Publication

Anatomy of higher-order non-Hermitian skin and boundary modes

2025

Abstract

The anomalous bulk-boundary correspondence in non-Hermitian systems featuring an intricate interplay between skin and boundary modes has attracted enormous theoretical and experimental attention. Still, in dimensions higher than one, this interplay remains much less understood. Here we provide insights from exact analytical solutions of a large class of models in any dimension d, with open boundaries in dc≤d directions, and by tracking their topological origin. Specifically, we show that amoeba theory accounting for the separation gaps of the bulk modes augmented with higher-dimensional generalizations of the biorthogonal polarization and the generalized Brillouin zone approaches accounting for the surface gaps of boundary modes provide a comprehensive understanding of these systems.

Official source

https://infoscience.epfl.ch/entities/publication/df019e01-a8ea-4284-a59d-7ab80df1c268

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2025

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/df019e01-a8ea-4284-a59d-7ab80df1c268

About this result

Related concepts (32)

Topological vector space

In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis. A topological vector space is a vector space that is also a topological space with the property that the vector space operations (vector addition and scalar multiplication) are also continuous functions. Such a topology is called a and every topological vector space has a uniform topological structure, allowing a notion of uniform convergence and completeness.

Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it - for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it - for example, both a latitude and longitude are required to locate a point on the surface of a sphere.

Topological order

In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states. Microscopically, topological orders correspond to patterns of long-range quantum entanglement. States with different topological orders (or different patterns of long range entanglements) cannot change into each other without a phase transition.

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