Thermalization with detailed-balanced two-site Lindblad dissipators

Abstract

The use of two-site Lindblad dissipator to generate thermal states and study heat transport raised to prominence since [J. Stat. Mech. (2009) P02035] by Prosen andŽnidarič. Here we propose a variant of this method based on detailed balance of internal levels of the two site Hamiltonian and characterize its performance. We study the thermalization profile in the chain, the effective temperatures achieved by different single and two-site observables, and we also investigate the decay of two-time correlations. We find that at a large enough temperature the steady state approaches closely a thermal state, with a relative error below 1% for the inverse temperature estimated from different observables.

Finite-temperature transport in one-dimensional quantum lattice models

“…That is, one can choose Lindblad operators such that in the absence of H, the steady state on those sites is a thermal state (or any other ρ) (Prosen andŽnidarič, 2009;Žnidarič et al, 2010). Such manysite driving is, for instance, required in order to have an efficient coupling to the energy density (being at least a 2-site operator) and therefore, is used to study energy transport (Mendoza-Arenas et al, 2015;Palmero et al, 2019;Prosen andŽnidarič, 2009;Žnidarič, 2011). An exception are weakly-coupled systems (Michel et al, 2003(Michel et al, , 2008Steinigeweg et al, 2009a), for which energy transport is essentially the same as spin transport.…”

Non-equilibrium boundary driven quantum systems: models, methods and properties

“…The simple outcome of this procedure is an equation of GKSL form that can technically also be obtained from ( 35) by setting all system energies zero (Palmer, 1977). In the Schrödinger picture it reads…”

“…If ρ S approaches a thermal state, then β O would be the same for all observables, while it will start to differ for different observables as ρ S is further away from a thermal state. A detailed analysis along these lines can be found in (Palmero et al, 2019;Žnidarič, 2011b). It is observed that the steady state has observables which have closer temperatures when the temperatures are higher and when the observables are on a smaller support (e.g.…”

Thermalization in the quantum Ising model—approximations, limits, and beyond

“…This approach is accurate for situations to describe steady states or when the bath produces a single relevant transition, for instance in weakly interacting qubits. It has been used to analyze transport in spin problems, where a one-dimensional many-body open system couples to baths via both the first and last site [10][11][12][13] or to study decoherence in strongly correlated systems [14][15][16][17]. However, as shown in [18][19][20][21] for single open qubits or qudits, the single-channel approach may not be sufficiently accurate to describe thermalization or even quantum transport [22].…”

“…The open quantum system dynamics of 1D spin chains have been studied in an end-cap scenario with the idea of a wire attached to either end, or else a subsystem of a much larger 1D spin chain. This approach amounts to independent baths coupled to both ends of the chain with Lindblad operators constructed in terms of Hermitian Majorana operators [10], or defined in terms of the first two and last two spins as in [11], a proposal recently extended in [13]. The basic aim of these proposals is to drive the system to its thermal state, by imposing a local version of the detailed balance condition.…”