Dimensional transmutation from non-Hermiticity

Abstract

Dimensionality plays a fundamental role in the classification of novel phases and their responses. In generic lattices of 2D and beyond, however, we found that non-Hermitian couplings do not merely distort the Brillouin zone (BZ), but can in fact alter its effective dimensionality. This is due to the fundamental non-commutativity of multi-dimensional non-Hermitian pumping, which obstructs the usual formation of a generalized complex BZ. As such, basis states are forced to assume "entangled" profiles that are orthogonal in a lower dimensional effective BZ, completely divorced from any vestige of lattice Bloch states unlike conventional skin states. Characterizing this reduced dimensionality is an emergent winding number intimately related to the homotopy of non-contractible spectral paths. We illustrate this dimensional transmutation through a 2D model whose topological zero modes are protected by a 1D, not 2D, topological invariant. Our findings can be readily demonstrated via the bulk properties of non-reciprocally coupled platforms such as circuit arrays, and provokes us to rethink about the fundamental role of geometric obstruction in the dimensional classification of topological states.

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Cited by in corpus (32)

• Experimental Realization of Geometry-Dependent Skin Effect in a Reciprocal Two-Dimensional Lattice
• Geometric Origin of Non-Bloch PT Symmetry Breaking
• Topological origin of non-Hermitian skin effect in higher dimensions and uniform spectra
• Experimental observation of exceptional bound states in a classical circuit network
• Activating non-Hermitian skin modes by parity-time symmetry breaking
• Percolation-induced PT symmetry breaking
• Edge theory of non-Hermitian skin modes in higher dimensions
• Kinked linear response from non-Hermitian cold-atom pumping
• Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice
• Exact Solutions Disentangle Higher-Order Topology in 2D Non-Hermitian Lattices
• Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions
• Dynamical suppression of many-body non-Hermitian skin effect in Anyonic systems
• Engineering topological states and quantum-inspired information processing using classical circuits
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Protected chaos in a topological lattice
• Numerical instability of non-Hermitian Hamiltonian evolutions
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Universal spectral moment theorem and its applications in non-Hermitian systems
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Nonlinear Hall effects with an exceptional ring
• Delocalization of skin steady states
• Non-reciprocity is necessary for robust dimensional reduction and strong responses in stochastic topological systems
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Restoration of non-Hermitian bulk-boundary correspondence by counterbalancing skin effect
• Real-time edge dynamics of non-Hermitian lattices
• Non-Hermitian ultra-strong bosonic clustering through interaction-induced caging
• Topologically protected negative entanglement
• Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes
• Unified Multipole Bott Indices for Non-Hermitian Skin Effect in Different Orders
• Interacting many-body non-Hermitian systems as Markov chains
• Reversing non-Hermitian skin accumulation with a non-local transverse switch
• Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems