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Dimensional analysis is a powerful tool that is used in physics and engineering to understand and predict the behavior of physical systems. The basic idea behind dimensional analysis is to express physical quantities in terms of fundamental dimensions such as the mass, length, and time. Derived dimensions like the velocity, acceleration, and force are derived from the combinations of these fundamental dimensions.
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Dimensional Transmutation from Non-Hermiticity.

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Non-Hermitian couplings can reduce the effective dimensionality of lattices, altering topological states. This dimensional transmutation is characterized by a winding number and has implications for classifying topological phases.

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Area of Science:

  • Condensed Matter Physics
  • Topological Matter
  • Quantum Mechanics

Background:

  • Dimensionality is crucial for classifying novel material phases and their responses.
  • Non-Hermitian couplings in generic lattices typically distort the Brillouin zone (BZ).

Purpose of the Study:

  • To investigate how non-Hermitian couplings affect the effective dimensionality of lattices.
  • To explore the implications of altered dimensionality on topological states and their classification.

Main Methods:

  • Analysis of non-Hermitian pumping in multidimensional lattices.
  • Characterization of emergent winding numbers related to spectral path homotopy.
  • Illustration using a 2D model with topological zero modes.

Main Results:

  • Non-Hermitian couplings can alter the effective dimensionality of a lattice, not just distort the BZ.
  • Basis states exhibit 'entangled' profiles in a lower-dimensional effective BZ, unlike conventional skin states.
  • Topological zero modes can be protected by lower-dimensional topological invariants.

Conclusions:

  • Dimensional transmutation due to non-Hermitian couplings fundamentally changes topological state classification.
  • Geometric obstruction plays a key role in the dimensional classification of topological states.
  • Findings are demonstrable in platforms like circuit arrays and necessitate rethinking topological phase characterization.