A causality-based divide-and-conquer algorithm for nonequilibrium Green’s function calculations with quantics tensor trains

Key findings from this study

• The study found that causality-exploiting divide-and-conquer algorithms enable stable extensions of simulated time domains in nonequilibrium Green's function calculations.
• The researchers demonstrate that quantics tensor train representations maintain efficient storage scaling despite temporal domain expansion.
• The authors report that their approach successfully captures slow relaxation dynamics in symmetry-broken phases where long simulation times are essential.

Overview

The authors propose a causality-based divide-and-conquer algorithm for computing nonequilibrium Green's functions using quantics tensor trains. This method exploits the causal structure inherent to Green's functions to enable stable temporal domain extensions. The approach integrates within nonequilibrium dynamical mean-field theory frameworks and targets simulations of quench dynamics in symmetry-broken phases requiring extended temporal windows.

Methods and approach

The algorithm leverages causality properties of Green's functions to partition computational domains. Quantics tensor trains provide the underlying tensor representation. The framework embeds within nonequilibrium dynamical mean-field theory for studying quench dynamics. Time domain extension proceeds without proportional increases in storage requirements for Green's function data.

Results

The authors demonstrate that their algorithm extends simulated time domains stably and efficiently. Storage costs for Green's function representation do not increase significantly during temporal extension. The approach successfully captures slow relaxation dynamics in symmetry-broken phases where long-time simulations prove necessary.

Implications

The causality-based divide-and-conquer framework addresses computational bottlenecks in nonequilibrium simulations requiring extended temporal coverage. By decoupling storage cost from simulation duration, the method enables investigation of relaxation phenomena inaccessible through standard approaches. This development expands the practical scope of nonequilibrium dynamical mean-field theory applications to systems exhibiting slow dynamics.

Scope and limitations

This summary is based on the study abstract and available metadata. It does not include a full analysis of the complete paper, supplementary materials, or underlying datasets unless explicitly stated. Findings should be interpreted in the context of the original publication.