Tensor-Network Method to Simulate Strongly Interacting Quantum Thermal Machines

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 systemreservoir 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.

Finite-temperature transport in one-dimensional quantum lattice models

“…Another hybrid way to model a bath is by describing it as a lead (with a certain number of lattice sites) that is in addition coupled to a Lindbladian dissipation. For noninteracting leads, one can construct dissipators that thermalize such free systems (Ajisaka et al, 2012;Dzhioev and Kosov, 2011;Guimarães et al, 2016), or model nontrivial spectral properties of the bath (Arrigoni et al, 2013;Brenes et al, 2020c;Schwarz et al, 2016). For a discussion of thermalization properties of such baths, see (Reichental et al, 2018).…”

Renormalized Lindblad driving: A numerically exact nonequilibrium quantum impurity solver

“…A class of such attempts is based on capturing the many-body correlations by modeling the environment as large (but finite) leads, and evolving the many-body state of this finite system toward a finite-time quasi-steady state, e.g., using the time-dependent density matrix renormalization group (tDMRG) method [18][19][20]. This approach has further been extended by treating the finite leads as open systems, governed by Lindblad dynamics, and similarly evolving in time toward a well-defined steady state [21][22][23]. The Lindblad approach has also been recently investigated in the context of density functional theory [24].…”

Modeling Energy Transfer in Quantum Thermal Machines

“…Answering these questions theoretically is a very difficult task, particularly for a system that is strongly coupled to its surroundings. Marlon Brenes from Trinity College Dublin and colleagues now report a new tool for simulating the non-equilibrium dynamics of such strongly coupled systems [1]. Significantly, the team's computational approach applies to a system of electrons whether the electrons' interactions with one another are weak or strong.…”

“…Brenes and co-workers take a similar path, but with novel applications of the tools for modeling the environment [1]. In their picture, a simple thermal machine or electronic system is coupled to a finite number of mesoscopic metal leads that, collectively, represent the primary bath (Fig.…”

“…Considering the primary bath and the system explicitly has become a prevalent way to account for strong system-environment coupling effects. The approach introduced by Brenes and colleagues is particularly valuable because it combines the novel use of mesoscopic leads with the ongoing development of efficient tensor network algorithms for open systems [1,10,11]. Looking forward, it would be of great interest to develop algorithms for system dynamics that incorporate time-dependent driving fields.…”