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Tensor-Network Method to Simulate Strongly Interacting Quantum Thermal Machines

Marlon Brenes, Juan José Mendoza-Arenas, Archak Purkayastha, Mark T. Mitchison, Stephen R. Clark, and John Goold
Phys. Rev. X 10, 031040 – Published 19 August 2020
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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 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.

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  • Received 7 January 2020
  • Revised 1 June 2020
  • Accepted 7 July 2020

DOI:https://doi.org/10.1103/PhysRevX.10.031040

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsAtomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

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Modeling Energy Transfer in Quantum Thermal Machines

Published 19 August 2020

A new modeling and computational approach allows for more complete simulations of particle and heat flow through tiny quantum devices.

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Authors & Affiliations

Marlon Brenes1,*, Juan José Mendoza-Arenas2, Archak Purkayastha1, Mark T. Mitchison1, Stephen R. Clark3, and John Goold1

  • 1School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
  • 2Departamento de Física, Universidad de los Andes, A. A. 4976, Bogotá D. C., Colombia
  • 3H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom

  • *Corresponding author. brenesnm@tcd.ie

Popular Summary

Nanoscale electronic devices form the backbone of modern technology, ranging from everyday computer hardware to next-generation energy-harvesting devices. As circuit components become progressively miniaturized, the behavior of devices starts to display new effects due to quantum interference and strong repulsive interactions between the electrons confined inside them. Increasingly, it has become clear that rather than being unhelpful complications, these unique features of the nanoscale present a multitude of opportunities to be harnessed. However, understanding and engineering any new quantum-enhanced functionality requires formidable many-body calculations. We address this problem by developing a general and efficient approach to simulate the flow of particles and energy across a quantum device connected to a circuit via metallic contacts.

Since the metallic contacts are much larger than the device itself—too large to model explicitly—we approximate them as a “mesoscopic reservoir”: a much smaller system whose energy and electric charge are continuously replenished by thermal dissipation. We then compute and compress the quantum state of this reduced open system using a so-called tensor network description. We show that this approach can be used to accurately model a quantum thermoelectric heat engine, which converts a temperature gradient into electrical power.

Our method works even in far-from-equilibrium scenarios and in the presence of strong interactions, superseding existing methods. This new capability opens up the exciting prospect of designing nanoscale electronic devices that harness strong quantum correlations to improve performance.

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Vol. 10, Iss. 3 — July - September 2020

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