Heisenberg spin networks for realizing quantum battery with the aid of Dzyaloshinskii Moriya interaction

TL;DR

This work addresses scalable quantum batteries by analyzing Heisenberg spin networks with DMI across open, closed, and highly connected geometries, including the supercube and Platonic solids, under Ising and XXZ Hamiltonians. The authors implement a charging protocol with a tunable battery contribution and evaluate performance via ergotropy and charging power, revealing that symmetry-rich connectivities enable near-ideal sinusoidal charging cycles and complete discharge with minimal residual energy at optimal $D$ and $J$. A key finding is that the supercube, and more broadly symmetric $c$-regular graphs (notably the icosahedron), support robust energy transfer and scalability, while adding diagonals or excessive connectivity can degrade cyclical behavior. These results establish symmetry and coordination as design principles for scalable quantum batteries and provide open-source code for reproducibility.

Abstract

This work investigates the energy storage properties of quantum spin chains in the context of quantum batteries by introducing Heisenberg spin network models organized into different configurations, open, closed, supercube geometries, and c regular graphs. The charging dynamics of these systems are examined using Hamiltonians that include contributions from the battery, spin spin interactions, and a transverse magnetic field. Incorporating the Dzyaloshinskii Moriya interaction into the charging Hamiltonian is found to enhance the ergotropy in the XXZ model, particularly for the supercube configuration, thereby improving quantum battery performance. To explore the role of structural variations, we extend our study to c regular graphs with system sizes ranging from 3 to 12 qubits, including highly symmetric geometries such as the tetrahedron, octahedron, and icosahedron. These analyzes reveal that such symmetric structures retain ideal sinusoidal charging discharging behavior when DMI is tuned appropriately, establishing symmetry and coordination as key principles for scalable quantum battery architectures.

Figures (11)

• Figure 1: Visualizing possible inter-qubit interaction and connections developed during the evolution.
• Figure 2: Ergotropy for Ising model ($\delta = 1, \Delta = 0$) without DM interaction ($D = 0$)
• Figure 3: Power for Ising model ($\delta = 1, \Delta = 0$) without DM interaction ($D = 0$)
• Figure 4: Ergotropy for Ising model ($\delta = 1, \Delta = 0$) with DM interaction strength D = 0, 1, 2
• Figure 5: Power for Ising model ($\delta = 1, \Delta = 0$) with DM interaction strength D = 0, 1, 2