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

TL;DR

This paper explores how different geometrical arrangements of Heisenberg spin networks, enhanced with Dzyaloshinskii Moriya interaction, can improve quantum battery performance by increasing ergotropy and maintaining ideal charging behavior.

Contribution

It introduces new configurations of spin networks and demonstrates how Dzyaloshinskii Moriya interaction enhances energy storage and charging efficiency in quantum batteries.

Findings

DMI increases ergotropy in XXZ models, especially in supercube configurations.

Symmetric geometries like tetrahedron and icosahedron maintain sinusoidal charging behavior.

Structural symmetry and coordination are key for scalable quantum battery design.

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.

Tables

Table 1. Table 1 : Different quantum battery structures with their corresponding DMI strength (D) for which ergotropy follows a sinusoidal curve

No. of qubits (n)	No. of connections (c)	DMI strength (D)
3	2	1.86
4	3	1.96
5	4	2.03
6	4	2.18
	5	2.07
7	6	2.11
8	5	2.30
	6	2.23
	7	2.13
9	6	2.36
	8	2.15
10	7	2.33
	8	2.25
	9	2.17
11	8	2.35
	10	2.18
12	7	2.52
	8	2.46
	9	2.33
	10	2.27
	11	2.20

Equations

$$H_B=\hslash {\omega }_0\sum _{i=1}^n{\sigma }_i^z,$$

$$|\psi (0)⟩=|\downarrow {⟩}^{\otimes n}.$$

$$H_C=H_x+H_{HS}+H_{DMz}.$$

$$H_x=\hslash \Omega \sum _{i=1}^n{\sigma }_i^x,$$

$$H_{HS}=\sum _{<i,j>}{J}_{ij}\overrightarrow{{\sigma }_i}\cdot \overrightarrow{{\sigma }_j},$$

$$H_{HS}=J\sum _{i<j}[(1+\delta ){\sigma }_i^x{\sigma }_j^x+(1-\delta ){\sigma }_i^y{\sigma }_j^y+\Delta {\sigma }_i^z{\sigma }_j^z]$$

$$H_{DM}=\sum _{i<j}\vec{D}\cdot ({\vec{\sigma }}_i\times {\vec{\sigma }}_j),$$

$${\color[rgb]{0,0,0}H_{DMz}=D_{z}\sum_{i<j}\left(\sigma_{i}^{x}\sigma_{j}^{y}-\sigma_{i}^{y}\sigma_{j}^{x}\right),}$$

$$H(t)=\{\begin{array}{ll}{H}_B,& t<0,\\ H_C+\lambda H_B,& 0\le t\le \tau ,\\ H_B,& t>\tau ,\end{array}$$

$$U=e^{-i(H_C+\lambda H_B)t}.$$

$$H_{int}$$

$$+D\sum _{i=1}^{n-1}({\sigma }_i^x{\sigma }_{i+1}^y-{\sigma }_i^y{\sigma }_{i+1}^x).$$

$$H_{int}$$

$$+D\sum _{i=1}^n({\sigma }_i^x{\sigma }_{i+1}^y-{\sigma }_i^y{\sigma }_{i+1}^x),$$

$$H_{int}$$

$$+\Delta {\sigma }_i^z{\sigma }_{i+1}^z]+D\sum _{i=1,i\in Z_{odd}}^8({\sigma }_i^x{\sigma }_{i+1}^y-{\sigma }_i^y{\sigma }_{i+1}^x)\}$$

$$+\{J\sum _{i=1,2,5,6}[(1+\delta ){\sigma }_i^x{\sigma }_{i+2}^x+(1-\delta ){\sigma }_i^y{\sigma }_{i+2}^y$$

$$+\Delta {\sigma }_i^z{\sigma }_{i+2}^z]+D\sum _{i=1,2,5,6}({\sigma }_i^x{\sigma }_{i+2}^y-{\sigma }_i^y{\sigma }_{i+2}^x)\}$$

$$+\{J\sum _{i=1}^4[(1+\delta ){\sigma }_i^x{\sigma }_{i+4}^x+(1-\delta ){\sigma }_i^y{\sigma }_{i+4}^y+\Delta {\sigma }_i^z{\sigma }_{i+4}^z]$$

$$+D\sum _{i=1}^4({\sigma }_i^x{\sigma }_{i+4}^y-{\sigma }_i^y{\sigma }_{i+4}^x)\}.$$

$$\zeta =\text{Tr}[H_B(\rho (t)-{\rho }_p)].$$

$$\zeta =⟨\psi (t)|H_B|\psi (t)⟩-{ϵ}_0,$$

$$P(t)=\frac{\zeta }{t}.$$

$$H_{int}$$

$$+D\sum _{(i,j)\in edges}{\sigma }_i^x{\sigma }_j^y-{\sigma }_i^y{\sigma }_j^x$$

Full text

Quantum Spin Chain, Quantum Battery, Dzyaloshinskii-Moriya interaction

††preprint: APS/123-QED

I Introduction

As classical electronics approach atomic-scale limits, quantum effects have become unavoidable in modern semiconductor devices operating at $3$–$5$ nanometers. This fundamental shift challenges conventional design and opens new avenues for quantum-enhanced technologies. Future technologies must therefore account for and utilize quantum phenomena such as superposition, entanglement, and interference [Horodecki2009] to exceed the capabilities of classical systems. Recent advances in the control of small quantum systems have facilitated the convergence of quantum information science [nielsen2010quantum] and thermodynamic principles, leading to the emergence of quantum thermodynamics [Vinjanampathy01102016, binder2018thermodynamics] as a distinct research domain.

A key application of quantum thermodynamics is the design of quantum batteries (QBs)- energy storage devices composed of quantum systems. The concept was first proposed by Alicki and Fannes [Alicki2013], and has since evolved through studies exploring the role of quantum coherence, many-body interactions, and collective charging in enhancing charging power and extractable work [bhattacharjee2021quantum, quach2023quantum, binder2018thermodynamics, Campaioli_2017, Ferraro2018, Quantum_vs_classical, global_ops, energy_transfer, Farre2020, Modi2011, Giorgi_2015]. QBs are typically charged through unitary operations, enabling minimal entropy production and potentially offering a quantum advantage over classical batteries. Additionally, recent experimental progress in constructing a nanographene-based spin-$\frac{1}{2}$ chain with tunable length [zhao2025spin] motivates the study of models that may be experimentally realizable.

Despite this progress, two critical gaps remain in the theoretical design of quantum batteries. Most existing studies focus on linear spin chains, central spin configurations, or all-to-all coupling schemes, with limited exploration of complex connectivity patterns [Sachdev1993, Rossini2020, kim2022]. Second, the role of anisotropic interactions- particularly the Dzyaloshinskii–Moriya interaction (DMI), which is known to induce spin canting and enhance entanglement- has not been adequately studied in structured spin networks. While some works have incorporated DMI in basic QB models, its combined influence with interaction topology on charging dynamics in scalable architectures [many-body-QB] remains largely unaddressed. In this work, we address these gaps by constructing and analyzing Heisenberg spin network quantum battery models across a variety of configurations. We begin with eight qubits arranged in three representative topologies- open chain, closed chain [Zheng2025], and a ”supercube” structure- as illustrated in Fig. 1. We then 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. In all cases, we incorporate anisotropic Heisenberg interactions and DMI into the charging Hamiltonian and evaluate performance using two established metrics: ergotropy (maximum extractable work) and charging power. Our approach builds on the spin chain model introduced in [many-body-QB], focusing specifically on antiferromagnetic Heisenberg spin chain Hamiltonians to construct QBs. Quantum batteries can be charged using either the parallel charging mode, where local fields act independently on each qubit, or the collective charging mode, where an interaction Hamiltonian acts globally on the system [Binder2015, Kamin_2_3_qb]. Prior studies have shown that collective charging provides a quantum advantage over parallel charging [Quantum_vs_classical, PhysRevResearch.4.043150, Peng2021, global_ops, kim2022].

Our results show that the supercube configuration, under specific interaction strengths (Heisenberg coupling $J=1$, DMI strength $D=1.7$), achieves a near-ideal sinusoidal charging-discharging cycle with negligible residual energy. By contrast, open and closed chains display reduced performance and irregular charging patterns, particularly in the presence of DMI. We further analyze the role of system size by varying the number of qubits and by enriching connectivity through additional couplings (e.g., body and face diagonals). These studies reveal that interaction strengths must be carefully tuned to preserve periodic and efficient energy transfer. Notably, highly symmetric geometries such as Platonic solids yield results comparable to or surpassing the supercube, highlighting the importance of uniform connectivity in stabilizing charging dynamics. To systematically probe scalability, we extend our study to a broad class of $c$-regular graphs with system sizes ranging from 3 to 12 qubits. This framework encompasses both generic regular connectivities and highly symmetric polyhedral skeletons, including the tetrahedron, octahedron, and icosahedron. At suitable DMI strengths, all of these structures exhibit ideal sinusoidal charging–discharging cycles, establishing symmetry and coordination as central design principles for scalable quantum batteries. We additionally provide a more detailed analysis of how the DM interaction influences the population dynamics of the eigenstates and how this behavior depends on the underlying geometry, presented in the newly added Appendix section. This expanded analysis further allows us to confirm that the observed charging behavior does not originate from specific initial states or limited parameter choices; rather, it helps diagnose whether features such as enhanced charging arise from interaction-driven dynamics instead of entanglement effects. Placing these results in the Appendix enables readers to explore the full dynamical behavior without interrupting the flow of the main discussion, while still keeping all supporting analyzes readily accessible. These findings indicate that charging efficiency, stability, and periodicity can be systematically engineered through interaction geometry, providing a new design axis for quantum energy storage systems and pointing toward strategies for scaling QBs beyond small sizes.

The structure of the article is as follows: Section II presents the proposed models, including their Hamiltonians and geometries (Section II.1), and performance metrics (Section II.2). Section III presents the results and comparative analysis across various models. Additionally, Appendix A provides an analysis of population dynamics with and without DMI. The study concludes in Section IV.

II Model and Performance Metrics for Quantum Battery