Efficient bond-adaptive approach for finite-temperature open quantum dynamics using the one-site time-dependent variational principle for matrix product states

Abstract

Recent tensor network techniques for simulating system-environment wave functions 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 system-bath entanglement. This avoids the need for multiple convergence runs with respect to bond dimensions and the unfavorable 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 nonequilibrium heat flows through a qubit spin, finding a $30\ifmmode\times\else\texttimes\fi{}$ and $10\ifmmode\times\else\texttimes\fi{}$ speed-up over 2TDVP and 1TDVP, respectively.