Variational Approaches for quantum matter in and out of equilibrium
This school shall introduce PhD students and junior postdoctoral fellows to advanced numerical techniques, aimed at tackling the physics of quantum many-body systems in and out-of equilibrium. The focus will be on the application of state-of-the-art variational approaches to problems emerging in condensed matter physics, quantum simulation and quantum computing.
Context
The last ten years have experienced an impressive progress in the level of precision and control reached in quantum simulators of quantum many-body physics (based e.g. on ultracold atoms, trapped ions, superconducting circuits, to cite the most relevant platforms), as well as in spectroscopic and transport measurements on bulk quantum materials. Hand-in-hand, increasingly sophisticated theoretical and computational tools have been developed in order to be able to describe quantitatively equilibrium as well as time-dependent phenomena in quantum many-body systems. At the same time, the fundamental question raises whether quantum devices may soon reach – or have already reached – a long-sought form of “computational advantage” with respect to their classical counterparts.
Computing equilibrium properties or even non-equilibrium dynamics of a general, interacting quantum many-body system is an extremely challenging computational task, with broad applications in moderns physics. In this school we will focus on selected model systems realized by quantum simulators or (bulk) condensed matter systems. In particular we want to address fundamental topics related to time-dependent driven and dissipative systems, 2entanglement dynamics, and complex equilibrium properties of strongly correlated quantum systems. In this context, a universal numerical strategy in order to compute the dynamics of a quantum system is based on a clever variational Ansatz on the quantum state, motivated by physical considerations as well as by quantum-information insights. Hence our choice of variational approaches as the overarching theme of this school.
On the methodological side, the school aims at introducing computational tools which bridge the gap between (under)graduate numerical courses and state- of-the-art techniques needed to address dynamical phenomena in closed or open quantum systems. In the main courses we plan to provide detailed descriptions of the variety of variational methods used in this context (in a broad sense), and, importantly, also practical examples based on small codes. A non-exhaustive list of computational methods addressed by the school include tensor-network states, variational Monte Carlo methods, semiclassical phase-space approaches, and machine learning techniques. More specialized techniques, practical applications and experimental results will be illustrated by invited seminars.
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