Unravelling quantum dynamics using flow equations

Abstract

The study of many-body quantum dynamics in strongly correlated systems is extremely challenging. To date, few numerical methods exist that are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, which is partly due to complexity theoretic obstructions. In this work, we present a technique able to overcome this obstacle, by combining continuous unitary flow techniques with the newly developed method of scrambling transforms. We overcome the assumption that approximately diagonalizing the Hamiltonian cannot lead to reliable predictions for relatively long times. Rather, we show that the method achieves good accuracy in both localized and delocalized phases and makes reliable predictions for a number of quantities including infinite-temperature autocorrelation functions. We complement our findings with rigorous incremental bounds on the truncation error. Our approach shows that, in practice, the exploration of intermediate-scale time evolution may be more feasible than is commonly assumed, challenging near-term quantum simulators.