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arXiv:2502.19561 · Advanced Quantum Technologies

Quantum Level‐Crossing Induced by Anisotropy in Spin‐1 Heisenberg Dimers: Applications to Quantum Stirling Engines

Bastián Castorene, V. G. de Paula, Francisco J. Peña, Clebson Cruz, Mario Reis, Patricio F. Vargas

Published Jul 1, 2025• 6 citations
arXivHTMLPDF

Abstract

Abstract This work explores the thermodynamic performance of a quantum Stirling heat engine implemented with an anisotropic spin‐1 Heisenberg dimer as the working medium. Using the Hamiltonian of the system, the interplay of anisotropy, magnetic field, and exchange interactions and their influence is analyzed on the energy spectrum and the quantum level crossing. These results reveal that double‐degenerate point (DDP) and a triple‐degenerate point (TDP) play pivotal roles in shaping the operational regimes and efficiency of the quantum Stirling engine. At those points, the Carnot efficiency reaches higher work output and enhanced stability, making it a robust candidate for optimal thermodynamic performance. These findings highlight the potential of anisotropic spin systems as viable platforms for quantum heat engines and contribute to advancing the field of quantum thermodynamics.

DOI
10.1002/qute.202500204

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Abstract This work explores the thermodynamic performance of a quantum Stirling heat engine implemented with an anisotropic spin‐1 Heisenberg dimer as the working medium. Using the Hamiltonian of the system, the interplay of anisotropy, magnetic field, and exchange interactions and their influence is analyzed on the energy spectrum and the quantum level crossing. These results reveal that double‐degenerate point (DDP) and a triple‐degenerate point (TDP) play pivotal roles in shaping the operational regimes and efficiency of the quantum Stirling engine. At those points, the Carnot efficiency reaches higher work output and enhanced stability, making it a robust candidate for optimal thermodynamic performance. These findings highlight the potential of anisotropic spin systems as viable platforms for quantum heat engines and contribute to advancing the field of quantum thermodynamics.
Quantum heat engines have attracted significant attention in recent years due to their potential to surpass classical thermodynamic limits by leveraging quantum effects such as entanglement and coherence. In this study, we analyze a quantum Stirling heat engine characterized by a working substance composed of a two-particle Heisenberg model with Dzyaloshinskii–Moriya (DM) interaction under an external magnetic field. We investigate the impact of the antisymmetric interaction on the engine’s efficiency across varying coupling parameters. Our findings demonstrate that the utilization of a two-qubit Heisenberg model in an entangled quantum Stirling heat engine can significantly enhance efficiency and performance. By optimizing the antisymmetric exchange parameters, we achieve substantial enhancements in engine efficiency, with results demonstrating that the efficiency attains remarkably high values compared to other cycles utilizing the same working substance. These enhancements are primarily influenced by the DM interaction and the entangled states of the working substance, leading to superior performance.
ABSTRACT We investigate a quantum Stirling engine whose working medium is a three‐qubit Heisenberg XXZ spin chain incorporating the Dzyaloshinskii‐Moriya interaction. The integration of a regenerator, which recovers internal energy during the isochoric processes, significantly enhances the efficiency of the engine, allowing it to approach the Carnot efficiency under appropriate parameters. Our analysis reveals a pronounced stage dependence of quantum correlations: at the end of the isothermal expansion, quantum entanglement and coherence of the thermal equilibrium state are positively correlated with the cycle efficiency, whereas at the end of the isothermal compression, they are negatively correlated with the efficiency. Furthermore, we demonstrate how external magnetic fields and coupling coefficients regulate these quantum correlations and the engine performance, including the work output and efficiency. This work provides a systematic comparison of the stage‐dependent roles of entanglement and coherence in a three‐qubit Stirling cycle, offering insights for designing high‐performance regenerative quantum thermal devices.
This study investigates the anisotropic effects on a system of three qubits with chain and ring topology, described by the antiferromagnetic Heisenberg XXX model subjected to a homogeneous magnetic field. We explore the Stirling and Otto cycles and find that easy-axis anisotropy significantly enhances engine efficiency across all cases. At low temperatures, the ring configuration outperforms the chain on both work and efficiency during the Stirling cycle. Additionally, in both topologies, the Stirling cycle achieves Carnot efficiency with finite work at quantum critical points. In contrast, the quasistatic Otto engine also reaches Carnot efficiency at these points but yields no useful work. Notably, the Stirling cycle exhibits all thermal operational regimes-engine, refrigerator, heater, and accelerator-unlike the quasistatic Otto cycle, which functions only as an engine or refrigerator.
A properly selected quantum heat engine consumes resources efficiently. Also, there are many parameters to determine the right option. In this study, we construct and compare the quantum mechanical counterparts of Stirling and Otto cycles for an experimentally achievable quantum working medium where two spins 1/2 interact through isotropic Heisenberg interaction in the tunable external magnetic field. We consider two comparison cases that operate heat cycles with the same system parameters or equal efficiencies. The quantum Stirling cycle produces more work than that of the Otto cycle under the same parameters or equal efficiency conditions. The quantum Stirling engine operates a wider range of coupling strengths. The work performed in the cycles is enhanced by coupling strength. On the other hand, we investigate the role of coupling strength on the performance of the non-regenerative quantum Stirling heat cycle under various magnitudes of the magnetic field. The distance between the applied magnetic fields at the initial and final points of the isothermal stage is found to be an enhancer for the work output and efficiency of the quantum Stirling cycle.
We study a quantum Otto heat engine whose working substance is an anisotropic two-qubit Heisenberg XYZ model. Independent local magnetic fields are used to control each spin individually. The influence of the longitudinal coupling, anisotropy, transverse coupling, and local fields on the net work output and efficiency is systematically examined. Reducing the longitudinal coupling is found to markedly improve both the maximum work and the peak efficiency. The engine performance reaches an optimum at a particular value of the anisotropy parameter. A local work analysis clarifies how work is produced during the cycle. Because of the asymmetric local fields and the intrinsic spin-spin interaction, the two qubits play markedly different thermodynamic roles; the interaction term itself contributes crucially to the total work. We further analyze the variation of quantum entanglement, quantified by concurrence, along the cycle. The results indicate that a pronounced change in entanglement between the hot and cold isomagnetic strokes is closely correlated with the efficiency enhancement. This work offers new insight into the operating principles and control of quantum Otto heat engines.
Recently, the influences of the Dzyaloshinski-Moriya (DM) interaction on the performances of the basic thermo-dynamical quantities have attracted a lot of attention. A large number of investigations on the quantum coupling systems with DM interaction have been carried out. However, the specific effects of spin-orbit coupling with the performance on the quantum heat engine have not been taken into account in previous studies. DM interaction is a special kind spin-orbit coupling. To enrich the research of the quantum heat engines, the investigation about the effect of DM interaction on its thermodynamic characteristics should be included. In this study, we construct two entangled quantum engines based on spin-1/2 systems with different DM interactions, with the spin exchange constant and magnetic field fixed. The quantum Otto engine and the quantum Stirling engine are discussed in this article. By numerical calculation, we obtain the expressions for several thermodynamic quantities and plot the isoline maps of the variation of the basic thermodynamic quantities such as heat transfer, work with D1 and D2 and their efficiency in the two engines. The results indicate that the DM interaction plays an important role in the thermodynamic quantities for the quantum Otto engine and the quantum Stirling engine. In addition, the positive work condition is discussed with different DM interactions, with the spin exchange constant and magnetic field. Furthermore fixed, it is found that the efficiency of quantum Otto engine cycle is smaller than the Carnot efficiency while the quantum Stirling cycle can exceed the Carnot efficiency by using the regenerator. Finally, the second law of thermodynamics is shown to be valid in the two entangled quantum systems.