Tree tensor network solver for real-time quantum impurity dynamics

TL;DR

This paper presents a novel tree tensor network impurity solver that efficiently simulates real-time dynamics of quantum impurity models, capturing multiscale entanglement with reduced computational complexity.

Contribution

The authors introduce a TTN-based impurity solver using a Cayley tree bath decomposition, improving accuracy and efficiency over traditional chain mappings.

Findings

Achieves high-resolution real-frequency spectral functions.

Reduces entanglement and computational cost compared to chain-based methods.

Enables accurate long-time dynamics and ground-state properties.

Abstract

We introduce a tree tensor network (TTN) impurity solver that enables highly efficient and accurate real-time simulations of quantum impurity models. By decomposing a noninteracting bath Hamiltonian into a Cayley tree, the method provides a tensor network representation that naturally captures the multiscale entanglement structure intrinsic to impurity-bath systems. This geometry differs from conventional chain-based mappings and yields a substantial reduction of entanglement, allowing accurate ground-state properties and long-time dynamics to be captured at significantly lower bond dimensions. Benchmark calculations for the single-impurity Anderson model demonstrate that the TTN solver achieves markedly enhanced resolution of real-frequency spectral functions, without invoking analytic continuation. This impurity solver provides a balanced, scale-uniform description of impurity physics and offers a versatile approach for real-time dynamical mean-field theory and related applications involving quantum impurity models.