Related papers: Hilbert Space Fragmentation from Generalized Symme…
\emph{Scalable spaces} are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their algebra of (flat) differential forms. This is a rational homotopy invariant property and all scalable spaces are…
We investigate the thermalization dynamics of 1D systems with local constraints coupled to an infinite temperature bath at one boundary. The coupling to the bath eventually erases the effects of the constraints, causing the system to tend…
We study the breaking of ergodicity measured in terms of return probability in the evolution of a quantum state of a spin chain. In the non ergodic phase a quantum state evolves in a much smaller fraction of the Hilbert space than would be…
Krylov complexity has emerged as a new probe of operator growth in a wide range of non-equilibrium quantum dynamics. However, a fundamental issue remains in such studies: the definition of the distance between basis states in Krylov space…
We study the symmetry breaking phenomenon for an elliptic equation involving the fractional Laplacian in a large ball. Our main tool is an extension of the Strauss radial lemma involving the fractional Laplacian, which might be of…
Successive divisions of compact metric spaces appear in many different areas of mathematics such as the construction of self-similar sets, Markov partitions associated with hyperbolic dynamical systems, dyadic cubes associated with a…
In the paper (Goloveshkin and Myagkov 2014) we proposed a two-dimensional energy-based model of fragmentation of rapidly expanding cylinder under plane strain conditions. The model allowed one to estimate the average fragment length and the…
We study the quantum dynamics of a simple translation invariant, center-of-mass (CoM) preserving model of interacting fermions in one dimension (1D), which arises in multiple experimentally realizable contexts. We show that this model…
We continue investigation of the renormalization group and decoupling of the quantized massive fields in curved space. In the present work we analyze a theory, where fields gain their masses due to the Spontaneous Symmetry Breaking (SSB),…
We identify the chaotic phase of the Bose-Hubbard Hamiltonian by the energy-resolved correlation between spectral features and structural changes of the associated eigenstates as exposed by their generalized fractal dimensions. The…
The Two Higgs Doublet Model invariant under the gauge group SU(2)xU(1) is known to have six additional global discrete or continuous symmetries of its scalar sector. We have discovered regions of parameter space of the model which are basis…
We introduce a notion of coarse embedding at infinity into Hilbert space for metric spaces, which is a weakening of the notion of fibred coarse embedding and a far generalization of Gromov's concept of coarse embedding. It turns out that a…
We explore the rich landscape of higher-form and non-invertible symmetries that emerge at low energies in generic ordered phases. Using that their charge is carried by homotopy defects (i.e., domain walls, vortices, hedgehogs, etc.), in the…
In this article we study the symmetry breaking phenomenon of solutions of noncooperative elliptic systems. We apply the degree for G-invariant strongly indefinite functionals to obtain simultaneously a symmetry breaking and a global…
We introduce generalized pinning fields in conformal field theory that model a large class of critical impurities at large distance, enriching the familiar universality classes. We provide a rigorous definition of such defects as certain…
The spreading of quantum states in Krylov space under unitary dynamics provides a natural framework for characterizing quantum complexity. Quantifiers of this spreading, such as the spread complexity and the inverse participation ratio,…
Field theories place one or more degrees of freedom at every point in space. Hilbert spaces describing quantum field theories, or their finite-dimensional discretizations on lattices, therefore have large amounts of structure: they are…
There has been recent interest in identifying entanglement as the fundamental concept from which space may emerge. We note that the particular way that a Hilbert space is decomposed into tensor factors is important in what the resulting…
We review the gauge symmetry breaking mechanism due to orbifold projections in orbifold model building. We explicitly show the existence of a scale of breaking if such a symmetry breaking is due to freely-acting orbifold operators only,…
We show, using covariant Lyapunov vectors, that the chaotic solutions of spatially extended dissipative systems evolve within a manifold spanned by a finite number of physical modes hyperbolically isolated from a set of residual degrees of…