Effective Theories of Quantum Phases of Matter

122:026 (Nordita, Stockholm)


Nordita, Stockholm

Carlos Hoyos , Dam Thanh Son , Sergej Moroz , Tomáš Brauner


Nordita, Stockholm, Sweden


Physical systems look different when observed at different resolutions: what appears as a continuum liquid to the naked eye becomes a cluster of jiggling atoms when observed at the resolution of an electron microscope. Effective field theory provides a description of physics in terms of degrees of freedom appropriate to a given resolution. Over the last couple of decades, physicists have developed effective field theory tools which, to a large extent, unify fields as diverse as atomic and condensed-matter physics, particle and nuclear physics, and cosmology. Numerous physical phenomena, first predicted and studied in high-energy physics, have found their realization in novel materials. On the other hand, the richness of condensed-matter physics provides a lasting source of inspiration for new developments in high-energy physics and cosmology. Extremely useful in general, the effective field theory tools become indispensable for quantum phases of matter whose low-energy physics is driven by collective excitations, either due to the presence of spontaneous symmetry breaking or due to strong microscopic interactions.

Despite the common interest in effective field theory techniques, it is rare that experts from different fields come together to share their results, which in some cases are obscured by the jargon particular to each community. This lack of communication sometimes leads to replication of results and increases time spent searching unfamiliar literature when some approach is not well-known in a particular field, even though it might be frequently used in another. This could be greatly improved by providing a common environment where scientists from different disciplines can share their expertise.

This four-week program aims to provide such a meeting ground, to cherish and strengthen interdisciplinary connections between different sub-fields of theoretical physics. We will do so by bringing together practitioners working on effective theories of quantum phases of matter across several branches of physics. Our goal is to map out important open problems with broad relevance and look for new directions towards their solution, to reinvigorate existing collaborations and foster new connections.


[Timetable - available from start of the program]

There will be one to two presentations every day, leaving ample time for informal discussions and collaboration. We plan to cover four main topics, each spanning over roughly one week, with the tentative schedule as outlined below. However, the participants are encouraged to self-organize, welcome to blend the topics, and bring in their own: it is the intention that experts on different branches of physics get to meet each other!

Week 1 (6-10 May 2019): Topology in effective field theories. Topology plays an indispensable role in the effective field theory approach. Topological terms such as Chern-Simons, Wess-Zumino and theta-terms are special because their coefficients are quantized and thus cannot be changed smoothly. This provides a pathway to distinguish (and sometime fully classify) different phases of matter, and the last decade has seen an explosion of new activities directed towards applying topology to quantum phases of matter. In most cases topological terms are tied to quantum anomalies and are responsible for new forms of dissipationless transport. Spin systems and quantum Hall fluids are paradigmatic quantum phases of matter governed by topological terms. More recently these terms have been identified in a wide range of novel systems, from quark-gluon plasma in high-energy physics to topological insulators and Weyl semimetals in condensed-matter physics.

Week 2 (13-17 May 2019): Dualities in effective field theories. A duality relates two theories that at first sight might look unrelated to each other. Since the discovery of the boson-vortex duality, dualities have become a standard tool for development of effective field theories and contributed with deep insights in physics of superconductors, superfluids, quantum Hall fluids and spin liquids. In high-energy physics, exact and approximate dualities have been studied for a long time, especially in the context of supersymmetric theories and string theory. Motivated in part by the developments in condensed-matter physics, new dualities in non-supersymmetric theories have recently attracted considerable interest. In recent years, a number of new dualities involving Dirac fermions have been discovered and their implications are now being thoroughly studied by members of both communities.

Week 3 (20-24 May 2019): Broken symmetry and Nambu-Goldstone bosons. The paradigm of spontaneous symmetry breaking underlies much of our understanding of the fundamental laws of nature. A wave of renewed interest in this classical topic has occurred in the last decade, with particular emphasis on the subtleties of broken symmetries in the nonrelativistic setting. Upon the initial works on classification of Nambu-Goldstone bosons for internal symmetries, the main focus is now gradually shifting towards spacetime symmetries and more detailed properties of Nambu-Goldstone bosons such as their scattering amplitudes. These developments have been of special interest in cosmology, where effective theories of spontaneously broken time translation invariance are used to capture general properties of the cosmological evolution and perturbations.

Week 4 (27-31 May 2019): Interplay of geometry and spacetime symmetries. The role of spacetime geometry in effective theories is yet another exciting avenue of current research. Recent years have seen the discovery of a number of deep relations between various geometric responses (such as the Wen-Zee terms and Hall viscosity) and the electromagnetic response (Hall conductivity). New ideas based on the classical Newton-Cartan geometry have also led to an elegant framework for the construction of effective theories of quantum phases of matter, which respects manifestly nonrelativistic general coordinate invariance. Thursday 30 May 2019 is a public holiday in Sweden.


Registration to the program is now closed.


Nordita offers free accommodation to all accepted participants in one of its partner facilities, the default being the Stockholm apartment hotel BizApartments.

Please be aware that unfortunately, scammers sometimes approach participants claiming to be able to provide accommodation and asking for credit card details. Please do not give this information to them. For successful applicants, Nordita will be in touch via email regarding accommodation. If you are in any doubt about the legitimacy of an approach, please get in contact with the organisers.

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