Exceptional non-Hermitian phases in disordered quantum wires

We demonstrate the occurrence of nodal non-Hermitian (NH) phases featuring exceptional degeneracies in chiral-symmetric disordered quantum wires, where NH physics naturally arises from the self-energy in a disorder-averaged Green's function description. Notably, we find that at least two nodal points in the clean Hermitian system are required for exceptional points to be effectively stabilized upon adding disorder. We identify and study experimental signatures of our theoretical findings both in the spectral functions and in mesoscopic quantum transport properties of the considered systems. Our results are quantitatively corroborated and exemplified by numerically exact simulations on a microscopic lattice model. The proposed setting provides a conceptually minimal framework for the realization and study of topological NH phases in quantum many-body systems.

Figure 1

(a) Illustration of the translation-invariant model Hamiltonian $H_0$ [see Eq. (2)]. (b) Illustration of the disorder term $V$ [see Eq. (3)]. $V$ consists of random amplitude intracell and nearest-neighbor (NN) terms. (c) Complex spectrum of the effective NH Hamiltonian $H_e$ [see Eq. (1)] of a disordered system microscopically described by the total Hamiltonian $H=H_0+V$ [see Eqs. (2) and (3)]. Exact numerical results are shown in orange, perturbative results within first Born approximation in blue. Two pairs of exceptional points connected by Fermi arcs are visible (see also inset). Parameters are $w=-1/\sqrt{2}, \alpha =0.7, s=(1+i)/\sqrt{2}, v=-0.5(1+i)/\sqrt{2}$.

Figure 2

(a) Spectrum of $H_e\left(k\right)$ in the conventional phase. The exact numerical result is plotted in orange, the FBA result is shown in blue for comparison. Parameters are $\alpha =0.7, s=(1+i)/\sqrt{2}, v=-0.5(1-i)/\sqrt{2}$. (b) Exact numerical result for the spectral function $A(k,\omega )$ of the exceptional phase. Parameters are $\alpha =0.7, s=(1+i)/\sqrt{2}, v=-0.5(1+i)/\sqrt{2}$. (c) Exact numerical result for the spectral function $A(k,\omega )$ of the conventional phase. Parameters are $\alpha =0.7, s=(1+i)/\sqrt{2}, v=-0.5(1-i)/\sqrt{2}$.

Figure 3

Energy-dependent two-terminal conductance of a disordered system [cf. Eqs. (2) and (3)] with $N=400$ sites in the exceptional and conventional phase (see plot legend). The result is averaged over 1000 disorder realizations. The parameters in the exceptional phase are $\alpha =0.3, s=(1+i)/\sqrt{2}, v=-0.5(1+i)/\sqrt{2}$ and in the ordinary phase $\alpha =0.3, s=(1+i)/\sqrt{2}, v=-0.5(1-i)/\sqrt{2}$. Inset: Amplitude of the zero-energy conductance peak (averaged over the energy interval [-0.015, 0.015]) in the exceptional phase as a function of system size in a semi-log plot along with an exponential fit $\sigma \left(l\right)={\sigma }_0{\mathrm{e}}^{-\ln \left(2\right)l/l_0}$ with ${\sigma }_0=0.93e^2/h, l_0=147.9$.

Figure 4

Linearization around $k_{\mathrm{t}}$.