Many-body approach to non-Hermitian physics in fermionic systems

Abstract

In previous studies, the topological invariants of 1D non-Hermitian systems have been defined in open boundary condition (OBC) to satisfy the bulk-boundary correspondence. The extreme sensitivity of bulk energy spectra to boundary conditions has been attributed to the breakdown of the conventional bulk-boundary correspondence based on the topological invariants defined under periodic boundary condition (PBC). Here we propose non-Hermitian many-body polarization as a topological invariant for 1D non-Hermitian systems defined in PBC, which satisfies the bulk-boundary correspondence. Employing many-body methodology in the non-Hermitian Su-Schrieffer-Heeger model for fermions, we show the absence of non-Hermitian skin effect due to the Pauli exclusion principle and demonstrate the bulk-boundary correspondence using the invariant defined under PBC. Moreover, we show that the bulk topological invariant is quantized in the presence of chiral or generalized inversion symmetry. Our study suggests the existence of generalized crystalline symmetries in non-Hermitian systems, which give quantized topological invariants that capture the symmetry-protected topology of non-Hermitian systems. PACS numbers:Introduction.-Recent progress in the study of non-Hermitian systems, such as open systems, dissipative systems with gain and loss, and also interacting solid-state systems , has uncovered various intriguing physical phenomena that do not exist in Hermitian systems. For instance, the characteristic complex energy spectra of non-Hermitian systems are theoretically predicted to host exceptional surfaces or bulk Fermi-arcs [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53], which are later realized in experiments [54,55]. Nowadays, there are growing research activities to extend the idea of topological Bloch theory developed in Hermitian systems to non-Hermitian Hamiltonians [56][57][58][59][60][61][62][63][64].One central issue in the study of topological phenomena in non-Hermitian systems is to understand the bulk-boundary correspondence (BBC). In Hermitian systems, it is wellestablished that the bulk topological invariants defined by Bloch wave functions in periodic boundary condition (PBC) predict robust boundary states in systems under open boundary condition (OBC) [65][66][67]. Contrary to this, in non-Hermitian systems, the bulk energy spectra exhibit extreme sensitivity to boundary conditions [68,69]. For instance, in recent studies of the non-Hermitian Su-Schrieffer-Heeger (SSH) model, it was shown that the bulk eigenstates, which are extended under PBC, are exponentially localized on one-side of the finite-size system with OBC [57,70]. This phenomenon is named the non-Hermitian skin effect in Ref. 70, which has been extensively discussed recently [70][71][72][73][74][75][76][77]. Since the energy spectra under PBC and OBC differ so drastically, there has been even a common belief that the bulk invariant defined under PBC has intrinsic limitations in explaining BBC of non-Hermitian systems in general. To circumve...

Symmetry breaking and spectral structure of the interacting Hatano-Nelson model

“…Thus, it is of fundamental interest to explore non-Hermitian phenomena in many-body systems with strong interactions . Most of the existing studies on this subject are focused on the issues of non-Hermitian many-body localization [49][50][51][52] and the non-Hermitian skin effect [54][55][56][57][58][59][60][61][62]. However, many-body interaction effects, especially on bulk fermionic properties, remain largely unexplored even in simple models.…”

Fate of fractional quantum Hall states in open quantum systems: Characterization of correlated topological states for the full Liouvillian

“…Among them, open quantum systems [51][52][53][54][55][56][57][58] also provide a unique platform of the following intriguing issue: the interplay between correlations and non-Hermitian topology [59][60][61][62][63][64][65]. Such systems interact with the environment and may lose energy or particles.…”

“…In the previous works [59][60][61][62][63][64][65], by focusing on the special time evolution, the correlated topological states were analyzed for the effective non-Hermitian Hamiltonian…”

Untying links through anti-parity-time-symmetric coupling

“…If the non-Hermiticity is = (0, 0, γ ), the topological phase transition and the existence of the edge state are unaltered because of the pseudo-anti-Hermiticity protection [34]; the topological properties of the non-Hermitian system are inherited by the EPs (exceptional rings or exceptional surfaces in 2D or 3D) [60][61][62][63][64][65][66][67]. If the non-Hermiticity is = (0, γ , 0), the non-Hermitian skin effect occurs under open boundary condition [54][55][56][57][58][59][68][69][70][71][72][73][74][75][76][77][78], the non-Hermitian Aharonov-Bohm effect under periodical boundary condition invalidates the conventional bulk-boundary correspondence [54], and the non-Bloch band theory is developed for topological characterization [77][78][79][80][81][82]. Here, the dissipation induced anti-PT -symmetric coupling corresponds to the imaginary part = (γ , 0, 0).…”