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arXiv:2607.06934

Anyon-induced non-Hermitian topological phases

Yi-An Wang, Kun Ding, Linhu Li

quant-phcond-mat.quant-gasSubmitted Jul 8, 2026• Announced Jul 9, 2026
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Abstract

We show that anyonic exchange statistics can activate non-Hermitian point-gap topology in models that are topologically trivial in its absence. The emergent topology oscillates more rapidly with the statistical phase as the anyon number increases, and exhibits a parity dependence on the particle number. A perturbative analysis reveals the mechanism: fractional statistics induces a mismatch between momentum terms that, combined with sublattice-dependent dissipation, produces particle-number-dependent non-reciprocity and complex spectral winding. As these effects rely on the formation and exchange of interaction-bound anyons, our results establish exchange statistics as a resource for enabling non-Hermitian topology under programmed dissipation.

Comments
21 pages, 7 figures. Comments are welcome

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We show that anyonic exchange statistics can activate non-Hermitian point-gap topology in models that are topologically trivial in its absence. The emergent topology oscillates more rapidly with the statistical phase as the anyon number increases, and exhibits a parity dependence on the particle number. A perturbative analysis reveals the mechanism: fractional statistics induces a mismatch between momentum terms that, combined with sublattice-dependent dissipation, produces particle-number-dependent non-reciprocity and complex spectral winding. As these effects rely on the formation and exchange of interaction-bound anyons, our results establish exchange statistics as a resource for enabling non-Hermitian topology under programmed dissipation.
We show that anyonic statistics fundamentally reshapes non-Hermitian many-body physics by intrinsically breaking pseudo-Hermiticity, leading to a unique real-complex spectral transition with characteristically dense states in ImEEE. This anyon-induced transition occurs even when bosonic and pseudofermionic counterparts remain entirely real, revealing a form of non-Hermitian criticality driven purely by exchange statistics. The resulting spectrum exhibits enhanced gaps in ImEEE that dynamically isolate dominant eigenstates, producing anomalously stable short-time quench dynamics for anyons. Our results identify anyonic statistics as an intrinsic mechanism for generating unconventional non-Hermitian critical behavior usually associated with highly non-local systems.
The standard topological approach to indistinguishable particles formulates exchange statistics by using the fundamental group to analyze the connectedness of the configuration space. Although successful in two and more dimensions, this approach gives only trivial or near-trivial exchange statistics in one dimension because two-body coincidences are excluded from configuration space. Instead, we include these path-ambiguous singular points and consider configuration space as an orbifold. This orbifold topological approach allows unified analysis of exchange statistics in any dimension and predicts possibilities for anyons in one-dimensional systems, including non-Abelian anyons obeying alternate strand groups. These results clarify the nontopological origin of fractional statistics in one-dimensional anyon models.
Anyons obeying fractional exchange statistics arise naturally in two dimensions: Hard-core two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent exchange paths can be associated to non-trivial geometric phases for abelian anyons. Braid-anyon exchange statistics can also be found in one dimension (1D), but this requires broken Galilean invariance to distinguish different ways for two anyons to exchange. However, recently it was shown that an alternative form of exchange statistics can occur in 1D because hard-core three-body constraints also make the configuration space not simply-connected. Instead of the braid group, the topology of exchange paths and their associated non-trivial geometric phases are described by the traid group. In this article we propose a first concrete model realizing this alternative form of anyonic exchange statistics. Starting from a bosonic lattice model that implements the desired geometric phases with number-dependent Peierls phases, we then define anyonic operators so that the kinetic energy term in the Hamiltonian becomes local and quadratic with respect to them. The ground-state of this traid-anyon-Hubbard model exhibits several indications of exchange statistics intermediate between bosons and fermions, as well as signs of emergent approximate Haldane exclusion statistics. The continuum limit results in a Galilean invariant Hamiltonian with eigenstates that correspond to previously constructed continuum wave functions for traid anyons. This provides not only an a-posteriori justification of our lattice model, but also shows that our construction serves as an intuitive approach to traid anyons, i.e. anyons intrinsic to 1D.
Topological quantum computation relies on braiding non-Abelian anyons, but requires the underlying topological order to survive imperfect state preparation and environmental noise. We show that the instability of topological order to wavefunction deformations and to decoherence, with the latter probed by syndrome distributions, is generically captured by stat-mech models whose G×Rep(G)G\times \textrm{Rep}(G)G×Rep(G) symmetry naturally exposes the corrupting anyonic excitations. As an example, we combine this framework with Monte-Carlo simulations to resolve the stability of D4D_4D4​ topological order under deformations and quantum channels that proliferate multiple non-Abelian anyon species that are individually unable to condense. We show that beyond a finite threshold, proliferation of two non-Abelian anyon species parasitically condenses a shared Abelian-anyon fusion outcome---destroying the topological order. Our symmetry-based approach suggests the resulting trivial phase is distinct from that obtained by condensing all Abelian anyons; in other words, the trivial phase "remembers" which anyons condensed. This framework provides a first step into identifying the relevant symmetry for optimal decoders, conditioned on syndrome measurements, of non-Abelian topological order.
According to a basic rule of fermionic and bosonic many-body physics, known as the linked cluster theorem, physical observables are not affected by vacuum bubbles, which represent virtual particles created from vacuum and self-annihilating without interacting with real particles. Here we show that this conventional knowledge must be revised for anyons, quasiparticles that obey fractional exchange statistics intermediate between fermions and bosons. We find that a certain class of vacuum bubbles of Abelian anyons does affect physical observables. They represent virtually excited anyons that wind around real anyonic excitations. These topological bubbles result in a temperature-dependent phase shift of Fabry-Perot interference patterns in the fractional quantum Hall regime accessible in current experiments, thus providing a tool for direct and unambiguous observation of elusive fractional statistics.
As opposed to classical mechanics, quantum mechanical particles can be truly identical and lead to new and interesting phenomena. Identical particles can be of different types, determined by their exchange symmetry, which in turn gives rise to statistical repulsion. The exchange symmetry is given by a representation of the exchange group; the fundamental group of the configuration space of identical particles. In three dimensions the exchange group is the permutation group and there are only two types of identical particles; bosons and fermions. While any number of bosons can be at the same place or in the same state, fermions repel each other. In two dimensions the exchange group is the braid group and essentially any exchange symmetry is allowed, such particles are called anyons. Abelian anyons are described by abelian representations of the exchange group and can be seen as giving a continuous interpolation between bosons and fermions. Non-abelian anyons are much more complex and their statistical repulsion is yet largely unexplored. We use the framework of modular tensor categories to show how the statistical repulsion of non-abelian anyons depends on the exchange symmetry. The Fibonacci anyon model is studied, for which explicit results are obtained. We also show how Fibonacci anyons can be used to implement topological quantum computation, providing topologically stable quantum information encoded in the state of non-abelian anyons that can be manipulated via the non-abelian exchange symmetry.