Related papers: Locality from the Spectrum
Canonical formalism of the rank-three tensor model has recently been proposed, in which "local" time is consistently incorporated by a set of first class constraints. By brute-force analysis, this paper shows that there exist only two forms…
For an anyon model in two spatial dimensions described by a modular tensor category, the topological S-matrix encodes the mutual braiding statistics, the quantum dimensions, and the fusion rules of anyons. It is nontrivial whether one can…
In the context of ground states of quantum many-body systems, the locality of entanglement between connected regions of space is directly tied to the locality of the corresponding entanglement Hamiltonian: the latter is dominated by local,…
We demonstrate that a complete class of flat-band lattices with underlying commutative local symmetries exhibit a locally fragmented Hilbert space. The equitable partition theorem ensures distinct parities for the compact localized states…
Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on regression problems, without routinely incorporating…
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…
The capabilities of the functional-analytic and of the functional-integral approach for the construction of the Hamiltonian as a self-adjoint operator on Hilbert space are compared in the context of non-relativistic quantum mechanics.…
A novel routine to investigate the scalar fields in a cosmological context is discussed in the framework of the Hamiltonian formalism. Starting from the Einstein-Hilbert action coupled to a Lagrangian density that contains two components -…
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant…
We shall show that the abstract and formal rules which govern the quantum kinematic and dynamics can be derived from a law of change of the information content or the degree of uncertainty that the system has a certain configuration in a…
We investigate further the relationship between the entanglement spectrum of a composite many-body system and the energy spectrum of a subsystem making use of concepts of canonical thermodynamics. In many important cases the entanglement…
The aim of this paper is to derive the global Hamiltonian form for a quantum system and bath, or more generally a quantum network with multiple quantum input field connections, based on the local descriptions. We give a new simple argument…
A broad range of quantum optimisation problems can be phrased as the question whether a specific system has a ground state at zero energy, i.e.\ whether its Hamiltonian is frustration free. Frustration-free Hamiltonians, in turn, play a…
The goal of this work is to define a notion of a quantum neural network to classify data, which exploits the low energy spectrum of a local Hamiltonian. As a concrete application, we build a binary classifier, train it on some actual data…
The Hamiltonian of a gravitational system defined in a region with boundary is quantized. The classical Hamiltonian, and starting point for the regularization, is required by functional differentiablity of the Hamiltonian constraint. The…
Free probability provides a framework for describing correlations between non-commuting observables in complex quantum systems whose Hilbert-space states follow maximum-entropy distributions. We examine the robustness of this framework…
We investigate means to describe the non-local properties of quantum systems and to test if two quantum systems are locally equivalent. For this we consider quantum systems that consist of several subsystems, especially multiple qubits. We…
Thermodynamics relies on the possibility to describe systems composed of a large number of constituents in terms of few macroscopic variables. Its foundations are rooted into the paradigm of statistical mechanics, where thermal properties…
We consider the created entities (events) in the first moments of universe creation. It is assumed that there exists a causal energetic relationship between all events (nodes) such that all nodes are placed on a world line and each node…
We show that the Hamiltonian dynamics of the self-interacting, abelian p-form theory in D=2p+2 dimensional space-time gives rise to the quasi-local structure. Roughly speaking, it means that the field energy is localized but on closed…