Many-body localization phase in a spin-driven chiral multiferroic chain

Many-body localization (MBL) is an emergent phase in correlated quantum systems with promising applications, particularly in quantum information. Here, we unveil the existence and analyze this phase in a chiral multiferroic model system. Conventionally, MBL occurrence is traced via level statistics by implementing a standard finite-size scaling procedure. Here, we present an approach based on the full distribution of the ratio of adjacent energy spacings. We find a strong broadening of the histograms of counts of these level spacings directly at the transition point from MBL to the ergodic phase. The broadening signals reliably the transition point without relying on an averaging procedure. The fast convergence of the histograms even for relatively small systems allows monitoring the MBL dynamics with much less computational effort. Numerical results are presented for a chiral spin chain with a dynamical Dzyaloshinskii-Moriya interaction, an established model to describe the spin excitations in a single-phase spin-driven multiferroic system. The multiferroic MBL phase is uncovered and it is shown how to steer it via electric fields.

Figure 1

Level statistics for a ferromagnetic nearest neighbor interaction $J_1=-1$, as a function of the strength of disorder $h$ of the magnetic field $B^z\in 〈-h,h〉$. The DM interaction term is zero and the system exhibits a precise GOE symmetry.

Figure 2

Level statistics for the ferromagnetic nearest neighbor interaction $J_1=-1$, as a function of the strength of disorder $h$ of the magnetic field $B^z\in 〈-h,h〉$. The DM interaction term is small $D=0.01$. The dominant symmetry of the system is GOE. The influence of GUE enhances with the system's size $L$.

Figure 3

The same as for Fig. 2 but for $D=0.02$.

Figure 4

Level statistics for $J_1=-1$, as a function of the strength of disorder $h$ of the magnetic field $B^z\in 〈-h,h〉$. The DM interaction term is stronger $D=0.05$. The symmetry of the system is mixed.

Figure 5

Level statistics for ferromagnetic nearest neighbor interaction $J_1=-1$. For (a) $D=0$. Increasing the randomness range $2h$ of the magnetic field $B^z\in 〈-h,h〉$ the system spectrum undergoes a transition from GOE to Poisson distribution, indicating a transition from ergodic to MBL phase. Curves correspond to different system sizes and are obtained by an ensemble average for random disorder. (b) Scaling collapse in the vicinity of the MBL transition is achieved by the scaling function $f\left(h\right)=L^{1/\nu }(h-h_c),\nu =1,h_c=4.7$. (c) With DM interaction $\left(D=0.2\right)$. Periodic boundary conditions are implemented and the system is of GUE type. Increasing randomness the system undergoes a transition from GUE to the Poisson distribution. (d) The rescaled phase transition curves from the ergodic to the MBL phase for $D=0.2,h_c=4.4,\nu =1,f\left(h\right)=L^{1/\nu }(h-h_c)$.

Figure 6

Histograms of counts for a fixed strength of disorder $h=5$ without DM interaction as a function of the consecutive level spacing $r$. Convergence is indicated for $L=14$.

Figure 7

Histograms of counts for the different strength of disorder $h$ with $J_1=-1$ without DM interaction as a function of the consecutive level spacing $r$. Broadening of the histogram corresponds to the critical strength of disorder and to the transition point. The larger $L$ is, the more distinguished the peaks are.

Figure 8

The fluctuation dependency on system size without $D$ and $J_1=-1$. The two datasets marked by red are the nearest to critical disorder.

Figure 9

Full width at half maximum $\sigma$ for the histograms as a function of disorder $h$. The graphs on the right side are with finite DM interaction, $D=0.2$.

Figure 10

$J_1=-1,D=0.2$, for fixed $h=5$. Additional site-dependent disorder of $10\%$ in $D$ was taken while different colors and marks refer to various realizations.