Magnetic field Controlled Anderson Delocalization in a Spinful Non-Hermitian Chain

Abstract

Anderson localization (AL) and the non-Hermitian skin effect (NHSE) represent two paradigmatic localization phenomena driven, respectively, by disorder and non-Hermiticity. In one-dimensional (1D) non-Hermitian systems, these factors are known to compete and provide a smooth crossover between AL and NHSE upon parameter tuning. Here, we show that this interplay is fundamentally enriched in spinful systems, where an external magnetic field acts as an additional degree to manipulate the localization behavior. By investigating a disordered 1D spinful non-Hermitian chain, we demonstrate that under appropriately correlated disorder configurations across spin sectors, the magnetic field enhances the AL $\rightarrow$ NHSE crossover. Interestingly, this facilitates the Anderson delocalization transition even in strongly disordered systems where states would otherwise be Anderson localized. By analyzing the inverse participation ratio and the mean center of mass, we map the resulting triple interplay between disorder, non-Hermiticity, and the magnetic field strength, identifying regimes of Anderson localization and skin accumulation. We further reveal that this magnetic field driven delocalization phenomenon originates from an effective suppression of disorder strength via Zeeman-induced inter-chain coupling across the spin sectors.

Figures (6)

• Figure 1: Schematic of a disordered spinful 1D Hatano-Nelson model subjected to gauge type $\mu,\nu = z$ such that $\theta_L$ is chosen imaginary.
• Figure 2: (a) Parameter plot illustrating localization regimes, obtained using $\langle \overline{\text{mcom}} \rangle$ for the spinless model with $t_R=1$ and $N=100$. The red region represents non-Hermiticity dominated region with left-localized skin states and white represents disorder dominated (or clean) regime hosting Anderson (or extended) states. (b) Representative Anderson states and (c) skin states in the disorder dominated and NH dominated region, respectively, obtained from one disorder realization. The result in (a) is averaged over 1000 disorder realizations. The '$\text{mcom}$' is discussed in Sec. \ref{['sub sec Triple interplay of disorder, non-Hermiticity, and Magnetic field']} in detail.
• Figure 3: (a-b) Eigenstates: $|\psi_n^{\uparrow}|, |\psi_n^{\downarrow}|$, and corresponding eigenspectrum of the system under external magnetic field ($B\hat{i}$) in the presence of symmetrically correlated disorder. The eigenstates retain Anderson localization even under the magnetic field influence. Only a few eigenstates have been plotted for clarity. (c-d) Similar plots for the case of anti-symmetrically correlated disorder. All the eigenstates exhibit NHSE following Anderson delocalization. The eigenspectrum (d) exhibits point gap with PBC (black) eigenenergies enclosing the OBC (green) eigenenergies. Parameters chosen include $(\theta_L,\theta_R) = (i/5, 1)$, $W/J=5$, $B/J=10$, and $N=100$. All of the above results are numerically obtained from one representative disorder realization.
• Figure 4: $\langle \overline{\text{IPR}} \rangle$ and $\langle \overline{\text{mcom}} \rangle$ plots. (a-c) Upper panel represents the $\langle \overline{\text{IPR}} \rangle$ and (d-f) lower panel represents the $\langle \overline{\text{mcom}} \rangle$ for both up- and down-spin sectors, under anti-symmetrically correlated disorder as a function of (a,d) disorder with $\theta_L=i/2$, $B/J=4$, (b,e) non-Hermiticity with $B/J=4$, $W/J=8$, and (c,f) magnetic field with $\theta_L=i/2$, $W/J=8$. The red (blue) curves indicate up(down)-spin sectors. The results are averaged over an ensemble of 1000 disorder configurations. Common parameters include $\theta_R=1$ and $N=100$.
• Figure 5: $\langle \overline{\text{mcom}} \rangle$ plots for both spin sectors having anti-symmetrically correlated disorders, represented in the (a,b)$B-W$ plane with $\theta_L=i/2$, (c,d)$\theta_L-B$ plane with $W/J=8$, and (e,f)$\theta_L-W$ plane with $B/J=4$. The upper (lower) panel represent up (down)-spin sector. The red (blue) region indicates left (right)-NHSE, and the white denotes Anderson localization (or extended states in limiting cases). The results are averaged over an ensemble of 1000 disorder realizations with $\theta_R=1$ and $N=100$.