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 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-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 non-quadratic interactions. 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.

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, 2019;Schwarz et al, 2016). For a discussion of thermalization properties of such baths, see (Reichental et al, 2018).…”

Rényi entropy singularities as signatures of topological criticality in coupled photon-fermion systems

“…Phase Diagram.-The ground state of the system has been obtained by performing DMRG simulations in a matrix product state description [46,47], using the opensource TNT library [48,49]. Notably, matrix product algorithms have been successfully applied to correlated systems embedded in a cavity [50,51], as well as to different interacting systems in star-like geometries [52][53][54][55]. In the following analysis, we consider separately each kind of cavity-chain coupling term and we sweep over µ.…”

Speed-ups to isothermality: Enhanced quantum thermal machines through control of the system-bath coupling

“…An interesting future direction is to combine these ideas with open systems techniques to deal with strong, time-dependent coupling such as the reaction-coordinate mapping [2,5,[62][63][64][65], or more sophisticated tensornetwork methods [66][67][68][69]. Another interesting direction is to characterise the work fluctuations due to such SI, which have been characterised in e.g.…”