Time evolution of one-dimensional Quantum Many Body Systems

TL;DR

This paper reviews recent numerical methods for studying the time evolution of one-dimensional strongly correlated quantum systems, focusing on exact diagonalization and DMRG techniques, with preliminary results on spinless fermions.

Contribution

It introduces recent developments in numerical schemes for one-dimensional quantum systems, enhancing the ability to analyze time-dependent strongly correlated phenomena.

Findings

Preliminary results for spinless fermions with nearest-neighbor interactions.

Comparison of numerical schemes with exact results to assess accuracy.

Advances in controlled approaches for time-dependent quantum systems.

Abstract

The level of current understanding of the physics of time-dependent strongly correlated quantum systems is far from complete, principally due to the lack of effective controlled approaches. Recently, there has been progress in the development of approaches for one-dimensional systems. We describe recent developments in the construction of numerical schemes for general (one-dimensional) Hamiltonians: in particular, schemes based on exact diagonalization techniques and on the density matrix renormalization group method (DMRG). We present preliminary results for spinless fermions with nearest-neighbor-interaction and investigate their accuracy by comparing with exact results.