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arXiv:2603.25045 · Physical Review A

Dynamics of two particles with quasiperiodic long-range interactions

Anonymous

Published Jul 30, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate the dynamics of two identical spinless fermions on a one-dimensional lattice with open boundary conditions (OBC), subject to quasiperiodic long-range interactions. Using numerical exact diagonalization (ED), we study this non-integrable system as a continuous-time quantum walk and uncover a robust correlated dynamical regime. This regime, characterized by an approximately constant inter-particle distance, emerges under sufficiently strong quasiperiodic modulation of the long-range interactions. Further, the study shows that the behavior is determined by the nature of the interaction and the choice of boundary condition. Notably, by tuning the phase of the quasiperiodic modulation, we observe three distinct manifestations of this phenomenon: localization, nearest-neighbor separation oscillations, and next-nearest-neighbor separation transitions -- each arising for specific initial separations. Furthermore, we identify the suppression of entanglement entropy in the system, including instances of oscillatory behavior. Our results highlight how quasiperiodic long-range interactions shape few-body quantum dynamics.

DOI
10.1103/z1jl-sc83

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We investigate the dynamics of two identical spinless fermions on a one-dimensional lattice with open boundary conditions (OBC), subject to quasiperiodic long-range interactions. Using numerical exact diagonalization (ED), we study this non-integrable system as a continuous-time quantum walk and uncover a robust correlated dynamical regime. This regime, characterized by an approximately constant inter-particle distance, emerges under sufficiently strong quasiperiodic modulation of the long-range interactions. Further, the study shows that the behavior is determined by the nature of the interaction and the choice of boundary condition. Notably, by tuning the phase of the quasiperiodic modulation, we observe three distinct manifestations of this phenomenon: localization, nearest-neighbor separation oscillations, and next-nearest-neighbor separation transitions -- each arising for specific initial separations. Furthermore, we identify the suppression of entanglement entropy in the system, including instances of oscillatory behavior. Our results highlight how quasiperiodic long-range interactions shape few-body quantum dynamics.
The quantum walk of two hard-core bosons in one-dimensional lattice under the effect of long-range inter-particle interaction is studied in detail. We also simulate the influence of an isolated defect that may exist in the lattice on the quantum walk of two particles by adding an additional potential energy to a certain lattice site. Using exact diagonalization method, the continuous-time quantum walk is directly simulated. The numerical simulations show that the range of interaction (long-range or short-range), the strength of the inter-particle interaction, the initial state of the two particles and the presence of the isolated defect have great influences on the quantum walk. Under the effect of strong long-range interaction, the particles initially located on the non-adjacent lattice sites have a co-walking behavior, while under the short-range interactions (nearest-neighbor interactions) only two particles initially located on the neighboring lattice sites can exhibit co-walking. After introducing the isolated defect into the system with strong interaction, two particles residing on the same side of the isolated defect keep co-walking, while two particles located on either sides of the isolated defect or one particle located on the isolated defect and the other particle staying on the side of the isolated defect, the two particles keep stationary or co-walking near the defect, displaying the characteristics of localization. By using the second-order perturbation theory of degenerate quantum system, a comprehensive theoretical analysis of the above numerical results is given. The theoretical analysis reveals the underlying physical law of quantum walks of two particles in one-dimensional lattice under the effects of strong long-range interaction and isolated defect in the lattice.
Due to the topological nature of the Aubry-Andr\'e-Harper (AAH) model, interesting edge states have been found existing in one-dimensional periodic and quasiperiodic lattices. In this article, we investigate continuous-time quantum walks of identical particles initially located on either edge of commensurate AAH lattices in detail. It is shown that the quantum walker is delocalized among the whole lattice until the strength of periodic modulation is strong enough. The inverse participation ratios (IPRs) for all of the eigenstates are calculated. It is found that the localization properties of the quantum walker is mainly determined by the IPRs of the topologically protected edge states. More interestingly, the edge states are shown to have an evident ``repulsion'' effect on quantum walkers initiated from the lattice sites inside the bulk. Furthermore, we examine the role of nearest-neighbor interaction on the quantum walks of two identical fermions. Clear enhancement of the repulsion effect by strong interaction has been shown.
Quasiperiodic potentials can be used to interpolate between localization and delocalization in one dimension. With the rise of optical platforms engineering dipolar interactions, a key question is the stability of quasicrystalline phases under these long-range interactions. In this work, we study repulsive ultracold dipolar fermions in a quasiperiodic optical lattice to characterize the behavior of interacting quasicrystals. We simulate the full time evolution of the typical experimental protocols used to probe quasicrystalline order and localization properties. We extract experimentally measurable dynamical observables and correlation functions to characterize the three phases observed in the noninteracting setting: localized, intermediate, and extended. We then study the stability of such phases to repulsive dipolar interactions. We find that dipolar interactions can completely alter the shape of the phase diagram by stabilizing the intermediate phase, mostly at the expense of the extended phase. Moreover, in the strongly interacting regime, a resonance-like behavior characterized by density oscillations appears. Remarkably, strong dipolar repulsions can also localize particles even in the absence of quasiperiodicity if the primary lattice is sufficiently deep. Our work shows that dipolar interactions in a quasiperiodic potential can give rise to a complex, tunable coexistence of localized and extended quantum states.
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We study many-body localization (MBL) for interacting one-dimensional lattice fermions in random (Anderson) and quasiperiodic (Aubry-Andre) models, focusing on the role of interaction range. We obtain the MBL quantum phase diagrams by calculating the experimentally relevant inverse participation ratio (IPR) at half-filling using exact diagonalization methods and extrapolating to the infinite system size. For short-range interactions, our results produce in the phase diagram a qualitative symmetry between weak and strong interaction limits. For long-range interactions, no such symmetry exists as the strongly interacting system is always many-body localized, independent of the effective disorder strength, and the system is analogous to a pinned Wigner crystal. We obtain various scaling exponents for the IPR, suggesting conditions for different MBL regimes arising from interaction effects.
We present numerically exact non-equilibrium dynamics of a one-dimensional Bose gas in quasi-periodic lattice that plays an intermediate role between the long-ranged order and truly disordered systems exhibiting unusual correlated phases. Precision control over lattice depth, interaction strength and filling factor enables the exploration of various correlated phases in a finite periodic lattice. We investigate the system dynamics when the secondary incommensurate lattice is abruptly switched on. To solve the many-body Schroedinger equation, we employ the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). The many-body dynamics are analyzed through distinct measures of the Glauber correlation functions and dynamical fragmentation. Our study reveals four distinct scenarios of localization process in the non-equilibrium dynamics. Weakly interacting non-fragmented superfluid of incommensurate filling in the primary lattice exhibits collapse-revival dynamics of localization. In contrast, a fragmented superfluid with commensurate filling exhibits dynamical Mott localization. A strongly correlated, fully fragmented Mott state shows a subtle competition with localization introduced by the secondary lattice that merely melts the Mott correlations. Interestingly, in the fermionized Mott regime, where the density in each well is fragmented, the intra-dimer correlations exhibit unexpected robustness. These findings provide new insights into many-body correlation dynamics and novel localization mechanisms in quasi-periodic lattices, paving the way for engineering exotic quantum behaviors in ultracold atomic systems.