#
Fermions from Cold Atoms to Neutron Stars:

Benchmarking the Many-Body Problem

## March 14 – May 20, 2011

Fermionic many-body theory lies at the heart of many physical systems, from cold atoms through superconductors and superfluids to nuclear matter and dense QCD, yet concrete and reliable results are difficult to obtain, even for the simplest systems. This program focused on the bridge between the microscopic description of the problem and the macroscopic physical applications: the many-body problem. The program aimed to build a quantitative understanding of the properties of fermionic many-body systems, especially few-species systems with resonant s-wave interactions (the resonant two component system is referred to as the unitary Fermi gas).

The primary goal for the program was to establish a set of benchmarks for testing and constraining the models used to calculate macroscopic and time-dependent properties of many-body systems in trapped fermionic atoms, dilute neutron matter in neutron stars, and dense QCD. A secondary objective was to foster interdisciplinary collaboration to study nuclear matter and dense QCD by simulating their properties through generalizations including three and four-component systems, different mass ratios, optical lattices, and induced interactions.

These goals were achieved. Several benchmarks for the symmetric unitary Fermi gas were presented, including precision experimental determination of the equation of state at the few percent level that were compared with different ab initio theoretical predictions with disagreements appearing at the level of a few standard deviations. To achieve this level of precision, all aspects of the experiments and calculations needed to be under strict control, including the interaction properties, trap geometry, and a careful understanding of systematic and statistical errors. Previous measurements and calculations at only the 10% level were unable to distinguish between many subtle but important effects. Several speakers emphasized the importance of careful extrapolation to thermodynamic, continuum, and zero effective range limits, including some quantitative characterizations. Precision theoretical benchmarks were presented for small systems including few-body systems in traps, particles in a periodic box, and analytic results for special cases where tractable. This program demonstrated that firm results at the few percent level can distinguish between approximations and therefore benchmark different many-body theories.

Benchmarks for novel results were also discussed, including the search for novel phases like FFLO supersolids, and p-wave or f-wave superfluidity (similar to liquid 3He) – especially in lower or mixed dimensional systems. The measurement and simulation of time-dependent systems was also a hot topic, and included discussions about colliding clouds (both experiment and theory), soliton collision, and vortex lattice equilibration. In addition, a special session addressed the question: Is there a “pseudo-gap” in the unitary Fermi gas? Although no definitive conclusion was reached, the session was valuable in focusing the question, emphasizing that not all signatures are conclusive.

Finally, many different theoretical techniques were presented, including several diagrammatic approaches (both perturbative truncation and Monte Carlo resummation), dynamical mean-field theory and its cluster extensions, fixed-node and auxiliary field Monte Carlo, density matrix renormalization group, exact diagonalization, and density functional theory. Many of these techniques and benchmarks have been summarized on the program wiki which will be made available to the public at a later date. Notably absent were precision benchmarks for three-dimensional systems with moderate polarization and participants were encouraged to address this challenge.

The three month program consisted of solicited lectures intermixed with presentations of new results, with ample time for collaboration and directed discussions. It concluded with an intensive experimental symposium week. The program attracted 107 participants, including 15 graduate students and 62 symposium participants. Seventy-eight talks were recorded and will be streamed as podcasts from the INT webpage (see below for comments and suggestions about the podcasting). Participants of the program included researchers working in many fields including the physics of cold atom systems, few-body systems, condensed matter physics, nuclear physics, and astrophysics. The range of topics discussed covered an extremely large number of phenomena: collective excitations, thermodynamic properties, pairing properties, hydrodynamics properties as well as the relation to the physics of quark-gluon plasma created in relativistic heavy-ion collisions, physics of neutron stars and some properties of atomic nuclei.

The program provided a fruitful environment for collaboration between experimentalists and theorists, and brought together the cold-atom and nuclear physics communities. Cross-discipline discussions addressed the possibilities of using cold-atoms to simulate nuclear matter, and to apply nuclear physics techniques to cold-atom and condensed matter systems.

Most participants were very positive about the program noting that it was among the best meetings they have attended. They valued the high interactivity, the ability to discuss with people outside their direct area of interest, the high quality of the talks presented, the very high attendance by key researchers in the field, and the success of the INT venue.