Understand
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems.
- Arguing that any efficient (possibly quantum) algorithm can only have a polynomially small energy resolution, we propose a (rigorous) polynomial-time (classical) algorithm that outputs a diagonal density operator supported on a microcanonical ensemble of an inverse polynomial bandwidth.
- The proof uses no other conditions for MBL but assumes that the effect of any local perturbation (e.g., injecting conserved charges) is restricted to a region whose radius grows logarithmically with time.
- A non-optimal version of this algorithm efficiently simulates the quantum phase estimation algorithm in 1D MBL systems; a heuristic version of the algorithm can be easily coded and used to, e.g., detect energy-tuned dynamical quantum phase transitions between MBL phases.