# Density-of-states of many-body quantum systems from tensor networks

## TL;DR

This paper introduces a tensor network-based method to compute the density of states and thermodynamic properties of many-body quantum systems, validated on 1D models with promising extension potential.

## Contribution

The authors develop a novel tensor network approach combining Hubbard-Stratonovich transformation and real-time evolution to evaluate spectral and thermodynamic properties.

## Key findings

- Accurately reproduces thermodynamic quantities for 1D models
- Method shows good agreement with exact results
- Potential for extension to higher-dimensional systems

## Abstract

We present a technique to compute the microcanonical thermodynamical properties of a manybody quantum system using tensor networks. The Density Of States (DOS), and more general spectral properties, are evaluated by means of a Hubbard-Stratonovich transformation performed on top of a real-time evolution, which is carried out via numerical methods based on tensor networks. As a consequence, the free energy and thermal averages can be also calculated. We test this approach on the one-dimensional Ising and Fermi-Hubbard models. Using matrix product states, we show that the thermodynamical quantities as a function of temperature are in very good agreement with the exact results. This approach can be extended to higher-dimensional system by properly employing other types of tensor networks.