Tensor-Network Method to Simulate Strongly Interacting Quantum Thermal Machines*

We present a methodology to simulate the quantum thermodynamics of thermal machines which are built from an interacting working medium in contact with fermionic reservoirs at a fixed temperature and chemical potential. Our method works at a finite temperature, beyond linear response and weak system-reservoir coupling, and allows for nonquadratic interactions in the working medium. The method uses mesoscopic reservoirs, continuously damped toward thermal equilibrium, in order to represent continuum baths, and a novel tensor-network algorithm to simulate the steady-state thermodynamics. Using the example of a quantum-dot heat engine, we demonstrate that our technique replicates the well-known Landauer-Büttiker theory for efficiency and power. We then simulate a three-site machine with nonquadratic interactions; remarkably, these lead to power enhancement without being detrimental to the efficiency. Finally, we demonstrate the capability of our method to tackle complex many-body systems by extracting the superdiffusive exponent for high-temperature transport in the isotropic Heisenberg model.

[1] M. Brenes et al., Phys. Rev. X 10, 032040 (2020)
[2] A. Levy and W. Dou, Physics 13, 129 (2020)