scholarly journals Thermal Simulations, Open Boundary Conditions and Switches

2018 ◽  
Vol 175 ◽  
pp. 07004 ◽  
Author(s):  
Yannis Burnier ◽  
Adrien Florio ◽  
Olaf Kaczmarek ◽  
Lukas Mazur

SU(N) gauge theories on compact spaces have a non-trivial vacuum structure characterized by a countable set of topological sectors and their topological charge. In lattice simulations, every topological sector needs to be explored a number of times which reflects its weight in the path integral. Current lattice simulations are impeded by the so-called freezing of the topological charge problem. As the continuum is approached, energy barriers between topological sectors become well defined and the simulations get trapped in a given sector. A possible way out was introduced by Lüscher and Schaefer using open boundary condition in the time extent. However, this solution cannot be used for thermal simulations, where the time direction is required to be periodic. In this proceedings, we present results obtained using open boundary conditions in space, at non-zero temperature. With these conditions, the topological charge is not quantized and the topological barriers are lifted. A downside of this method are the strong finite-size effects introduced by the boundary conditions. We also present some exploratory results which show how these conditions could be used on an algorithmic level to reshuffle the system and generate periodic configurations with non-zero topological charge.

1994 ◽  
Vol 09 (24) ◽  
pp. 2207-2216 ◽  
Author(s):  
H.J. de VEGA ◽  
A. GONZÁLEZ-RUIZ

The nested Bethe ansatz is generalized to open and independent boundary conditions depending on two continuous and two discrete free parameters. This is used to find the exact eigenvectors and eigenvalues of the An−1 vertex models and SU (n) spin chains with such boundary conditions. The solution is found for all diagonal families of solutions to the reflection equations in all possible combinations. The Bethe ansatz equations are used to find the first order finite size correction.


2017 ◽  
Vol 3 (1) ◽  
Author(s):  
Vardan Kaladzhyan ◽  
Cristina Bena

We investigate the formation of Majorana fermions in finite-size graphene strips with open boundary conditions in both directions, in the presence of an in-plane magnetic field and in the proximity of a superconducting substrate. We show that for long enough strips the Majorana states can form in the presence of a Rashba-like spin-orbit coupling, as well as in the presence of an inhomogeneous magnetic field. We find that, unlike infinite graphene ribbons in which Majorana states arise solely close to the bottom of the band and the Van Hove singularities, for finite-size systems this can happen also at much smaller doping values, close to the Dirac points, and depends strongly on the type of the short edges of the systems (e.g. armchair vs. zigzag), as well as on the width of the ribbons.


2017 ◽  
Author(s):  
Wolfgang Soeldner ◽  
Gunnar S. Bali ◽  
Sara Collins ◽  
Fabian Hutzler ◽  
Meinulf Gockeler ◽  
...  

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Linhu Li ◽  
Ching Hua Lee ◽  
Jiangbin Gong

AbstractNon-Hermitian systems have been shown to have a dramatic sensitivity to their boundary conditions. In particular, the non-Hermitian skin effect induces collective boundary localization upon turning off boundary coupling, a feature very distinct from that under periodic boundary conditions. Here we develop a full framework for non-Hermitian impurity physics in a non-reciprocal lattice, with periodic/open boundary conditions and even their interpolations being special cases across a whole range of boundary impurity strengths. We uncover steady states with scale-free localization along or even against the direction of non-reciprocity in various impurity strength regimes. Also present are Bloch-like states that survive albeit broken translational invariance. We further explore the co-existence of non-Hermitian skin effect and scale-free localization, where even qualitative aspects of the system’s spectrum can be extremely sensitive to impurity strength. Specific circuit setups are also proposed for experimentally detecting the scale-free accumulation, with simulation results confirming our main findings.


Sign in / Sign up

Export Citation Format

Share Document