Numerical Approaches to Quantum Many-Body Systems

January 22 - 30, 2009

Overview

Quantum many-body systems can give rise to remarkable collective states of matter that have no counterpart in their classical analogs. Archetypal examples include superfluids, superconductors, and insulating quantum liquids in the context of condensed matter physics. But collective quantum phenomena are also ubiquitous in nuclear physics, quantum chemistry, high-energy physics, traditional atomic physics as well as ultracold atoms. Quantum information technology not only takes quantum effects for granted, but goes a step further and aims at “taming the quantum” by controlling collective quantum states for applications like quantum computing.

In connecting such complex emergent behavior to a microscopic picture in terms of short-ranged interactions between the elementary quantum mechanical degrees of freedom, analytical approaches can often provide qualitative guidance. Unbiased numerical simulations play a crucial role in verifying the underlying assumptions. Quantitative guidance in mapping out phase diagrams (in terms of the microscopic interactions) and the respective phase transitions is often obtained solely by numerical methods. In the interplay between theory and experiment, computational physics has established itself as a vital discipline for quantum many-body physics.

Yet there are a number of outstanding problems that for decades have resisted solution, most prominently the many fermion problem. Other examples include quantum spin systems with frustrating or competing interactions that can suppress any type of ordering and thereby give rise to spin liquid behavior, or quantum systems out of equilibrium. These outstanding problems and the continuing search for new quantum states of matter have made it ever more obvious that the established numerical tools despite their successes are not capable of solving these problems without major breakthroughs.

The continuing demand for new methods has motivated the development of a plethora of novel algorithms over recent years which significantly extend the applicability of well-established techniques such as quantum Monte Carlo (QMC) methods and the density matrix renormalization group (DMRG) approach. In a remarkable interplay between quantum information theory and computational condensed matter physics, time-dependent renormalization group techniques have been developed and reformulations of DMRG in terms of matrix product states (MPS) and extensions to projected entangled pair states (PEPS) have created the intriguing potential to simulate the two-dimensional fermion problem or frustrated quantum spin systems. In classical statistical mechanics it has been realized that extended ensemble sampling techniques can overcome the equilibration problem caused by competing interactions or phases and the resulting rough energy landscapes even when there are no non-local update techniques available. Finally, a new class of continuous-time impurity solvers has recently been developed for dynamical meanfield theory (DMFT) calculations that will allow one to study the many-fermion problem in this approximation at considerably lower temperatures.

It is the aim of this workshop to bring together an interdisciplinary group of researchers from mathematics, physics, quantum information, computer science, and other related disciplines, to discuss advances in the computational description of quantum many-body systems.

The workshop will consist of two parts: During the first three days we will have a short course for young researchers with lectures and hands-on tutorials on state-of-the-art numerical techniques. In the second week, there will be a more regular workshop with 5 days of lectures and discussions by experts in the field.

Organizing Committee

Ulrich Schollwöck (RWTH Aachen)
Simon Trebst (Microsoft Station Q, Station Q)
Guifre Vidal (University of Queensland)