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arXiv:2006.09283 · Physical review. B./Physical review. B

Exceptional points in Fermi liquids with quadrupolar interactions

Rui Aquino, Daniel Gustavo Barci

Published Nov 11, 2020• 12 citations
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Abstract

We show the existence of non-Hermitian degeneracies, known as exceptional points, in the collective mode spectrum of Fermi liquids with quadrupolar interactions. Through a careful analysis of the analytic properties of the dynamic quadrupolar susceptibility, we show that, in the weak attractive region, two stable collective modes coalesce to an exceptional point. We completely characterize this singularity, explicitly showing its topological properties. Experimental signatures are also discussed.

DOI
10.1103/physrevb.102.201110

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We show the existence of non-Hermitian degeneracies, known as exceptional points, in the collective mode spectrum of Fermi liquids with quadrupolar interactions. Through a careful analysis of the analytic properties of the dynamic quadrupolar susceptibility, we show that, in the weak attractive region, two stable collective modes coalesce to an exceptional point. We completely characterize this singularity, explicitly showing its topological properties. Experimental signatures are also discussed.
We consider a Fermi liquid model with density-density as well as quadrupolar forward scattering interactions parametrized by the Landau parameters F0{F}_{0}F0​ and F2{F}_{2}F2​. Using bosonization and a decimation technique, we compute collective modes and spectral functions for a huge range of interactions, ranging from strong repulsion to strong attraction in either angular momentum channel. We present a dynamical phase diagram showing a region of parameters where the collective mode structure changes abruptly, possibly signaling a dynamical phase transition.
Non-Hermitian quantum systems can exhibit spectral degeneracies known as exceptional points, where two or more eigenvectors coalesce, leading to a nondiagonalizable Jordan block. It is known that symmetries can enhance the abundance of exceptional points in noninteracting systems. Here we investigate the fate of such symmetry protected exceptional points in the presence of a symmetry preserving interaction between fermions and find that (i) exceptional points are stable in the presence of the interaction. Their propagation through the parameter space leads to the formation of characteristic exceptional ``fans.'' In addition, (ii) we identify a new source for exceptional points which are only present due to the interaction. These points emerge from diagonalizable degeneracies in the noninteracting case. Beyond their creation and stability, (iii) we also find that exceptional points can annihilate each other if they meet in parameter space with compatible many-body states forming a third order exceptional point at the endpoint. These phenomena are well captured by an ``exceptional perturbation theory'' starting from a noninteracting Hamiltonian.
We show that interactions in quantum spin liquids can result in non-Hermitian phenomenology that differs qualitatively from mean-field expectations.We demonstrate this in two prominent cases through the effects of phonons and disorder on a Kitaev honeycomb model.Using analytic and numerical calculations, we show the generic appearance of exceptional points and rings depending on the symmetry of the system.Their existence is reflected in dynamical observables including the dynamic structure function measured in neutron scattering.The results point to different phenomenological features in realizable spin liquids that must be incorporated into the analysis of experimental data and also indicate that spin liquids could be generically stable to wider classes of perturbations.
This Letter addresses the problem of constructing a proper bosonized description of the collective modes in strongly interacting (non-)Fermi liquids which is specific to two spatial dimensions. Although, in a mild form, this subtlety exists in the Fermi liquid as well, the discussion focuses on the effects of long-ranged and/or retarded interactions which can completely destroy the fermionic quasiparticles. The present analysis provides a further insight into the nature and properties of the collective bosonic modes in such systems.
An exceptional point (EP) is exclusive for non-Hermitian systems and distinct from that at a degeneracy point (DP), supporting intriguing dynamics which can be utilized to probe quantum phase transitions and prepare eigenstates in a Hermitian many-body system. In this paper, we investigate the transition from a DP for a Hermitian system to an EP driven by non-Hermitian terms. We present a theorem on the existence of a transition between a DP and EP for a general system. Specifically, one of twofold degenerate eigenstates of a Hermitian system becomes a coalescing state when a selected non-Hermitian term is added. The obtained EP is robust to the strength of non-Hermitian terms. We illustrate the theorem by an exactly solvable quasi-one-dimensional model, which allows for the existence of a transition between fully degenerate and exceptional spectra driven by non-Hermitian tunnelings in real and kkk spaces, respectively. We also study the EP dynamics for generating coalescing edge modes in Su-Schrieffer-Heeger-like models. This finding reveals the ubiquitous connection between DPs and EPs.
This note addresses the problem of constructing a proper bosonized description of the collective modes in strongly interacting (non-)Fermi liquids which is specific to two spatial dimensions. Although, in a mild form, this subtlety exists in the Fermi liquid as well, the discussion focuses on the effects of long-ranged and/or retarded interactions which can completely destroy the fermionic quasiparticles. The present analysis also provides a further insight into the nature and properties of the collective bosonic modes in such systems.