Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces

TL;DR

This paper presents an adaptive time-dependent DMRG algorithm based on TEBD and matrix product states, enabling efficient simulation of time evolution in one-dimensional quantum systems with potential applications in non-equilibrium transport and dissipative dynamics.

Contribution

It translates TEBD into the matrix product state framework, integrating it with DMRG techniques to create a versatile adaptive time-dependent DMRG method.

Findings

Effective simulation of time evolution in quantum systems.

Enhanced DMRG algorithms with TEBD integration.

Comparison shows improved performance over previous methods.

Abstract

An algorithm for the simulation of the evolution of slightly entangled quantum states has been recently proposed as a tool to study time-dependent phenomena in one-dimensional quantum systems. Its key feature is a time-evolving block-decimation (TEBD) procedure to identify and dynamically update the relevant, conveniently small subregion of the otherwise exponentially large Hilbert space. Potential applications of the TEBD algorithm are the simulation of time-dependent Hamiltonians, transport in quantum systems far from equilibrium and dissipative quantum mechanics. In this paper we translate the TEBD algorithm into the language of matrix product states in order to both highlight and exploit its resemblances to the widely used density-matrix renormalization-group (DMRG) algorithms. The TEBD algorithm being based on updating a matrix product state in time, it is very accessible to the DMRG community and it can be enhanced by using well-known DMRG techniques, for instance in the event of good quantum numbers. More importantly, we show how it can be simply incorporated into existing DMRG implementations to produce a remarkably effective and versatile ``adaptive time-dependent DMRG'' variant, that we also test and compare to previous proposals.