We show that ferromagnetic interactions can enhance the adiabatic performance of a quantum spin chain engine at low temperatures. The enhancement in work output is particular pronounced, increasing exponentially with interaction strength. The performance enhancement occurs in the paramagnetic phase and is qualitatively explained by considering just the ground and first excited state, in which case the system exhibits bipartite entanglement. As the temperature is increased, thermal occupation of higher energy states diminishes performance. We find that these thermal fluctuations are smallest for long-range interactions, resulting in the highest efficiency. Diabatic work extraction degrades performance due to quantum friction. We identify an approximate, experimentally realisable counterdiabatic drive that can mitigate friction for weak interactions.
We show that ferromagnetic interactions can enhance the adiabatic performance of a quantum spin chain engine at low temperatures. The enhancement in work output is particular pronounced, increasing exponentially with interaction strength. The performance enhancement occurs in the paramagnetic phase and is qualitatively explained by considering just the ground and first excited state, in which case the system exhibits bipartite entanglement. As the temperature is increased, thermal occupation of higher energy states diminishes performance. We find that these thermal fluctuations are smallest for long-range interactions, resulting in the highest efficiency. Diabatic work extraction degrades performance due to quantum friction. We identify an approximate, experimentally realisable counterdiabatic drive that can mitigate friction for weak interactions.
Although the idea of combining thermodynamics with quantum mechanics is more than a century old, quantum thermodynamics has seen significant development over the past few decades. Understanding work, heat, and entropy in the quantum regime has become increasingly important, particularly in light of advances in quantum technologies. This thesis investigates work processes in quantum spin chains. Quantum work processes can involve genuinely quantum features such as entanglement, coherence, and measurement back-action, which are absent in classical thermodynamic descriptions, making their characterization an area of ongoing interest in quantum thermodynamics. Focusing first on a single work step, we show that the frictional work due to finite-time driving for a non-integrable quantum spin chain can be well quantified by the diagonal entropy production. We further demonstrate that integrability breaking enhances work extraction in the adiabatic limit, while suppressing it in the non-adiabatic regime. We then study a quantum Otto cycle using the transverse-field Ising model as the working substance. We determine how different types of operation (engine, refrigerator, accelerator, heater) can emerge for different parameter regimes. We show that with infinitesimal work strokes, a thermal machine behaves either as an engine or an accelerator, and that these regimes can be characterized by equilibrium transverse magnetization. At low temperatures, these regimes are governed by low-energy excitations, while at high temperatures they follow from a free-energy expansion in inverse temperature. Frictional effects can emerge and suppress the engine performance during non-adiabatic driving. We show that these effects can be mitigated using an optimised drive protocol based on a geometric formulation of the path of the system through parameter space. Overall, this thesis provides a comprehensive understanding of how integrability, coherence, finite-time driving, and non-adiabatic transitions govern work extraction and thermal machine operation in quantum spin chains, and paves the way for understanding these processes in other quantum many-body systems.
Abstract We start with a revision study of two coupled spin- 1 / 2 under the influence of Kaplan–Shekhtman–Entin-Wohlman–Aharony interaction and a magnetic field. We first show the role of idle levels, i.e. levels that do not couple to the external magnetic field, when the system is working as a heat engine as well as when it is a refrigerator. Then we extend the results reported in Altintas and Müstecaplıoğlu (2015 Phys. Rev. E 92 022142) by showing that it is not necessary to change both the magnetic field as well as the coupling parameters to break the extensive property of the work extracted globally from two coupled spin- 1 / 2 as has been demonstrated there. Then we study the role of increasing the number of coupled spins on efficiency, extractable work, and coefficient of performance (COP). First, we consider two- and three-coupled spin- 1 / 2 Heisenberg X X X -chain. We prove that the latter can outperform the former in terms of efficiency, extractable work, and COP. Then we consider the Ising model, where the number of interacting spins ranges from two to six. We show that only when the number of interacting spins is odd the system can work as a heat engine in the strong coupling regime. The enhancements in efficiency and COP are explored in detail. Finally, this model confirms the idea that entanglement and quantum correlations are not the reasons behind the enhancements observed in efficiency, extractable work, and COP, but only due to the structure of the energy levels of the Hamiltonian of the working substance. In addition to this, the extensive property of global work as well, is not affected by entanglement and quantum correlations.
The maximum work extractable from a quantum system is achieved when the system is driven adiabatically. Frictional work ⟨W⟩fric then quantifies the difference in work output between adiabatic and non-adiabatic driving. Here we show that frictional work in a non-integrable spin chain is well-characterized by the diagonal entropy production ΔSd associated with the build up of quantum coherence. We show that, over a broad range of parameters, ⟨W⟩fric≈TτΔSd, with Tτ the effective temperature of the final time-evolved state. The relationship breaks down for fast protocols at low temperatures, in which case frictional work is instead well-described by the quantum relative entropy between the time-evolved state and a Gibbs-state approximation of the adiabatic state. We compare our results to those obtained from an integrable spin chain, in which case the system is no longer described by a single temperature. In this case, the frictional work is described by a sum of terms for each independent subspace of the spin chain, which are at different effective temperatures. Finally, we show how integrability breaking can enhance work extraction in the adiabatic limit, but degrade work extraction in sufficiently non-adiabatic regimes.
Abstract Long-range interacting quantum devices provides a promising route for quantum technology applications. Here, the presence of long-range interactions is shown to enhance the performances of a quantum heat engine featuring a many-body working substance. We focus on the paradigmatic example of a Kitaev chain undergoing a quantum Otto cycle and show that a substantial thermodynamic advantage may be achieved as the range of the interactions among its constituents increases. The advantage is most significant for the realistic situation of a finite time cycle: the presence of long-range interactions reduces the non-adiabatic energy losses, by suppressing the detrimental effects of dynamically generated excitations. This effect allows mitigating the trade-off between power and efficiency, paving the way for a wide range of experimental and technological applications.
We propose a many-body quantum engine powered by the energy difference between the entangled ground state of the interacting system and local separable states. Performing local energy measurements on an interacting many-body system can produce excited states from which work can be extracted via local feedback operations. These measurements reveal the quantum vacuum fluctuations of the global ground state in the local basis and provide the energy required to run the engine. The reset part of the engine cycle is particularly simple: The interacting many-body system is coupled to a cold bath and allowed to relax to its entangled ground state. We illustrate our proposal on two types of many-body systems: A chain of coupled qubits and coupled harmonic oscillator networks. These models faithfully represent fermionic and bosonic excitations, respectively. In both cases, analytical results for the work output (average value and standard deviation) and efficiency of the engine are derived. We prove the efficiency is controlled by the ``local entanglement gap,'' the energy difference between the many-body ground state and the lowest-energy eigenstate of the local Hamiltonian. In all the examples analyzed in this work, for a large number of coupled subsystems, the average work output scales linearly or faster and dominates over fluctuations, while the efficiency limits to a constant. In the qubit chain case, we highlight the impact of a quantum phase transition on the engine's performance as work and efficiency sharply increase at the critical point. In the case of a one-dimensional oscillator chain, we show the efficiency approaches unity as the number of coupled oscillators increases, even at finite work output.
We examine a quantum heat engine with an interacting many-body working medium consisting of the long-range Kitaev chain to explore the role of long-range interactions in the performance of the quantum engine. By analytically studying two types of thermodynamic cycles, namely, the Otto cycle and Stirling cycle, we demonstrate that the work output and efficiency of a long-range interacting heat engine can be boosted by the long-range interactions, in comparison to the short-range counterpart. We further show that in the Otto cycle there exists an optimal condition for which the maximum enhancement in work output and efficiency can be achieved simultaneously by the long-range interactions. But, for the Stirling cycle, the condition which can give the maximum enhancement in work output does not lead to the maximum enhancement in efficiency. We also investigate how the parameter regimes under which the engine performance is enhanced by the long-range interactions evolve with a decrease in the range of interactions.