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arXiv:2311.14117 · Physical Review A

Flux-enhanced localization and reentrant delocalization in the quench dynamics of two interacting bosons on a Bose-Hubbard ladder

Mrinal Kanti Giri, Biswajit Paul, Tapan Mishra

Published Apr 9, 2024• 8 citations
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Abstract

We study the quench dynamics of two bosons possessing on-site repulsive interaction on a two-leg ladder and show that the presence of uniform flux piercing through the plaquettes of the ladder favors the localization of the bound states in the dynamics. We find that, when the two bosons are symmetrically initialized on the edge rung of the ladder, they tend to edge-localize in their quantum walk, a phenomenon which is not possible in the absence of flux. However, when the bosons are initialized on the bulk rung they never localize and exhibit linear spreading in their quantum walk. Interestingly, however, we find that, in the later case, a finite flux favors localization of the bulk bound states in the presence of sufficiently weak quasiperiodic disorder, which is otherwise insufficient to localize the particles in the absence of flux. In both cases, we obtain that the localization in the dynamics strongly depends on the combined effect of the flux and interaction strengths, as a result of which we obtain a signature of reentrant delocalization as a function of flux (interaction) for fixed interaction (flux) strengths.

DOI
10.1103/physreva.109.043308

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cond-mat.quant-gasCross-listedarXiv:2609.37059•Sep 30, 2026
We study the quench dynamics of two bosons possessing on-site repulsive interaction on a two-leg ladder and show that the presence of uniform flux piercing through the plaquettes of the ladder favors the localization of the bound states in the dynamics. We find that, when the two bosons are symmetrically initialized on the edge rung of the ladder, they tend to edge-localize in their quantum walk, a phenomenon which is not possible in the absence of flux. However, when the bosons are initialized on the bulk rung they never localize and exhibit linear spreading in their quantum walk. Interestingly, however, we find that, in the later case, a finite flux favors localization of the bulk bound states in the presence of sufficiently weak quasiperiodic disorder, which is otherwise insufficient to localize the particles in the absence of flux. In both cases, we obtain that the localization in the dynamics strongly depends on the combined effect of the flux and interaction strengths, as a result of which we obtain a signature of reentrant delocalization as a function of flux (interaction) for fixed interaction (flux) strengths.
We study the quantum walk of two interacting bosons on a two-leg ladder lattice in the presence of an artificial magnetic field. By considering a uniform flux piercing through the ladder, we show that in the limit of strong on-site repulsion and dominant rung hopping, an initially slow dynamics becomes fast, then slow and fast again with increase in the flux strength, indicating a re-entrant dynamics. This unusual behavior is found to be associated with the formation, breaking, and reformation of a bound pair state along the rung of the ladder. In addition to this we also find a reentrant behavior in the chiral dynamics where the chirality in the system first increases and then decreases with increase in interaction. We establish this unusual reentrant behavior in the dynamics by analyzing the radial velocity, spreading of correlation, center-of-mass shearing, and energy band diagrams.
Quantum simulation in experiments of many-body systems may bring new phenomena which are not well studied theoretically. Motivated by a recent work of quantum simulation on a superconducting ladder circuit, we investigate the rung-pair localization of the Bose-Hubbard ladder model without quenched disorder. Our results show that, in the hard-core limit, there exists a rung-pair localization both at the edges and in the bulk. Using the center-of-mass frame, the two-particle system can be mapped to an effective single-particle system with an approximate sublattice symmetry. Under the condition of the hard-core limit, the effective system is forced to have a defect at the left edge leading to a zero-energy flatband, which is the origin of the rung-pair localization. We also study the multiparticle dynamics of the Bose-Hubbard ladder model, which is beyond the single-particle picture. In this case, we find that the localization can still survive despite the existence of interaction between the pairs. Moreover, the numerical results show that the entanglement entropy exhibits a long-time logarithmic growth and the saturated values satisfy a volume law. This phenomenon implies that the interaction plays an important role during the dynamics, although it cannot break the localization. Our results reveal another interesting type of disorder-free localization related to a zero-energy flatband, which is induced by on-site interaction and specific lattice symmetry.
We investigate the quantum many-body dynamics of bosonic atoms hopping in a two-leg ladder with strong on-site contact interactions. We observe that when the atoms are prepared in a staggered pattern with pairs of atoms on every other rung, singlon defects, i.e., rungs with only one atom, can localize due to an emergent topological model, even though the underlying model in the absence of interactions admits only topologically trivial states. This emergent topological localization results from the formation of a zero-energy edge mode in an effective lattice formed by two adjacent chains with alternating strong and weak hoping links (Su-Schrieffer-Heeger chains) and opposite staggering which interface at the defect position. Our findings open the opportunity to dynamically generate nontrivial topological behaviors without the need for complex Hamiltonian engineering.
We investigate the quantum many-body dynamics of bosonic atoms hopping in a two-leg ladder with strong on-site contact interactions. We observe that when the atoms are prepared in a staggered pattern with pairs of atoms on every other rung, singlon defects, i.e., rungs with only one atom, can localize due to an emergent topological model, even though the underlying model in the absence of interactions admits only topologically trivial states. This emergent topological localization results from the formation of a zero-energy edge mode in an effective lattice formed by two adjacent chains with alternating strong and weak hoping links (Su-Schrieffer-Heeger chains) and opposite staggering which interface at the defect position. Our findings open the opportunity to dynamically generate nontrivial topological behaviors without the need for complex Hamiltonian engineering.
Flux ladders constitute the minimal setup enabling a systematic understanding of the rich physics of interacting particles subjected simultaneously to strong magnetic fields and a lattice potential. In this paper, the ground-state phase diagram of a flux-ladder model is mapped out using extensive density-matrix renormalization-group simulations. The emphasis is put on parameters which can be experimentally realized exploiting the internal states of potassium atoms as a synthetic dimension. The focus is on accessible observables such as the chiral current and the leg-population imbalance. Considering a particle filling of one boson per rung, we report the existence of a Mott-insulating Meissner phase as well as biased-ladder phases on top of superfluids and Mott insulators. Furthermore, we demonstrate that quantum quenches from suitably chosen initial states can be used to probe the equilibrium properties in the transient dynamics. Concretely, we consider the instantaneous turning on of hopping matrix elements along the rungs or legs in the synthetic flux-ladder model, with different initial particle distributions. We show that clear signatures of the biased-ladder phase can be observed in the transient dynamics. Moreover, the behavior of the chiral current in the transient dynamics is discussed. The results presented in this paper provide guidelines for future implementations of flux ladders in experimental setups exploiting a synthetic dimension.
Proximity effects, in which one subsystem imprints its properties onto another, offer a route to controlling quantum matter. For localization, this raises the question of whether an extended system can be localized by its neighbor, and then delocalized again, in the regime of weak quasiperiodic disorder. Here, we demonstrate this behavior in a coupled Aubry--André ladder, where a staggered detuning applied to only one leg localizes the neighboring, undetuned leg through inter-leg hybridization, even before the detuned leg itself localizes. Upon further increasing the detuning, the undetuned leg undergoes re-entrant delocalization, while the detuned leg remains localized. Finite-size scaling supports the persistence of these regimes in the thermodynamic limit. On an IBM Quantum processor, we experimentally observe their dynamical signatures: strongly suppressed wave-packet spreading in the proximity-localized regime and its recovery upon re-entrant delocalization. Our results establish leg-selective detuning as a reversible control knob for localization and transport in coupled quantum systems.