Focus Workshop
Entanglement Spectra in Complex Quantum Wavefunctions (ESICQW12)
November 2012
Coordinators: B. Andrei Bernevig, Masud Haque, Andreas M. Läuchli

Overview. The Focus Workshop was designed to explore emerging results on the entanglement spectrum in quantum many-particle systems. The entanglement spectrum has surprised a rapidly growing community through ongoing discoveries of a remarkable amount of information contained in its structure. The quantity provides a novel opportunity for wavefunction tomography, the mapping out of the anatomy of complex many-particle wavefunctions. It also contains information about topological order in several ways. The time was appropriate for a critical evaluation of results on the entanglement spectrum that have appeared in the past few years. Since the topic is growing rapidly but still at an early stage of development, a high-intensity one-week workshop was envisaged to help consolidate the community emerging around this topic. The Focus Workshop was very successful in fulfilling this goal. We believe the event has inspired new directions and new questions through communication between researchers who have studied entanglement spectra in diverse models.

Format. There were 30 talks, a colloquium, and two after-dinner poster sessions during the FocusWorkshop. The talks were not organized by subtopic; instead different subtopics were mixed into each session. This seemed to work well as participants at each session got exposure to a variety of emerging themes. F. Duncan M. Haldane was the speaker for the Workshop Colloquium, which was a major highlight of the week. The colloquium was delivered to a packed auditorium and heavily attended, not only by the Workshop attendees and MPI-PKS members, but also by many people from neighboring Dresden institutes.

Scientific highlights. A prominent theme at the workshop was entanglement spectra in topological states of matter, including fractional quantum Hall states and fractional Chern insulators. This was the setting in which entanglement spectra first gained widespread attention, and the more recent advances were presented and discussed in thorough detail during the Workshop. In addition, entanglement spectra were discussed by speakers and poster presenters in various non-topological states (Bose-Hubbard system, Kugel- Khomskii model, higher-dimensional AKLT models, etc) where it has more recently been explored in some detail, or where its study has led to yet unexplained results. Another recurrent theme involved matrix product and tensor network representations of many-body states and entanglement spectra in such representations.

Talk slides online. The organizers placed slides of all talks online. This provides a snapshot of this emerging field at this point of time, and should be a useful reference for many researchers working in or entering this field.