scholarly journals Extended SSH Model in Non-Hermitian Waveguides with Alternating Real and Imaginary Couplings

2020 ◽  
Vol 10 (10) ◽  
pp. 3425 ◽  
Author(s):  
Ziwei Fu ◽  
Nianzu Fu ◽  
Huaiyuan Zhang ◽  
Zhe Wang ◽  
Dong Zhao ◽  
...  
Keyword(s):  
Chiral Symmetry ◽  
Zero Mode ◽  
Periodic Structures ◽  
Topological Invariant ◽  
Waveguide Array ◽  
Topological Properties ◽  
Absolute Value ◽  
Optical Routers ◽  
Break Chiral Symmetry ◽  
Ssh Model

We studied the topological properties of an extended Su–Schrieffer–Heeger (SSH) model composed of a binary waveguide array with alternating real and imaginary couplings. The topological invariant of the periodic structures remained quantized with chiral symmetry even though the system was non-Hermitian. The numerical results indicated that phase transition arose when the absolute values of the two couplings were equal. The system supported a topological zero mode at the boundary of nontrivial structures when chiral symmetry was preserved. By adding onsite gain and loss to break chiral symmetry, the topological modes dominated in all supermodes with maximum absolute value of imaginary energy. This study enriches research on the SSH model in non-Hermitian systems and may find applications in optical routers and switches.

scholarly journals Particle-antiparticle duality and fractionalization of topological chiral solitons

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Chang-geun Oh ◽  
Sang-Hoon Han ◽  
Seung-Gyo Jeong ◽  
Tae-Hwan Kim ◽  
Sangmo Cheon
Keyword(s):  
Chiral Symmetry ◽  
Time Reversal ◽  
Chiral Symmetry Breaking ◽  
Chain Model ◽  
Fractional Charge ◽  
Topological Solitons ◽  
Practical Applications ◽  
Topological System ◽  
Ssh Model ◽  
Chiral Solitons

AbstractAlthough a prototypical Su–Schrieffer–Heeger (SSH) soliton exhibits various important topological concepts including particle-antiparticle (PA) symmetry and fractional fermion charges, there have been only few advances in exploring such properties of topological solitons beyond the SSH model. Here, by considering a chirally extended double-Peierls-chain model, we demonstrate novel PA duality and fractional charge e/2 of topological chiral solitons even under the chiral symmetry breaking. This provides a counterexample to the belief that chiral symmetry is necessary for such PA relation and fractionalization of topological solitons in a time-reversal invariant topological system. Furthermore, we discover that topological chiral solitons are re-fractionalized into two subsolitons which also satisfy the PA duality. As a result, such dualities and fractionalizations support the topological $$\mathbb {Z}_4$$ Z 4 algebraic structures. Our findings will inspire researches seeking feasible and promising topological systems, which may lead to new practical applications such as solitronics.

scholarly journals Real Tropicalization and Analytification of Semialgebraic Sets

2020 ◽  
Author(s):  
Philipp Jell ◽  
Claus Scheiderer ◽  
Josephine Yu
Keyword(s):  
Inverse Limit ◽  
Point Of View ◽  
General Point ◽  
Real Spectrum ◽  
Closed Field ◽  
Topological Properties ◽  
Absolute Value ◽  
The Real ◽  
Semialgebraic Set ◽  
Refined Version

Abstract Let $K$ be a real closed field with a nontrivial non-archimedean absolute value. We study a refined version of the tropicalization map, which we call real tropicalization map, that takes into account the signs on $K$. We study images of semialgebraic subsets of $K^n$ under this map from a general point of view. For a semialgebraic set $S \subseteq K^n$ we define a space $S_r^{{\operatorname{an}}}$ called the real analytification, which we show to be homeomorphic to the inverse limit of all real tropicalizations of $S$. We prove a real analogue of the tropical fundamental theorem and show that the tropicalization of any semialgebraic set is described by tropicalization of finitely many inequalities, which are valid on the semialgebraic set. We also study the topological properties of real analytification and tropicalization. If $X$ is an algebraic variety, we show that $X_r^{{\operatorname{an}}}$ can be canonically embedded into the real spectrum $X_r$ of $X$, and we study its relation with the Berkovich analytification of $X$.

scholarly journals Scalar effective potential for D7 brane probes which break chiral symmetry

2006 ◽  
Vol 2006 (05) ◽  
pp. 011-011 ◽  
Author(s):  
Riccardo Apreda ◽  
Johanna Erdmenger ◽  
Nick Evans
Keyword(s):  
Chiral Symmetry ◽  
Effective Potential ◽  
Break Chiral Symmetry

θ STATISTICS AND TOPOLOGICAL PROPERTIES IN THE (2+1)-DIMENSIONAL CP1 MODEL

1993 ◽  
Vol 08 (36) ◽  
pp. 3455-3465
Author(s):  
KAI HUANG ◽  
SHIKE HU
Keyword(s):  
Boundary Condition ◽  
Space Time ◽  
Topological Invariant ◽  
Topological Properties ◽  
Topological Term

It is shown that the instanton in the (2+1)-dimensional CP 1 model is the kink of the second kind, and the instantons allowing θ statistics is due to Π1( Map ((R2, S1), S3, S1))n)=Z. When taking a compactified time S1, the space-time manifold is D2×S1, and the coefficient θ of the Hopf term is quantized as θ=k/(2π), where k∈ℤ. Two kinds of topological term are also shown not to be topological invariant under the boundary condition.

On the Topology of Sheet Metal Parts

1998 ◽  
Vol 120 (1) ◽  
pp. 10-16 ◽  
Author(s):  
H. Lipson ◽  
M. Shpitalni
Keyword(s):  
Sheet Metal ◽  
Conceptual Design ◽  
Topological Invariant ◽  
Manufacturing Processes ◽  
Qualitative Model ◽  
Topological Properties ◽  
Metal Parts ◽  
Sheet Metal Parts ◽  
Thin Walled ◽  
Euler Operators

This paper analyzes the topological properties of sheet metal parts represented schematically (zero thickness, zero bend radii). Although such parts are usually non-manifold objects, the paper establishes a general topological invariant f = s + b + e + w − v − gnm + m regarding the number of facets, components, bends, free edges, welds, vertices holes and volumes, respectively. Corresponding Euler operators are derived, providing a basis for a modeling system for sheet metal parts. With this invariant, it is possible to reason about manufacturing processes, such as number of components and arrangement of bend lines and weld lines, using only a single qualitative model of the product. This capability is particularly useful in the preliminary stage of conceptual design. A corresponding topological invariant v − e + f = s + m − gnm is also proposed for general sheet models and thin walled objects.

Distinguishing the Topological Zero Mode and Tamm Mode in a Microwave Waveguide Array

2019 ◽  
Vol 531 (12) ◽  
pp. 1900347 ◽  
Author(s):  
Tao Chen ◽  
Ye Yu ◽  
Yiwen Song ◽  
Dong Yu ◽  
Hongmei Ye ◽  
...  
Keyword(s):  
Zero Mode ◽  
Waveguide Array

scholarly journals Chiral symmetry and fermion doubling in the zero-mode Landau levels of massless Dirac fermions with disorder

2013 ◽  
Author(s):  
Tohru Kawarabayashi ◽  
Takahiro Honda ◽  
Hideo Aoki ◽  
Yasuhiro Hatsugai
Keyword(s):  
Chiral Symmetry ◽  
Zero Mode ◽  
Landau Levels ◽  
Dirac Fermions

scholarly journals Defective edge states and anomalous bulk-boundary correspondence for topological insulators under non-Hermitian similarity transformation

2020 ◽  
Vol 34 (09) ◽  
pp. 2050146
Author(s):  
C. Wang ◽  
X.-R. Wang ◽  
C.-X. Guo ◽  
S.-P. Kou
Keyword(s):  
Chiral Symmetry ◽  
Topological Insulators ◽  
Skin Effect ◽  
Similarity Transformation ◽  
Topological Invariant ◽  
Inversion Symmetry ◽  
Edge States ◽  
Boundary Correspondence ◽  
Zhang Model ◽  
Symmetry Protected

It was known that for non-Hermitian topological systems due to the non-Hermitian skin effect, the bulk-edge correspondence is broken down. In this paper, by using one-dimensional Su–Schrieffer–Heeger model and two-dimensional (deformed) Qi–Wu–Zhang model as examples, the focus is on a special type of non-Hermitian topological system without non-Hermitian skin effect — topological systems under non-Hermitian similarity transformation. In these non-Hermitian systems, the defective edge states and the breakdown of bulk-edge correspondence are discovered. To characterize the topological properties, a new type of inversion symmetry-protected topological invariant — total [Formula: see text] topological invariant — has been introduced. In topological phases, defective edge states appear. With the help of the effective edge Hamiltonian, it was found that the defective edge states are protected by (generalized) chiral symmetry and thus the (singular) defective edge states are unstable against the perturbation breaking the chiral symmetry. In addition, the results are generalized to non-Hermitian topological insulators with inversion symmetry in higher dimensions. This work could help people to understand the defective edge states and the breakdown of bulk-edge correspondence for non-Hermitian topological systems.

How center vortices break chiral symmetry

2016 ◽  
Author(s):  
Manfried Faber ◽  
Roman Höllwieser
Keyword(s):  
Chiral Symmetry ◽  
Break Chiral Symmetry
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