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

Abstract

We study the Hatano-Nelson model, i.e., a one-dimensional non-Hermitian chain of spinless fermions with nearest-neighbor nonreciprocal hopping, in the presence of repulsive nearest-neighbor interactions. At half filling, we find two PT transitions, as the interaction strength increases. The first transition is marked by an exceptional point between the first and the second excited state in a finite-size system and is a first-order symmetry-breaking transition into a charge-density wave regime. Persistent currents characteristic of the Hatano-Nelson model abruptly vanish at the transition. The second transition happens at a critical interaction strength that scales with the system size and can thus only be observed in finite-size systems. It is characterized by a collapse of all energy eigenvalues onto the real axis. We further show that in a strong interaction regime, but away from half filling, the many-body spectrum shows point gaps with nontrivial winding numbers, akin to the topological properties of the single-particle spectrum of the Hatano-Nelson chain, which indicates the skin effect of extensive many-body eigenstates under open boundary conditions. Our results can be applied to other models such as the non-Hermitian Su-Schrieffer-Heeger-type model and contribute to an understanding of fermionic many-body systems with non-Hermitian Hamiltonians.

Non-Hermitian boost deformation

“…6). This behavior is similar to the interacting Hatano-Nelson model [32,33]. The small cluster of states that is not observed for the weakly interacting cases should be due to the strong interaction effect.…”

“…This model is solvable using a similarity transformation that reduces the wave functions to the Hermitian counterparts, by which the skin effect and unconventional Anderson transition are captured. Even in the presence of many-body interactions, the skin effect still survives [24][25][26][27][28][29][30][31][32][33]. Interestingly, Hatano and Nelson also argue that the imaginary gauge field can be understood as a Galilean boost.…”

Topological classification of non-Hermitian Hamiltonians with frequency dependence

“…Non-Hermitian Hamiltonians also appear in the context of open and driven quantum systems [31][32][33][34][35][36][37][38][39][40][41]. Driven systems permit non-Hermitian Hamiltonians with eigenvalues with positive or negative imaginary parts, even in the absence of explicit interactions.…”

Topological Spin Excitations in Non-Hermitian Spin Chains with a Generalized Kernel Polynomial Algorithm

“…The point gap topology is unique for non-Hermitian systems and it encodes the origin of the NHSE [16][17][18]. Recently, the generalization of NH topology as well as other interesting aspects of NH physics such as parity-time symmetry breaking [19][20][21] and exceptional points [22][23][24][25] to NH many-body systems have attracted much interest [26][27][28][29][30].…”

“…where ω is a complex number, jGS L;R i are left and right eigenvectors corresponding to the eigenvalue of smallest real part [29,46], and δ 2 ðω − HÞ ¼ P n δðℜðω − E n ÞÞδðℑðω − E n ÞÞjΨ R;n ihΨ L;n j. Since ω is complex, Sðω; lÞ is no longer a function of a single variable, and does not have the Chebyshev expansion Eq.…”