# Adaptively truncated Hilbert space based impurity solver for dynamical mean-field theory

## TL;DR

This paper introduces an adaptive Hilbert space truncation impurity solver for dynamical mean-field theory, effective where quantum Monte Carlo methods fail, by exploiting model sparsity and adaptive truncation for accurate Green function calculations.

## Contribution

It develops a novel impurity solver using adaptive Hilbert space truncation, improving accuracy and efficiency in challenging DMFT scenarios.

## Key findings

- Successfully benchmarks on the 1D Hubbard model.
- Achieves accurate Green functions avoiding unphysical self-energies.
- Outperforms traditional methods in specific regimes.

## Abstract

We present an impurity solver based on adaptively truncated Hilbert spaces. The solver is particularly suitable for dynamical mean-field theory in circumstances where quantum Monte Carlo approaches are ineffective. It exploits the sparsity structure of quantum impurity models, in which the interactions couple only a small subset of the degrees of freedom. We further introduce an adaptive truncation of the particle or hole excited spaces, which enables computations of Green functions with an accuracy needed to avoid unphysical (sign change of imaginary part) self-energies. The method is benchmarked on the one-dimensional Hubbard model.