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arXiv:2503.02565 · Physical Review Letters

Interaction Induced Anderson Transition in a Kicked One Dimensional Bose Gas

H. Olsen, P. Devillard, Gianni Aupetit-Diallo, Patrizia Vignolo, Mathias Albert

Published Oct 3, 2025• 3 citations
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Abstract

We investigate the Lieb-Liniger model of one-dimensional bosons subjected to periodic kicks. In both the noninteracting and strongly interacting limits, the system undergoes dynamical localization, leading to energy saturation at long times. However, for finite interactions, we reveal an interaction-driven transition from an insulating to a metallic phase at a critical kicking strength, provided the number of particles is three or more. Using the Bethe ansatz solution of the Lieb-Liniger gas, we establish a formal correspondence between its dynamical evolution and an Anderson model in N spatial dimensions, where N is the number of particles. This theoretical prediction is supported by extensive numerical simulations for three particles, complemented by finite-time scaling analysis, demonstrating that this transition belongs to the orthogonal Anderson universality class.

DOI
10.1103/dyxq-qkmd

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We investigate the Lieb-Liniger model of one-dimensional bosons subjected to periodic kicks. In both the noninteracting and strongly interacting limits, the system undergoes dynamical localization, leading to energy saturation at long times. However, for finite interactions, we reveal an interaction-driven transition from an insulating to a metallic phase at a critical kicking strength, provided the number of particles is three or more. Using the Bethe ansatz solution of the Lieb-Liniger gas, we establish a formal correspondence between its dynamical evolution and an Anderson model in N spatial dimensions, where N is the number of particles. This theoretical prediction is supported by extensive numerical simulations for three particles, complemented by finite-time scaling analysis, demonstrating that this transition belongs to the orthogonal Anderson universality class.
Abstract We study the interplay of interactions and quasiperiodic driving in the Lieb–Liniger model of one-dimensional bosons subjected to a sequence of delta kicks. Building on the known mapping between the kicked rotor and the Anderson model, we show that both interparticle interactions and quasiperiodic modulations of the kicking strength can independently and simultaneously generate synthetic dimensions. In the absence of modulation, interactions between two bosons already promote an effective two-dimensional Anderson model. Introducing one or two additional incommensurate frequencies further extends the system to three and four effective dimensions, respectively. Through extensive numerical simulations of the two-body dynamics and finite-time scaling analysis, we observe Anderson localization and the associated critical behavior characteristic of the orthogonal universality class. This combined use of interactions and quasiperiodic driving thus provides a versatile framework for emulating Anderson localization and its transition in arbitrary dimensions.
The kicked rotor system is a textbook example of how classical and quantum dynamics can drastically differ. The energy of a classical particle confined to a ring and kicked periodically will increase linearly in time whereas in the quantum version the energy saturates after a finite number of kicks. The quantum system undergoes Anderson localization in angular-momentum space. Conventional wisdom says that in a many-particle system with short-range interactions the localization will be destroyed due to the coupling of widely separated momentum states. Here we provide evidence that for an interacting one-dimensional Bose gas, the Lieb-Liniger model, the dynamical localization can persist at least for an unexpectedly long time.
Abstract We review our recent results on Anderson localization in systems of two interacting particles coupled by contact interactions. Based on an exact mapping to an effective single-particle problem, we numerically investigate the occurrence of metal-insulator phase transitions for the pair in two-(2D) and three-dimensional (3D) disordered lattices. In two dimensions, we find that interactions cause an exponential enhancement of the pair localization length with respect to its single-particle counterpart, but do not induce a delocalization transition. In particular we show that previous claims of 2D interaction-induced Anderson transitions are the results of strong finite-size effects. In three dimensions we find that the pair undergoes a metal-insulator transition belonging to the same (orthogonal) universality class of the noninteracting model. We then explore the phase diagram in the space of energy E, disorder W and interaction strength U, which reveals a rich and counterintuitive structure, endowed with multiple metallic and insulating phases. We point out that this phenomenon originates from the molecular and scattering-like nature of the pair states available at given energy and disorder strength.
The quantum kicked rotor is well known to display dynamical localization in the noninteracting limit. In the interacting case, while the mean-field (Gross-Pitaevskii) approximation displays a destruction of dynamical localization, its fate remains debated beyond mean field. Here we study the kicked Lieb-Liniger model in the few-body limit. We show that for any interaction strength, two kicked interacting bosons always dynamically localize, in the sense that the energy of the system saturates at long times. However, contrary to the noninteracting limit, the momentum distribution $\mathrm{\ensuremath{\Pi}}(k)$ of the bosons is not exponentially localized, but decays as C/k4\mathcal{C}/{k}^{4}C/k4, as expected for interacting quantum particles, with Tan's contact C\mathcal{C}C which remains finite at long times. We discuss how our results will impact the experimental study of kicked interacting bosons.
Understanding the interplay of interaction and disorder in quantum transport poses long-standing scientific challenges for theory and experiment. While highly controlled ultracold atomic platforms combining atomic interactions with spatially disordered lattices have led to remarkable advances, the extension of such controlled studies to phenomena in high-dimensional disordered systems, such as the three-dimensional Anderson metal-insulator transition has been limited. Kicked quantum gases provide an alternate experimental platform that captures the Anderson model in momentum space and features dynamical localization as the analog of Anderson localization. Here, we utilize a momentum space lattice platform using quasiperiodically kicked ultracold atomic gases to experimentally investigate interaction effects on the three-dimensional dynamical Anderson metal-insulator transition. We observe interaction-driven subdiffusion and a divergence of delocalization onset time on approaching the phase boundary. Mean-field numerical simulations show qualitative agreement with experimental observations, but with significant quantitative deviations.
We investigate the relaxation dynamics of the integrable Lieb-Liniger model of contact-interacting bosons in one dimension following a sudden quench of the collisional interaction strength. The system is initially prepared in its noninteracting ground state and the interaction strength is then abruptly switched to a positive value, corresponding to repulsive interactions between the bosons. We calculate equal-time correlation functions of the nonequilibrium Bose field for small systems of up to five particles via symbolic evaluation of coordinate Bethe-ansatz expressions for operator matrix elements between Lieb-Liniger eigenstates. We characterize the relaxation of the system by comparing the time-evolving correlation functions following the quench to the equilibrium correlations predicted by the diagonal ensemble and relate the behavior of these correlations to that of the quantum fidelity between the many-body wave function and the initial state of the system. Our results for the asymptotic scaling of local second-order correlations with increasing interaction strength agree with the predictions of recent generalized thermodynamic Bethe-ansatz calculations. By contrast, third-order correlations obtained within our approach exhibit a markedly different power-law dependence on the interaction strength as the Tonks-Girardeau limit of infinitely strong interactions is approached.