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

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.

arXiv comment8 pages, 7 figures

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• Algorithms for quantum simulation at finite energies
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• Measuring von Neumann entanglement entropies without wave functions
• Classical algorithms for many-body quantum systems at finite energies
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• Quantum topological data analysis via the estimation of the density of states
• Energy-filtered quantum states and the emergence of non-local correlations
• Variational Microcanonical Estimator
• Many Body Density of States of a system of non interacting spinless fermions