Origin and emergent features of many-body dynamical localization

TL;DR

The paper addresses whether interactions can destroy dynamical localization (DL) in a quantum kicked rotor by studying the kicked Lieb–Liniger model and mapping it to a high-dimensional lattice with on-site pseudorandomness and hybrid exponential–algebraic couplings. The authors analyze the CM and relative-momentum sectors, showing exponential localization in CM momentum persists while interactions induce algebraic tails in relative momentum, with a cross-over of the tail exponent from about 4 to 3 as $g$ grows; DL can break down at large kick $K$ and intermediate interaction strength, while DL remains in the $g\to 0$ and $g\to\infty$ limits (Tonks–Girardeau). The study uses generalized fractal dimensions and level-spacing statistics to detect multifractality and near-integrability in certain parameter regions, supporting a phase diagram featuring MBDL and delocalization. The results offer a microscopic mechanism for many-body dynamical localization in strongly correlated quantum gases and predict observable signatures in momentum distributions after quenches, with implications extending to larger particle numbers and experimental realizations.

Abstract

The question of whether interactions can break dynamical localization in quantum kicked rotor systems has been the subject of a long--standing debate. Here, we introduce an extended mapping from the kicked Lieb--Liniger model to a high--dimensional lattice model and reveal universal features: on--site pseudorandomness and hybrid exponential--algebraic decay couplings with increasing momenta. We find that the exponent and the amplitude of the algebraic decay undergo a crossover as the interaction strength increases. This mapping predicts the existence of dynamical localization and its breakdown at large kick strengths and intermediate interaction strengths. An analysis of the generalized fractal dimension and level--spacing ratio supports these findings, highlighting the presence of near integrability and multifractality in different regions of parameter space. Our results offer an explanation for the occurrence of many--body dynamical localization, particularly in strongly correlated quantum gases, and are anticipated to generalize to systems of many particles.

Figures (16)

• Figure 1: (a) Schematic of the kicked LL system in coordinate (upper) and momentum (lower) space, where blue and red curves denote the pulsed sinusoidal potential and the contact interactions, respectively. In momentum space, the kinetic energy component is represented by a quadratic potential defined over a momentum lattice. The periodic kicks introduce the couplings between adjacent momentum states. Boson-boson interactions result in momentum scattering, where the total momentum is conserved ($n+m=p+q$). (b) Schematic phase diagram of the kicked LL system as a function of the kick strength $K$ and the interaction strength $g$.
• Figure 2: (a-c) The off-diagonal term $\lvert W_{0\mathcal{I}}\rvert$ as a function of energy $E_{\mathcal{I}}-E_0$ for (a) $g=10^{-1}$, (b) $g=10^{1}$, and (c) $g=10^3$ in log-log scale (blue dots). The black lines stand for the Bethe-Ansatz results. The black circles and squares represent the off-diagonal term for the mapped free bosons and fermions, respectively. The green and red dashed lines denote algebraic decay scaling as ${E_{\mathcal{I}}}^{-2}$ and ${E_{\mathcal{I}}}^{-3/2}$, respectively. The insets show the histograms of the on-site term $V_{\mathcal{I}}$, fitted by a Lorentzian distribution. The momentum cut-off, the kick strength, and the particle number are $M=100$, $K=0.5$ and $N=2$, respectively. (d-f) show the same data as in (a-c) but for $N=3$ and $M=35$. (g, h) show the decay exponent $\lambda$ and amplitude $A$ as a function of $g$, respectively.
• Figure 3: The decay exponent $\lambda$ (a) and the amplitude $A$ (b) as a function of $\gamma$ for different $N$. The inset of (a) illustrates the typical two-particle excitations $\{m_1,m_N\}$ of the excited state $\lvert\mathcal{I}\rangle$, while the other quasi-momenta $\{m_2\cdots m_{N-1}\}$ are kept identical to their ground-state value $\lvert0\rangle$.
• Figure 4: (a) The GFD $D_3$ as a function of $g$ and $K$. (b) The averaged energy-level-spacing ratio $\langle r\rangle$ as a function of $g$ and $K$ for $M=32$. The black dashed line denotes where the LL parameter is $\gamma=1$. (c) Different $D_{\beta}$, $b_{\beta}$, and $\langle r\rangle$ as a function of $g$ for $K=1.0$. The shaded areas denote different regimes. The number of bosons is $N=3$.
• Figure 5: (a) The hopping amplitude as a function of the standard deviation $\Delta p$ for $N=3$ and different values of $g$ in log-log scale. The black dashed line and the black dot-dashed line denote algebraic decay scaling as ${\Delta p}^{-2}$ and ${\Delta p}^{-1}$, respectively. The inset shows the hopping amplitude as a function of the CM momentum $p_\mathrm{c}$ in semi-log scale. The upper boundary of the gray shaded area denotes the single-particle hopping $\lvert U^{\mathrm{S}}_{m0}\rvert$. The cut-off and the kick strength are $M=30$ and $K=1$, respectively. (b) The same data as in (a) but for $N=2$ and $M=75$. (c) The momentum distribution $n(m)$ after $100$ kicks for the particle number $N=3$ and different interaction strengths $g$ in log-log scale. The cut-off and the kick strength are $M=50$ and $K=1$, respectively. The gray dashed line and the gray dot-dashed line denote algebraic decay scaling as ${m}^{-4}$ and ${m}^{-2}$, respectively. (d) The same data as in (c) but for $N=2$ and $M=75$.