps arise from isometric immersions of space forms into space forms via their…
Network tomography means to estimate internal link states from end-to-end path measurements. In conventional network tomography, to make packets transmissively penetrate a network, a cooperation between transmitter and receiver nodes is…
Complex network theory (CNT) is gaining a lot of attention in the scientific community, due to its capability to model and interpret an impressive number of natural and anthropic phenomena. One of the most active CNT field concerns the…
In the context of the coarse-graining of loop quantum gravity, we introduce loopy and tagged spin networks, which generalize the standard spin network states to account explicitly for non-trivial curvature and torsion. Both structures relax…
We give a leisurely, albeit woefully incomplete, overview of quantum field theory, its relevance to condensed matter systems, and spin systems, which proceeds via a series of illustrative examples. The goal is to provide readers from the…
A class of theories of gravitation that naturally incorporates preferred frames of reference is presented. The underlying space-time geometry consists of a partial parallelization of space-time and has properties of Riemann-Cartan as well…
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…
We present a tensor-network-based method for simulating a weakly-measured quantum circuit. In particular, we use a Markov chain to efficiently sample measurements and contract the tensor network, propagating their effect forward along the…
The efficient simulation of complex quantum systems remains a central challenge due to the exponential growth of Hilbert space with system size. Tensor network methods have long been established as powerful approximation schemes, and their…
Tree tensor network descriptions of critical quantum spin chains are empirically known to reproduce correlation functions matching CFT predictions in the continuum limit. It is natural to seek a more complete correspondence, additionally…
We present a new scheme which numerically evaluates the real-time path integral for $\phi^4$ real scalar field theory in a lattice version of the closed-time formalism. First step of the scheme is to rewrite the path integral in an…
Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
Loop Quantum Gravity defines the quantum states of space geometry as spin networks and describes their evolution in time. We reformulate spin networks in terms of harmonic oscillators and show how the holographic degrees of freedom of the…
We investigate path integral formalism for continuum theory. It is shown that the path integral for the soft modes can be represented in the form of a lattice theory. Kinetic term of this lattice theory has a standard form and potential…
In this paper we attempt to understand Lorentzian tensor networks, as a preparation for constructing tensor networks that can describe more exotic backgrounds such as black holes. To define notions of reference frames and switching of…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
Co-evolving time series appears in a multitude of applications such as environmental monitoring, financial analysis, and smart transportation. This paper aims to address the following challenges, including (C1) how to incorporate explicit…
We demonstrate that perturbative expansions for quantum many-body systems can be rephrased in terms of tensor networks, thereby providing a natural framework for interpolating perturbative expansions across a quantum phase transition. This…
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…