Understanding strongly correlated systems has been a significant challenge in theoretical physics. However, as computational capabilities continue to improve with the dissemination of new or improved methods, numerical analysis is getting increasingly important. Recent developments in numerically exact methods include applying tensor networks and artificial neural networks to study quantum phase transitions, thus characterizing the controversial phases of new quantum matters in equilibrium and out-of-equilibrium conditions. Because all numerical methods have shortcomings and advantages, we need cross-fertilizations between new and traditional methods. They would result in potentially significant progress in unveiling the elusive nature of the perturbative and non-perturbative phase structure of the theories under consideration.
Thermalization of isolated quantum systems is one of the fundamental issues of statistical physics. Computational methods are essential in uncovering physical mechanisms that drive a system to thermalize or not. Finding quantum systems that escape thermalization is crucial to developing many possible quantum technological devices. For example, non-thermalizing quantum systems would be perfect candidates for building concrete examples of quantum memories. More generally, the field of quantum technologies is emerging as a new branch of physics that promises to revolutionize our society in many different aspects. For all these achievements, numerical methods, combined with analytical tools, are at the core of recent developments.
On the other hand, numerical analysis of matrix models and AdS/CFT correspondence has shed light on non-perturbative studies of quantum gravity and strongly correlated systems. Much progress in understanding the quantum nature of spacetime has been made via quantum Monte Carlo simulations of matrix models such as IKKT or BFSS models. AdS/CFT correspondence, with the help of numerical methods, provides a fruitful arena to investigate quantum gravity, strongly coupled systems, and quantum information theory. Numerical techniques have been extensively used in reconstructing spacetime and emergent gravity from gauge theory data with the help of tools such as holographic renormalization group, multi-scale entanglement renormalization ansatz (MERA), tensor networks, and deep learning.
The program aims at bringing together different communities of theoretical physicists who are working on numerical methods to investigate those types of questions. Cross-fertilizing ideas and finding common ground should inspire new ways of thinking about these problems and stimulate more rapid progress.