Related papers: Grobner Bases for Finite-temperature Quantum Compu…
We extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions. Let P -> Sigma be a principal G-bundle over space and let F be a vector bundle associated to P whose…
We give a criterion for a collection of polynomials to be a universal Gr\"{o}bner basis for an ideal in terms of the multidegree of the closure of the corresponding affine variety in $(\mathbb{P}^1)^N$. This criterion can be used to give…
We perform the fidelity analysis for Boltzmann-Gibbs-like states in order to investigate whether the topological order of 1D fermionic systems at zero temperature is maintained at finite temperatures. We use quantum walk protocols that are…
Grothendieck constructed a Cousin complex for abelian sheaves on an arbitrary topological space. In a special setting, its dual called the BGG resolution is applicable in representation theory. Arkhipov proposed a complex whose dual is only…
We introduce the theory of monoidal Groebner bases, a concept which generalizes the familiar notion in a polynomial ring and allows for a description of Groebner bases of ideals that are stable under the action of a monoid. The main…
We provide necessary and sufficient conditions for simplicial complexes whose determinantal facet ideals admit reduced Grobner bases under diagonal term orders. Building on and extending foundational results for binomial edge ideals and…
Finitely generated modules over the polynomial ring in $n$ indeterminates are isomorphic to quotients of finite rank free modules. We introduce a theory of relative Gr\"obner bases for those quotients of free modules and, equivalently, for…
The Feynman-Vernon path integral formalism is used to derive the density matrix of a quantum oscillator that is linearly coupled to an environmental reservoir. Although low-temperature reservoirs thermalize the oscillator to the usual…
Preliminaries for Many-Particle approach to quantization of Einstein-Hilbert theory of gravitation are presented in this paper. Einstein-Friedmann Spacetime is detailed discussed from this point of view. Von Neumann-Araki-Woods second…
In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…
Fock space quantization of Hamiltonian constraints of General Relativity and thermodynamics of quantum states for flat Friedmann-Lemaitre-Robertson-Walker metrics is presented.
The quantum gravity path integral's measure can be written as the product of classical backgrounds and quantum fluctuations about each background. After proving that fluctuations about the background do not diffuse in Hilbert space and obey…
The complexity of computing the solutions of a system of multivariate polynomial equations by means of Groebner bases computations is upper bounded by a function of the solving degree. In this paper, we discuss how to rigorously estimate…
We construct the quantum double ramification hierarchy associated with the Gromov-Witten theory of elliptic curves. We use results of Oberdieck and Pixton on the intersection numbers of the double ramification cycle, the Gromov-Witten…
Two models were recently proposed to explore the robust hardness of Gr\"obner basis computation. Given a polynomial system, both models allow an algorithm to selectively ignore some of the polynomials: the algorithm is only responsible for…
We study the time-dependent Bogoliubov--de-Gennes equations for generic translation-invariant fermionic many-body systems. For initial states that are close to thermal equilibrium states at temperatures near the critical temperature, we…
Algorithmic computation in polynomial rings is a classical topic in mathematics. However, little attention has been given to the case of rings with an infinite number of variables until recently when theoretical efforts have made possible…
We provide both a general framework for discretizing de Rham sequences of differential forms of high regularity, and some examples of finite element spaces that fit in the framework. The general framework is an extension of the previously…
We consider relativistic U(1) gauge theories in 2+1 dimensions, with N_b species of complex bosons and N_f species of Dirac fermions at finite temperature. The quantum phase transition between the Higgs and Coulomb phases is described by a…
Long-range quantum systems, in which the interactions decay as $1/r^{\alpha}$, are of increasing interest due to the variety of experimental set-ups in which they naturally appear. Motivated by this, we study fundamental properties of…