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arXiv:2512.15130 · Journal of Statistical Mechanics Theory and Experiment

Defect-Driven Nonlinear and Nonlocal Perturbations in Quantum Chains

Anish Acharya, Luca Giuggioli, Shamik Gupta

quant-phcond-mat.stat-mechSubmitted Dec 17, 2025• Announced Dec 18, 2025• 1 citation
v1 · Dec 17, 2025v2 · Apr 13, 2026
arXivHTMLPDF

Abstract

Transport and localization in isolated quantum systems are typically attributed to spatially-extended disorder, leaving the influence of a few controllable defects largely unexplored despite their relevance to engineered quantum platforms. We introduce an analytic framework showing how a single defect profoundly reshapes wave-function spreading on a finite isolated and periodic tight-binding lattice. Adapting the defect technique from classical random-walk studies, we obtain exact time-resolved site-occupation probabilities and several observables of interest. Even one defect induces striking nonlinear and nonlocal effects, including non-monotonic suppression of transport, enhanced localization at distant sites, and strong sensitivity to the initial particle position at long times. These results demonstrate that minimal perturbations can generate unexpected long-time transport signatures, establishing a microscopic defect-driven mechanism of quantum localization.

Journal reference
J. Stat. Mech.: Theory Exp. 043102 (2026)
DOI
10.1088/1742-5468/ae5f82
Comments
6 figures, supplementary information added

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Transport and localization in isolated quantum systems are typically attributed to spatially-extended disorder, leaving the influence of a few controllable defects largely unexplored despite their relevance to engineered quantum platforms. We introduce an analytic framework showing how a single defect profoundly reshapes wave-function spreading on a finite isolated and periodic tight-binding lattice. Adapting the defect technique from classical random-walk studies, we obtain exact time-resolved site-occupation probabilities and several observables of interest. Even one defect induces striking nonlinear and nonlocal effects, including non-monotonic suppression of transport, enhanced localization at distant sites, and strong sensitivity to the initial particle position at long times. These results demonstrate that minimal perturbations can generate unexpected long-time transport signatures, establishing a microscopic defect-driven mechanism of quantum localization.
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Abstract Particle transport and localization phenomena in condensed-matter systems can be modeled using a tight-binding lattice Hamiltonian. The ideal experimental emulation of such a model utilizes simultaneous, high-fidelity control and readout of each lattice site in a highly coherent quantum system. Here, we experimentally study quantum transport in one-dimensional and two-dimensional tight-binding lattices, emulated by a fully controllable 3 × 3 array of superconducting qubits. We probe the propagation of entanglement throughout the lattice and extract the degree of localization in the Anderson and Wannier-Stark regimes in the presence of site-tunable disorder strengths and gradients. Our results are in quantitative agreement with numerical simulations and match theoretical predictions based on the tight-binding model. The demonstrated level of experimental control and accuracy in extracting the system observables of interest will enable the exploration of larger, interacting lattices where numerical simulations become intractable.
Abstract In this work, we study in the framework of the so-called driven tight-binding chain (TBC) the issue of quantum unitary dynamics interspersed at random times with stochastic resets mimicking non-unitary evolution due to interactions with the external environment, the driven TBC involves a quantum particle hopping between the nearest-neighbour sites of a one-dimensional lattice and subject to an external forcing field that is periodic in time. We consider the resets to be taking place at exponentially-distributed random times. Using the method of stochastic Liouville equation, we derive exact results for the probability at a given time for the particle to be found on different sites and averaged with respect to different realizations of the dynamics. We establish the remarkable effect of localization of the TBC particle on the sites of the underlying lattice at long times. The system in the absence of stochastic resets exhibits delocalization of the particle, whereby the particle does not have a time-independent probability distribution of being found on different sites even at long times, and, consequently, the mean-squared displacement of the particle about its initial location has an unbounded growth in time. One may induce localization in the bare model only through tuning the ratio of the strength to the frequency of the field to have a special value, namely, equal to one of the zeros of the zeroth order Bessel function of the first kind. We show here that localization may be induced by a far simpler procedure of subjecting the system to stochastic resets.