RG without arbitrariness

We like to encode our understanding of complex materials in simple microscopic models. For example, to describe magnetism we typically identify localized moments as the key players. Simple model Hamiltonians are then proposed to capture the interactions between these local degrees of freedom. While this route of building an understanding of nature is appealing, it suffers from one key shortcoming: Observations are rarely done at the microscopic scale, but are rather capturing the physics at scales encompassing vast numbers of microscopic building blocks. For the theoretical description of phases of matter, this discrepancy between the simple microscopic models and the necessity to describe phenomena at large scales represents a formidable challenge.

Over the last century, physicists have developed a very powerful tool to go about this task. By successively bunching local degrees of freedom together we can make our way to bigger scales. We start, e.g., to combine a number of local magnetic moments into a super-moment. Cleverly analysing the underlying Hamiltonian, one can formulate an effective model for the newly created degrees of freedom. By iterating this procedure, we eventually arrive at our final answers at large scales. This tool, going under the name of real-space RG (renormalization group), is powerful, yet it tends to develop a quite crucial dependence on ad-hoc decisions by the theoretical physicist.

With our research, we try to replace these ad-hoc decisions with an over-arching, model indpendent principle. One can ask the question why this would lead to any advantage over the more tranditional approach of taking the ad-hoc decisions based on human insight. We are of the firm believe, that what holds us from understanding complex phases of matter such as strongly interacting disordered quantum magnets, is the failure of this mode of operation. Using ideas from information theory, in particular the optimization of the mutual information retained in the RG procedure, we could show how we can replace the model-by-model decision by a general rule. We are currently investigating the role of disorder in this procedure, with the vision to make progress in so far poorly understood quantum sping glasses.