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arXiv:2307.00849 · Physical Review Research

Protection of correlation-induced phase instabilities by exceptional susceptibilities

M. Reitner, Lorenzo Crippa, D. Fus, Jan Carl Budich, A. Toschi, Giorgio Sangiovanni

Published May 6, 2024• 7 citations
arXivHTMLPDF

Abstract

At thermal equilibrium, we find that generalized susceptibilities encoding the static physical response properties of Hermitian many-electron systems possess inherent non-Hermitian (NH) matrix symmetries. This leads to the generic occurrence of exceptional points (EPs), i.e., NH spectral degeneracies, in the generalized susceptibilities of prototypical Fermi-Hubbard models, as a function of a single parameter such as chemical potential. We demonstrate that these EPs are necessary to promote correlation-induced thermodynamic instabilities, such as phase separation occurring in the proximity of a Mott transition, to a topologically stable phenomenon. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.l022031

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At thermal equilibrium, we find that generalized susceptibilities encoding the static physical response properties of Hermitian many-electron systems possess inherent non-Hermitian (NH) matrix symmetries. This leads to the generic occurrence of exceptional points (EPs), i.e., NH spectral degeneracies, in the generalized susceptibilities of prototypical Fermi-Hubbard models, as a function of a single parameter such as chemical potential. We demonstrate that these EPs are necessary to promote correlation-induced thermodynamic instabilities, such as phase separation occurring in the proximity of a Mott transition, to a topologically stable phenomenon. Published by the American Physical Society 2024
Non-Hermtian (NH) Hamiltonians effectively describing the physics of dissipative systems have become an important tool with applications ranging from classical metamaterials to quantum many-body systems. Exceptional points, the NH counterpart of spectral degeneracies, are among the paramount phenomena unique to the NH realm. While realizations of second-order exceptional points have been reported in a variety of microscopic models, higher-order ones have largely remained elusive in the many-body context, as they in general require fine tuning in high-dimensional parameter spaces. Here, we propose a microscopic model of correlated fermions in three spatial dimensions and demonstrate the occurrence of interaction-induced fourth-order exceptional points that are protected by chiral symmetry. We demonstrate their stability against symmetry-breaking perturbations and investigate their characteristic analytical and topological properties.
Non-Hermitian (NH) quantum systems host exceptional points (EPs), where eigenstates and eigenvalues coalesce, leading to unconventional many-body phenomena absent in Hermitian systems. While NH fermionic systems with complex interactions exhibit superfluid (SF) breakdown with EPs, spin-dependent asymmetric hopping can stabilize a NH superfluid (NH-SF) that coexists with EPs. In this work, we investigate the quasi-one-dimensional NH attractive Fermi-Hubbard model by using NH-BCS theory. We demonstrate that, when the system is regarded as weakly-coupled chains, the exceptional SF phase becomes unstable and metastable (exceptional) SF state appears between the stable SF and normal states. In the one-dimensional limit, the exceptional SFs disappear entirely and EPs only appear on the phase boundary between the normal and SF states. These results reveal how dimensional crossover governs the stability of the exceptional SF, providing the insights into the interplay between dimensionality and dissipation, with potential relevance for experimental implications in ultracold atoms.
The emergence of various types of degeneracies plays a crucial role in optimizing and engineering different physical phenomena in non-Hermitian physics. In our work, we focus on the derogatory Exceptional Points (EPs), which are characterized by multiple Jordan blocks corresponding to the same eigenvalue. We demonstrate that, under certain infinitesimal perturbations, a derogatory EP can be converted into an EP of different structure without varying the total order of degeneracy. In particular, such conversion can increase the size of the largest Jordan block and, hence, the sensitivity of the eigenspectrum to parameter variation, which is an important feature for practical applications. Furthermore, by analyzing all possible conversions, we introduce hierarchies of degeneracies of the same order that appear when perturbing non-Hermitian systems. We systematically explore hierarchies in the absence of any symmetry and when pseudo-Hermitian symmetry is present. Our study facilitates engineering various degeneracies of non-Hermitian systems, paving the way to extending the implications of non-Hermitian physics.
Abstract Exceptional points are interesting physical phenomena in non-Hermitian physics at which the eigenvalues are degenerate and the eigenvectors coalesce. In this paper, we find that in projected non-Hermitian two-level systems (sub-systems under projecting partial Hilbert space) the singularities of exceptional points (EPs) is due to basis defectiveness rather than energy degeneracy or state coalescence. This leads to the discovery of extended exceptional points (EEPs). For EEPs, more subtle structures (e.g. the so-called Bloch peach), additional classification, and ‘hidden’ quantum phase transitions are explored. By using the topologically protected sub-space from two edge states in the non-Hermitian Su–Schrieffer–Heeger model as an example, we illustrate the physical properties of different types of EEPs.
The exploration of the effect of non-Hermitian (NH) in quantum systems is gaining renewed momentum as a result of the recent progress in experiments. It has been indicated that the ability to engineer the orders of exceptional points (EPs) can be fundamental to its applications in quantum control, such as accelerating entanglement generation; however, an initial survey of the interactions between different orders of EPs is still missing. In this work, we try to partially address this issue by employing a non-reciprocally coupled cavity system which can be experimentally realizable with a two-dimensional reconfigurable NH gauged laser array. With deliberate design, our systems display both second and third orders of EPs. The sign of a novel, purely quantum continuous entanglement phase transition is observed, which reveals how multi-EP interactions alter entanglement dynamics across different regimes while maintaining accelerated generation. Our findings reveil the genuinely quantum NH physics of higher-order EPs, which has opened up a new avenue for future investigations of the higher-order degeneracy application and the dynamic phase transitions of quantum systems.
Non-Hermitian systems can manifest rich static and dynamical properties at their exceptional points (EPs). Here, we identify yet another class of distinct phenomena that is hinged on EPs, namely, the emergence of a series of non-Hermitian conservation laws. We demonstrate these distinct phenomena concretely in the non-Hermitian Heisenberg chain and formulate a general theory for identifying these emergent non-Hermitian conservation laws at EPs. By establishing a one-to-one correspondence between the constants of motion (COMs) at EPs and those in corresponding auxiliary Hermitian systems, we trace their physical origin back to the presence of emergent symmetries in the auxiliary systems. Concrete simulations on quantum circuits show that these emergent conserved dynamics can be readily observed in current digital quantum computing systems.