Search results for "topological [model]"

Symmetry-protected intermediate trivial phases in quantum spin chains

2015

Symmetry-protected trivial (SPt) phases of matter are the product-state analogue of symmetry-protected topological (SPT) phases. This means, SPt phases can be adiabatically connected to a product state by some path that preserves the protecting symmetry. Moreover, SPt and SPT phases can be adiabatically connected to each other when interaction terms that break the symmetries protecting the SPT order are added in the Hamiltonian. It is also known that spin-1 SPT phases in quantum spin chains can emerge as effective intermediate phases of spin-2 Hamiltonians. In this paper we show that a similar scenario is also valid for SPt phases. More precisely, we show that for a given spin-2 quantum cha…

Spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the star lattice: Competing valence-bond-solid phases studied by means of tensor networks

2018

Using the infinite Projected Entangled Pair States (iPEPS) algorithm, we study the ground-state properties of the spin-$1/2$ quantum Heisenberg antiferromagnet on the star lattice in the thermodynamic limit. By analyzing the ground-state energy of the two inequivalent bonds of the lattice in different unit-cell structures, we identify two competing Valence-Bond-Solid (VBS) phases for different antiferromagnetic Heisenberg exchange couplings. More precisely, we observe (i) a VBS state which respects the full symmetries of the Hamiltonian, and (ii) a resonating VBS state which, in contrast to previous predictions, has a six-site unit-cell order and breaks $C_3$ symmetry. We also studied the g…

2014

Here we investigate the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of topologically-ordered systems such as the toric code, double semion, color code, and quantum double models. As happens for the entanglement entropy, we find that for sufficiently large block sizes the geometric entanglement is, up to possible sub-leading corrections, the sum of two contributions: a bulk contribution obeying a boundary law times the number of blocks, and a contribution quantifying the underlying pattern of long-range entanglement of the topologically-…

MR3730338 Reviewed de Jeu, Marcel(NL-LEID-MI); Tomiyama, Jun(J-TOKYM) The closure of ideals of ℓ1(Σ) in its enveloping C∗-algebra. (English summary) …

2018

Given a compact Hausdorff space X and a homeomorphism σ on X, denote by Σ=(X,σ) a topological dynamical system. Then the associated Banach ∗-algebra ℓ1(Σ) is defined as ℓ1(Σ)={a:Z→C(X), ∥a∥:=∑n∈Z∥a(n)∥<∞} with a crossed product–type product (aa′)(n)=∑k∈Za(k)⋅αk(a′(n−k)) and involution a∗(n)=αn(a(−n))¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯, where C(X) denote the space of complex-valued continuous functions on X, and α(f):=f∘σ−1 for f∈C(X). If C∗(Σ) is the enveloping C∗-algebra of ℓ1(Σ), considering a primitive ideal I of ℓ1(Σ), the authors show that there exists a ∗-representation π of ℓ1(Σ) on Hilbert space such that the kernel is I, and that the closure in C∗(Σ) of an ideal of ℓ1(Σ) is an ideal of C∗(Σ).

Attention-Based Landmark Selection in Autonomous Robotics

2007

This paper describes a robotic architecture that uses visual attention mechanisms for autonomous navigation in unknown indoor environments. A foveation mechanism based on a bottom-up attention system allows the robot to autonomously select landmarks, defined as salient points in the camera images. Landmarks are memorized in a behavioral fashion by coupling sensing and acting to achieve a representation that is view and scale independent. Selected landmarks are stored in a topological map. During the navigation a top-down mechanism controls the attention system to achieve robot localization. Experiments and results show that our system is robust to noise and odometric errors, being at the sa…

Attention-based environment perception in autonomous robotics

2007

This paper describes a robotic architecture that uses visual attention mechanisms for autonomous navigation in unknown indoor environments. A foveation mechanism based on classical bottom-up gaze shifts allows the robot to autonomously select landmarks, defined as salient points in the camera images. Landmarks are memorized in a behavioral fashion, coupling sensing and acting to achieve a representation view and scale independent. Selected landmarks are stored in a topological map; during the navigation a top-down mechanism controls the attention system to achieve robot localization. Experiments and results show that our system is robust to noise and odometric errors, being at the same time…

A topological phase transition between small-worlds and fractal scaling in urban railway transportation networks?

2009

Abstract Fractal and small-worlds scaling laws are applied to study the growth of urban railway transportation networks using total length and total population as observational parameters. In spite of the variety of populations and urban structures, the variation of the total length of the railway network with the total population of conurbations follows similar patterns for large and middle metropolis. Diachronous analysis of data for urban transportation networks suggests that there is second-order phase transition from small-worlds behaviour to fractal scaling during their early stages of development.

Lyapunov exponent and topological entropy plateaus in piecewise linear maps

2013

We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory.

A new measure for the attitude to mobility of Italian students and graduates: a topological data analysis approach

2022

AbstractStudents’ and graduates’ mobility is an interesting topic of discussion especially for the Italian education system and universities. The main reasons for migration and for the so called brain drain, can be found in the socio-economic context and in the famous North–South divide. Measuring mobility and understanding its dynamic over time and space are not trivial tasks. Most of the studies in the related literature focus on the determinants of such phenomenon, in this paper, instead, combining tools coming from graph theory and Topological Data Analysis we propose a new measure for the attitude to mobility. Each mobility trajectory is represented by a graph and the importance of the…

Topological Minimally Entangled States via Geometric Measure

2014

Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and toric code models on a torus with non-trivial topological partitions. Our calculations are done either quasi-exactly for small system sizes, or using the tensor network approach in [R. Orus, T.-C. Wei, O. Buerschaper, A. Garcia-Saez, arXiv:1406.0585] for large sizes. As a byproduct of our methods, we see that the minimisation of the geometric entanglement can also determine the number of Abelian quasiparticle excitations in a given model. The results in …