Related papers: Topological quantum order: stability under local p…
Thermal stability of the Topological Color Code in presence of a thermal bath is studied. We study the Lindblad evolution of the observables in the weak coupling limit of the Born-Markov approximation. The auto-correlation functions of the…
In this note, we consider the dynamics associated to an epsilon-perturbation of an integrable Hamiltonian system in action-angle coordinates in any number of degrees of freedom and we prove the following result of "micro-diffusion": under…
A `coherent system' $(\Cal E,V)$, consists of a holomorphic bundle plus a linear subspace of its space of holomorphic sections. Based on the usual notion in Geometric Invariant Theory, a notion of slope stability has been defined for such…
The tensor product representation of quantum states leads to a promising variational approach to study quantum phase and quantum phase transitions, especially topological ordered phases which are impossible to handle with conventional…
Attractive interaction between spinless fermions in a two-dimensional lattice drives the formation of a topological superfluid. But the topological phase is dynamically unstable towards phase separation when the system has a high density of…
We study the entanglement spectrum of a translationally-invariant lattice system under a random partition, implemented by choosing each site to be in one subsystem with probability $p\in[0, 1]$. We apply this random partitioning to a…
Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for the quarter-plane Toeplitz extension, two…
We study a class of diffusion processes arising from random perturbations of conservative Hamiltonian systems. Under a set of abstract hypotheses -- including basic structural assumptions on the Hamiltonian, a weak Lyapunov structure, and a…
Topological lattice defects, such as dislocations and grain boundaries (GBs), are ubiquitously present in the bulk of quantum materials and externally tunable in metamaterials. In terms of robust modes, localized near the defect cores, they…
The five-band Hubbard model for a $d$ band with one electron per site is a model which has very interesting properties when the relevant ions are located at sites with high (e. g. cubic) symmetry. In that case, if the crystal field…
The Hamiltonian of a system of three quantum mechanical particles moving on the three-dimensional lattice $\Z^3$ and interacting via zero-range attractive potentials is considered. For the two-particle energy operator $h(k),$ with $k\in…
The existence of thresholdless vortex solitons trapped at the core of disclination lattices that realize higher-order topological insulators is reported. The study demonstrates the interplay between nonlinearity and higher-order topology in…
A gapped ground state of a quantum spin system has a natural length scale set by the gap. This length scale governs the decay of correlations. A common intuition is that this length scale also controls the spatial relaxation towards the…
We study the spontaneous symmetry breaking of O(3) scalar field on a fuzzy sphere $S_F^2$. We find that the fluctuations in the background of topological configurations are finite. This is in contrast to the fluctuations around a uniform…
We propose a framework for the connection between local symmetries of discrete Hamiltonians and the design of compact localized states. Such compact localized states are used for the creation of tunable, local symmetry-induced bound states…
The supermembrane theory on $R^{10}x S^1$ is investigated, for membranes that wrap once around the compact dimension. The Hamiltonian can be organized as describing $N_s$ interacting strings, the exact supermembrane corresponding to $N_s\to…
Stability criteria have been derived and investigated in the last decades for many kinds of periodic traveling wave solutions to Hamiltonian PDEs. They turned out to depend in a crucial way on the negative signature of the Hessian matrix of…
In a full solution for a scalar quantum field coupled to an accelerating isotropic universe, all constituent non-autonomous modes of elementary excitation cease to oscillate and become unstable at a discrete sequence of times. After…
We investigate a family of quasiperiodic continuous elastic beams, the topological properties of their vibrational spectra, and their relation to the existence of localized modes. We specifically consider beams featuring arrays of ground…
In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined…