Abstract
We show that in a generic, ergodic quantum many-body system the interactions induce a non-trivial topology for an arbitrarily small non-hermitean component of the Hamiltonian. This is due to an exponential-in-system-size proliferation of exceptional points which have the hermitian limit as an accumulation (hyper-)surface. The nearest-neighbour level repulsion characterizing hermitian ergodic many-body sytems is thus shown to be a projection of a richer phenomenology where actually all the exponentially many pairs of eigenvalues interact. The proliferation and accumulation of exceptional points also implies an exponential difficulty in isolating a local ergodic quantum many-body system from a bath, as a robust topological signature remains in the form of exceptional points arbitrarily close to the hermitian limit.
Highlights
Exceptional points are a particular type of spectral degeneracy where groups of complex eigenvalues coalesce as well as the corresponding eigenvectors
An important physical implication of our results concerns the interaction between the levels
We verify in a generic quantum many-body system the hypothesis that this scenario is a projected manifestation of the more complex phenomenology of eigenvalue braiding through exceptional points in the complex plane
Summary
Exceptional points are a particular type of spectral degeneracy where groups of complex eigenvalues coalesce as well as the corresponding eigenvectors. This is due to an exponential-in-system-size proliferation of exceptional points which have the Hermitian limit as an accumulation (hyper)surface. The connection between level repulsion in the Hamiltonian spectrum of an ergodic system and the distribution of exceptional point has been so far argued based on toy models [53] and demonstrated at fine-tuned points of models without local degrees of freedom which become classical in the thermodynamic limit [54,55]. In order to implement the specific non-Hermitian term in our Hamiltonian (1), which involves multiple spins, the correlation length in the bath should amount to at least two lattice sites, which makes the Kossakowski matrix in the Lindblad equation nondiagonal
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