scholarly journals Entanglement topological invariants for one-dimensional topological superconductors

2020 ◽  
Vol 101 (8) ◽  
Author(s):  
P. Fromholz ◽  
G. Magnifico ◽  
V. Vitale ◽  
T. Mendes-Santos ◽  
M. Dalmonte
Keyword(s):  
Topological Invariants ◽  
One Dimensional ◽  
Topological Superconductors

scholarly journals Assessing Bound States in a One-Dimensional Topological Superconductor: Majorana versus Tamm

2021 ◽  
Author(s):  
Niccolò Traverso Ziani ◽  
Lucia Vigliotti ◽  
Matteo Carrega ◽  
Fabio Cavaliere
Keyword(s):  
Quantum Computation ◽  
Bound States ◽  
Research Activity ◽  
One Dimensional ◽  
Majorana Bound States ◽  
Topological Superconductors ◽  
Topological Quantum ◽  
Tamm State ◽  
Topological Quantum Computation ◽  
Intense Research

Majorana bound states in topological superconductors have attracted intense research activity in view of applications in topological quantum computation. However, they are not the only example of topological bound states that can occur in such systems. We here study a model in which both Majorana and Tamm bound states compete. We show both numerically and analytically that, surprisingly, the Tamm state remains partially localized even when the spectrum becomes gapless. Despite this fact, we demonstrate that the Majorana polarization shows a clear transition between the two regimes.

scholarly journals Topological invariants and interacting one-dimensional fermionic systems

2012 ◽  
Vol 86 (20) ◽  
Author(s):  
Salvatore R. Manmana ◽  
Andrew M. Essin ◽  
Reinhard M. Noack ◽  
Victor Gurarie
Keyword(s):  
Topological Invariants ◽  
One Dimensional ◽  
Fermionic Systems

The application of numerical topological invariants in simulations of knotted rings: A comprehensive Monte Carlo approach

2020 ◽  
pp. 2150005
Author(s):  
Franco Ferrari ◽  
Yani Zhao
Keyword(s):  
Monte Carlo ◽  
Discrete Version ◽  
Topological Invariants ◽  
One Dimensional ◽  
Knot Invariants ◽  
Knot Invariant ◽  
Sampling Process ◽  
Energy Domain ◽  
Sharp Corners ◽  
Monte Carlo Framework

In this work, a general Monte Carlo framework is proposed for applying numerical knot invariants in simulations of systems containing knotted one-dimensional ring-shaped objects like polymers and vortex lines in fluids, superfluids or other quantum liquids. A general prescription for smoothing the sharp corners appearing in discrete knots consisting of segments joined together is provided. Smoothing is very important for the correct evaluation of numerical knot invariants. A discrete version of framing is adopted in order to eliminate singularities that are possibly arising when computing the invariants. The presented algorithms for smoothing, eliminating potentially dangerous singularities and speeding up the calculations are quite general and can be applied to any discrete knot defined off- or on-lattice. This is one of the first attempts to use numerical knot invariants in order to avoid potential topology breakings during the sampling process taking place in computer simulations, in which millions of knot conformations are randomly generated. As an application, the energy domain of knotted polymer rings subjected to short-range interactions is studied using the so-called Vassiliev knot invariant of degree 2.

scholarly journals Bath-induced decoherence in finite-size Majorana wires at non-zero temperature

2021 ◽  
Author(s):  
Niels Breckwoldt ◽  
Thore Posske ◽  
Michael Thorwart
Keyword(s):  
Time Scale ◽  
Finite Size ◽  
Information Storage ◽  
One Dimensional ◽  
Topological Superconductors ◽  
Topological Quantum ◽  
Intermediate Time ◽  
Topological Errors ◽  
The One ◽  
Intermediate Time Scale

Abstract Braiding Majorana zero-modes around each other is a promising route towards topological quantum computing. Yet, two competing maxims emerge when implementing Majorana braiding in real systems: On the one hand, perfect braiding should be conducted adiabatically slowly to avoid non-topological errors. On the other hand, braiding must be conducted fast such that decoherence effects introduced by the environment are negligible, which are generally unavoidable in finite-size systems. This competition results in an intermediate time scale for Majorana braiding that is optimal, but generally not error-free. Here, we calculate this intermediate time scale for a T-junction of short one-dimensional topological superconductors coupled to a bosonic bath that generates fluctuations in the local electric potential, which stem from, e.g., environmental photons or phonons of the substrate. We thereby obtain boundaries for the speed of Majorana braiding with a predetermined gate fidelity. Our results emphasize the general susceptibility of Majorana-based information storage in finite-size systems and can serve as a guide for determining the optimal braiding times in future experiments.

scholarly journals Suppression of2πphase slip due to hidden zero modes in one-dimensional topological superconductors

2013 ◽  
Vol 87 (6) ◽  
Author(s):  
David Pekker ◽  
Chang-Yu Hou ◽  
Doron L. Bergman ◽  
Sam Goldberg ◽  
İnanç Adagideli ◽  
...  
Keyword(s):  
One Dimensional ◽  
Zero Modes ◽  
Topological Superconductors
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