An Efficient Bond-adaptive approach for Finite-temperature Open Quantum Dynamics using the one-site Time-Dependent Variational Principle for Matrix Product States

Angus J Dunnett , Alex W. Chin (1, 2, 3)

1 INSP-E12 - Photonique et cohérence de spin
2 INSP - Institut des Nanosciences de Paris
3 UFR 925 - Sorbonne Université - Faculté de Physique

Recent tensor network techniques for simulating system-environment wavefunctions have provided profound insights into non-Markovian dissipation and decoherence in open quantum systems. Here, we propose a dynamically adaptive one-site Time-Dependent-Variational-Principle (A1TDVP) method for matrix product states in which local bond dimensions grow to capture developing systembath entanglement. This avoids the need for multiple convergence runs w.r.t. bond dimensions and the unfavourable local Hilbert space scaling of two-site methods. A1TDVP is thus ideally suited for open quantum dynamics in finite-temperature bosonic environments, as the initial states typically have low bond dimension but require very large local physical dimensions. We demonstrate this with simulations of non-equilibrium heat flows through a qubit spin, finding a 30x and 10x speed-up over 2TDVP and 1TDVP, respectively.

Domaines: Physique Quantique [quant-ph]; Arithmétique des ordinateurs; Modélisation et simulation; Traitement du signal et de l'image [eess.SP]; Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]; Matière Molle [cond-mat.soft]; Science des matériaux [cond-mat.mtrl-sci]; Biophysique [physics.bio-ph]; Chimie-Physique [physics.chem-ph]; Physique Numérique [physics.comp-ph]; Agrégats Moléculaires et Atomiques [physics.atm-clus]

Angus J Dunnett, Alex W. Chin. An Efficient Bond-adaptive approach for Finite-temperature Open Quantum Dynamics using the one-site Time-Dependent Variational Principle for Matrix Product States. 2021. ⟨hal-03429585⟩