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arXiv:2407.04101 · Physical Review Letters

Universal Work Statistics in Long-Range Interacting Quantum Systems

Andrea Solfanelli, Nicolò Defenu

Published Jan 23, 2025• 4 citations
arXivHTMLPDF

Abstract

We determine the conditions under which the presence of long-range interactions reduce the energy losses due to defect generation during nonadiabatic evolution, crucial for enhancing the power to efficiency ratio of quantum thermal devices. In order to do so, we investigate the response of long-range systems to diverse external drivings, emphasizing their robustness against dynamic excitation in comparison to generic local systems. This phenomenon is demonstrated through the study of the quantum work statistics, revealing insights into energy transfer efficiency and dynamical quantum criticality. Our results demonstrate the benefits of including a long-range interacting medium for quantum thermodynamics application, highlighting the potential to optimize finite-time quantum thermal cycles. Thanks to the effective dimension approach our findings can be drawn in full generality and, then, specified to different experimentally relevant scenarios.

DOI
10.1103/physrevlett.134.030402

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We determine the conditions under which the presence of long-range interactions reduce the energy losses due to defect generation during nonadiabatic evolution, crucial for enhancing the power to efficiency ratio of quantum thermal devices. In order to do so, we investigate the response of long-range systems to diverse external drivings, emphasizing their robustness against dynamic excitation in comparison to generic local systems. This phenomenon is demonstrated through the study of the quantum work statistics, revealing insights into energy transfer efficiency and dynamical quantum criticality. Our results demonstrate the benefits of including a long-range interacting medium for quantum thermodynamics application, highlighting the potential to optimize finite-time quantum thermal cycles. Thanks to the effective dimension approach our findings can be drawn in full generality and, then, specified to different experimentally relevant scenarios.
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.
The nonequilibrium thermodynamics of interacting quantum many-body systems is investigated within the framework of thermal time-dependent density functional theory using a generalized linear-response formulation for the full quantum work statistics. A first-principles route is established to reconstruct the relaxation function that underlies linear-response theory, thereby moving beyond phenomenological descriptions and enabling a consistent evaluation of all moments of the dissipated-work distribution in interacting systems. The predictive power of the approach is demonstrated for the Hubbard model subject to a staggered external potential, where the evolution of the relaxation dynamics during the Mott-to-band-insulator crossover reveals how distinct many-body phases shape the out-of-equilibrium thermodynamic response. These results provide a microscopic and transferable framework for quantum thermodynamics in correlated systems, bridging thermal density functional theory and nonequilibrium work statistics.
Enhanced experimental capabilities to control nonlocal and power-law decaying interactions are currently fueling intense research in the domain of quantum many-body physics. Compared to their counterparts with short-ranged interactions, long-range interacting systems display novel physics, such as nonlinear light cones for the propagation of information or inequivalent thermodynamic ensembles. In this work, we consider generic long-range open quantum systems in arbitrary dimensions and focus on the so-called strong long-range regime. We prove that in the thermodynamic limit local properties, captured by reduced quantum states, are described by an emergent noninteracting theory. Here, the dynamics factorizes and the individual constituents of the system evolve independently such that no correlations are generated over time. In this sense, long-range interacting systems are locally noninteracting. This has significant implications for their relaxation behavior, for instance, in relation to the emergence of long-lived quasistationary states or to the absence of thermalization.
Quantum thermalization of closed systems -- i.e. the relaxation of local properties to their thermodynamic value along the Hamiltonian evolution -- is generically expected in non-integrable systems at finite energy density. In this work we show that quantum spin systems with at least one spin component coupled through long-range ferromagnetic interactions, and a second spin component coupled to a field, cannot in general thermalize to a paramagnetic state whenever they have a finite, negative energy per spin. The long-range interactions we consider decay as a power law of the distance, ∼r−α\sim r^{-α}∼r−α with α<dα< dα<d, where ddd is the number of spatial dimensions of the system. The lack of thermalization is generic to an infinite family of Hamiltonians, and it is not associated to any form of integrability. It can instead be understood by the anomalous features of the thermodynamics of the system in the paramagnetic phase, which cannot be reflected in the properties of the eigenstates. This leads to a breakdown of eigenstate typicality and of the eigenstate thermalization hypothesis. Interestingly, the non-thermal states emerging at long times in the dynamics display long-range multipartite entanglement, elevating the breakdown of thermalization to a resource.
Long-range interacting systems such as nitrogen vacancy centers in diamond and trapped ions serve as useful experimental setups to probe a range of nonequilibrium many-body phenomena. In particular, via driving, various effective Hamiltonians with physics potentially quite distinct from short-range systems can be realized. In this Letter, we derive general bounds on the linear response energy absorption rates of periodically driven systems of spins or fermions with long-range interactions that are sign changing and fall off as 1/rα1/r^\alpha1/rα with α>d/2\alpha > d/2α>d/2. We show that the disordered averaged energy absorption rate at high temperature decays exponentially with the driving frequency. This strongly suggests the presence of a prethermal plateau in which dynamics is governed by an effective, static Hamiltonian for long times, and we provide numerical evidence to support such a statement. Our results are relevant for understanding timescales of both heating and hence new dynamical regimes described by effective Hamiltonians in such long-range systems.
In recent years, advancements in the manipulation and control of atomic, molecular, and optical (AMO) systems have significantly expanded the study of long-range interacting quantum systems. Platforms such as Rydberg atoms, atoms in optical cavities and trapped ions have demonstrated the ability to realise many-body quantum systems featuring long-range couplings, making them promising candidates for quantum computing and simulation. This manuscript investigates the unique properties of these systems, with a focus on their potential to enhance quantum technologies by exploiting the long-range nature of the couplings. Specifically, we examine the application of long-range systems to enhance the power-to-efficiency ratio in quantum thermal devices, analyse their role in stabilising out-of-equilibrium phases such as discrete Floquet time-crystals, and characterise the scaling of entanglement in these systems. The results provide new insights into the potential of long-range interacting systems to overcome limitations faced by systems with local interactions, offering valuable pathways for the development of efficient quantum technologies.