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Theory and Practice of Science and Technology

Domain Wall Confinement and Deconfinement under Pöschl-Teller Potential on Quantum Simulation

Sun Mingwei

Published Jan 1, 2026• 0 citations
Publisher

Abstract

We investigate domain wall confinement and deconfinement through quantum simulation of an effective low-energy Hamiltonian describing the relative motion of a domain wall pair. By mapping the problem onto a discretized Pöschl-Teller potential. Confinement, partial confinement and deconfinement regimes are identified via spatial variance and local probability observables. The close agreement between exact numeric and ideal quantum simulation highlights the emergent single particle description of domain wall physics. Experiments on IBM quantum hardware expose the role of noise and finite-depth dynamics in near-term simulations of non-equilibrium many-body phenomena.

DOI
10.47297/taposatwsp2633-456902.20260701

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We investigate domain wall confinement and deconfinement through quantum simulation of an effective low-energy Hamiltonian describing the relative motion of a domain wall pair. By mapping the problem onto a discretized Pöschl-Teller potential. Confinement, partial confinement and deconfinement regimes are identified via spatial variance and local probability observables. The close agreement between exact numeric and ideal quantum simulation highlights the emergent single particle description of domain wall physics. Experiments on IBM quantum hardware expose the role of noise and finite-depth dynamics in near-term simulations of non-equilibrium many-body phenomena.
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This work explores the qualitative dynamics of false vacuum decay in two dimensions, focusing on its realization through quantum annealing. Theoretical foundations are outlined and mapped onto quantum hardware, with several encoding strategies evaluated. Among these, the coupled domain wall encoding emerges as the most efficient, minimizing qubit usage while maintaining distance and rotational symmetries crucial for faithful modeling on a QPU. The study also addresses fidelity concerns: instead of the expected uniform distribution in the absence of an encoded potential, the coupled domain wall representation exhibited a bias toward anti-ferromagnetic states, which can be attributed to coupler imperfections. To mitigate this, techniques such as shimming and spin-reversal transformations were tested. Spin-reversal transformations proved to be most effective, both reducing variance as well as eliminating bias without requiring additional corrective iterations, thus offering a lightweight error-mitigation scheme. Building on this foundation, the decay process was simulated using modified Pöschl-Teller potentials combined with a local and global minimum. The results qualitatively reproduced the exponential decay, depending on the distance between the minima, in agreement with semiclassical quantum field theory.
The phenomenon of confinement is well known in high-energy physics and can also be realized for low-energy domain-wall excitations in one-dimensional quantum spin chains. A bound state consisting of two domain walls can behave like a meson, and recently, Vovrosh et al. [PRX Quantum 3, 040309 (2022)] demonstrated that a pair of mesons could dynamically form a metastable confinement-induced bound state (consisting of four domain walls) akin to a hadronic state. However, the protocol discussed by Vovrosh et al. involving the use of interactions with characteristically nonmonotonic distance dependence is not easy to come by in nature, thus posing a challenge for its experimental realization. In this regard, Rydberg atoms can provide the required platform for simulating confinement-related physics. We exploit the flexibility offered by interacting Rydberg-dressed atoms to engineering modified spin-spin interactions for the one-dimensional transverse-field Ising model. Our numerical simulations show how Rydberg-dressed interactions can give rise to a variety of effective potentials that are suitable for hadron formation, which opens the possibility of simulating confinement physics with Rydberg platforms as a viable alternative to current trapped-ion experiments.
Abstract Metastable domain-wall networks in correlated materials can relax on timescales vastly longer than the microscopic processes that move their elementary constituents. Motivated by the slow domain-wall rearrangements observed in 1T-TaS 2_22​ , we study a phenomenological spin model designed to isolate the interplay between local domain-wall hopping and environmental noise. The model contains discrete registry-like configurations, energetic costs for domain walls, and a transverse-field-induced hopping channel, and is implemented on a superconducting quantum annealer with more than 2000 logical degrees of freedom. A Schrieffer–Wolff analysis shows that the intrinsic hopping amplitude arises at second order in the transverse field and is therefore fast on device timescales. However, the measured reconfiguration rate saturates to a finite value at low effective temperature and depends only weakly on the hopping amplitude. This indicates that domain-wall motion is not limited by bare tunnelling, but by quasi-static longitudinal-field noise that detunes neighboring configurations and intermittently permits local hopping events. These results demonstrate how noise can slow domain-wall motion in a minimal quantum-simulation model and suggest a possible mechanism for ultra-slow relaxation in charge-ordered materials.