Tensor-network method to simulate strongly interacting quantum thermal machines

TL;DR

This paper introduces a tensor-network approach for simulating the thermodynamics of strongly interacting quantum thermal machines at finite temperature, capturing complex interactions and many-body effects beyond traditional methods.

Contribution

The authors develop a novel tensor network algorithm that handles non-quadratic interactions and continuum baths, enabling detailed simulation of quantum thermal machines in regimes previously inaccessible.

Findings

Replicates Landauer-Büttiker efficiency and power predictions for quantum-dot heat engines.

Demonstrates power enhancement due to non-quadratic interactions in multi-site machines.

Extracts super-diffusive transport behavior in the isotropic Heisenberg model.

Abstract

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 fixed temperature and chemical potential. Our method works at finite temperature, beyond linear response and weak system-reservoir coupling, and allows for non-quadratic interactions in the working medium. The method uses mesoscopic reservoirs, continuously damped towards 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-B\"uttiker theory for efficiency and power. We then go beyond the quadratic limit to demonstrate the capability of our method by simulating a three-site machine with non-quadratic interactions. Remarkably, we find that such interactions lead to power enhancement, without being detrimental to the efficiency. Furthermore, we demonstrate the capability of our method to tackle complex many-body systems by extracting the super-diffusive exponent for high-temperature transport in the isotropic Heisenberg model. Finally, we discuss transport in the gapless phase of the anisotropic Heisenberg model at finite temperature and its connection to charge conjugation-parity, going beyond the predictions of single-site boundary driving configurations.