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-...

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Bibliographic Details
Published in:Physical review. X 2020-08, Vol.10 (3), p.031040, Article 031040
Main Authors: Brenes, Marlon, Mendoza-Arenas, Juan José, Purkayastha, Archak, Mitchison, Mark T., Clark, Stephen R., Goold, John
Format: Article
Language:English
Subjects:
Algorithms
Chemical potential
Circuits
Conjugation
Display devices
Electric contacts
Electronic devices
Energy conversion efficiency
Energy dissipation
Energy harvesting
Flow simulation
Heat engines
Heisenberg theory
High temperature
Many body interactions
Mathematical analysis
Open systems
Quantum dots
Reservoirs
Statistical models
Strong interactions (field theory)
Tensors
Thermodynamics
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Summary: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 go beyond the quadratic limit to demonstrate the capability of our method by simulating a three-site machine with nonquadratic 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 superdiffusive exponent for high-temperature transport in the isotropic Heisenberg model. Finally, we discuss transport in the gapless phase of the anisotropic Heisenberg model at a finite temperature and its connection to charge conjugation parity, going beyond the predictions of single-site boundary driving configurations.
ISSN:2160-3308
2160-3308
DOI:10.1103/PhysRevX.10.031040