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Certifying Ground-state Properties of Quantum Many-body Systems by Wang, Jie; Surace, Jacopo; Frérot, Irénée; Legat, Benoît; Renou, Marc-Olivier; Magron, Victor; Acín, Antonio is a scholarly article available to read on EtoBox.

What is Certifying Ground-state Properties of Quantum Many-body Systems about?

A ubiquitous problem in quantum physics is to understand the ground-state properties of many-body systems. Confronted with the fact that exact diagonalisation quickly becomes impossible when increasing the system size, variational approaches are typically employed as a scalable alternative: energy is minimised over a subset of all possible states and then different physical quantities are computed over the solution state. Despite remarkable success, rigorously speaking, all what variational methods offer are upper bounds on the ground-state energy. On the other hand, so-called relaxations of the ground-state problem based on semidefinite programming represent a complementary approach, providing lower bounds to the ground-state energy. However, in their current implementation, neither variational nor relaxation methods offer provable bound on other observables in the ground state beyond the energy. In this work, we show that the combination of the two classes of approaches can be used to derive certifiable bounds on the value of any observable in the ground state, such as correlation functions of arbitrary order, structure factors, or order parameters. We illustrate the power of thi

Author

Wang, Jie; Surace, Jacopo; Frérot, Irénée; Legat, Benoît; Renou, Marc-Olivier; Magron, Victor; Acín, Antonio

Published

2023

Language

EN