Statistical physics of constrained and long-range interacting quantum systems: thermalization and critical properties

Ramandeep S. Johal, Renuka Rai

In this paper, we address the possibility of generalising the standard analysis of thermal contact between a sample system and a heat bath, by including long range interactions between them. As a concrete example, both system and bath are treated within the long range Ising model. For this model, we derive the equilibrium probability distribution of the energy of the sample system. Equilibrium properties of the system magnetisation and stability of the solutions is discussed. We find existence of a metastable phase below a critical temperature of the bath.

Naomichi Hatano

Andrea Solfanelli, Nicolò Defenu

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.

Dvira Segal, Manas Kulkarni, Kunal L. Tiwari

Patrick Adelhardt, Jan Alexander Koziol, Anja Langheld +1 more

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.

Winton Brown, Dhrubo Jyoti, Lorenza Viola