## Mid-Term Report Summary - QUSIMGAS (Quantum Simulation of Many-Body Physics in Ultracold Gases)

We briefly summarize the main results and implementation along the "methodology" lines of the grant.

1) with path integral Monte Carlo (PIMC) simulations (bosonic systems with short and long-range interactions, supersolids) we studied the optical conductivity and the amplitude mode for U(1) models in 2 dimensions [Phys Rev Lett 112,030402] in collaboration with Prof Prokof'ev (UMass Amherst) and his team. Further, a novel theory for strong disorder in 1d bosonic systems has been proposed [Phys Rev B 89, 054204] (in collaboration with Profs Svistunov and Prokof'ev ) and a review on disordered bosonic systems written [Comptes Rendus Physique, Vol 14, Issue 8, p712-724]. We also worked on the demixing of SU(2) symmetric supersolid mixtures [Phys Rev A 88,033628] (in collaboration with Prof Boninsegni from the University of Alberta) and the dimensional crossover of the Bose-Hubbard model [Phys Rev A 89, 023605] (together with the student Janik Schoenmeier-Kromer). For systems with long-range interactions, we focused on He4 confined to a cylindrical nanopore explaining the different states using liquid crystal terminology and a topological defect (a disclination with Frank index n=1) [Phys Rev Lett 113,045301]. We also argued the quantum nature of dislocations and grain boundaries in solid He4 crystals [Phys Rev B 90, 184508] in collaboration with prof. Kuklov from CSI, CUNY, New York. Finally, in [Phys Rev Lett 113, 260403] we studied a spin-1/2 system locally coupled to an external bath (in collaboratoin with Dr Zi Cai and Prof Schollwoeck from the LMU Munich). It showed a critical phase, a phase with density wave order at half filling, and a phase that is best seen as a collection of Calgeira-Leggett systems. It is also worth noting that we found Kosterlitz-Thouless transitions with a non-universal value of the Luttinger parameter at the transition point when the coupling to the bath is present. The continuation of the grant for the PIMC topic seems to be very successful without major obstacles.

2) for impurity problems (polarons, nano-systems), Dario Huegel and the PI have been working on extensions of the bosonic dynamical mean-field theory [Phys Rev B 91,224510]. For thermodynamic properties, this study has been progressing rapidly and shown great field-theoretical control over the system. We also looked at out-of-equilibrium systems but more analysis is needed there. The present goal is to develop a cluster method which would be relevant for bosonic lattice systems with synthetic magnetic and gauge fields of relevance to current cold atomic gas experiments. Fermionic systems have been studied by Marcin Raczkowksi (post-doc) using cluster DMFT methods and auxiliary field quantum Monte Carlo simulations, resulting in a paper on a dimensional 1d-2d crossover for fermionic systems of relevance to the organic superconductors [Phys Rev B 91,045137].

3) for diagrammatic Monte Carlo (fermionic many-body systems), PhD student Peter Kroiss and the PI have been working on the Fermi polaron problem. This has progressed steadily and resulted in two papers published in PRB for the quasi-2d system and for the 3d system with mass imbalance, respectively [Phys Rev B 90,104510, Phys Rev B 91,144507]. The key new insight was the reordering of the series by counting the number of hole propagators. PhD student Sebastian Schultess is working on the main goal of the ERC project, namely the physics of screening for fermionic models with long-range interactions, in collaboration with Peter Kroiss and the PI. Finally, an existing collaboration centered around the Troyer group of ETH Zurich has resulted in two diagrammatic Monte Carlo papers for the two-dimensional Hubbard model. In the first one [Phys Rev Lett 113,195301], the spin-up particles preferentially hop along the x-direction and the spin-down particles preferentially along the y-direction. This breaks the spin SU(2) symmetry explicitly and was suggested as a model for an elusive Bose metal phase. However, it was found that the system will still order in the ground state by pairing atoms of the same spin at exponentially low temperatures. In the second paper [arXiv:1509.05050] , SU(2) symmetry is maintained but we investigate the case of population imbalance. It was shown that, for moderately attractive interactions, there exists a region in the phase diagram where the leading instability is towards the Fulde-Ferrel-Larkin-Ovchinnikov pairing, which is a superconducting instability towards a phase with non-zero center of mass pairing. Previous numerical studies could not unambiguously determine the existence of this controversial phase.

1) with path integral Monte Carlo (PIMC) simulations (bosonic systems with short and long-range interactions, supersolids) we studied the optical conductivity and the amplitude mode for U(1) models in 2 dimensions [Phys Rev Lett 112,030402] in collaboration with Prof Prokof'ev (UMass Amherst) and his team. Further, a novel theory for strong disorder in 1d bosonic systems has been proposed [Phys Rev B 89, 054204] (in collaboration with Profs Svistunov and Prokof'ev ) and a review on disordered bosonic systems written [Comptes Rendus Physique, Vol 14, Issue 8, p712-724]. We also worked on the demixing of SU(2) symmetric supersolid mixtures [Phys Rev A 88,033628] (in collaboration with Prof Boninsegni from the University of Alberta) and the dimensional crossover of the Bose-Hubbard model [Phys Rev A 89, 023605] (together with the student Janik Schoenmeier-Kromer). For systems with long-range interactions, we focused on He4 confined to a cylindrical nanopore explaining the different states using liquid crystal terminology and a topological defect (a disclination with Frank index n=1) [Phys Rev Lett 113,045301]. We also argued the quantum nature of dislocations and grain boundaries in solid He4 crystals [Phys Rev B 90, 184508] in collaboration with prof. Kuklov from CSI, CUNY, New York. Finally, in [Phys Rev Lett 113, 260403] we studied a spin-1/2 system locally coupled to an external bath (in collaboratoin with Dr Zi Cai and Prof Schollwoeck from the LMU Munich). It showed a critical phase, a phase with density wave order at half filling, and a phase that is best seen as a collection of Calgeira-Leggett systems. It is also worth noting that we found Kosterlitz-Thouless transitions with a non-universal value of the Luttinger parameter at the transition point when the coupling to the bath is present. The continuation of the grant for the PIMC topic seems to be very successful without major obstacles.

2) for impurity problems (polarons, nano-systems), Dario Huegel and the PI have been working on extensions of the bosonic dynamical mean-field theory [Phys Rev B 91,224510]. For thermodynamic properties, this study has been progressing rapidly and shown great field-theoretical control over the system. We also looked at out-of-equilibrium systems but more analysis is needed there. The present goal is to develop a cluster method which would be relevant for bosonic lattice systems with synthetic magnetic and gauge fields of relevance to current cold atomic gas experiments. Fermionic systems have been studied by Marcin Raczkowksi (post-doc) using cluster DMFT methods and auxiliary field quantum Monte Carlo simulations, resulting in a paper on a dimensional 1d-2d crossover for fermionic systems of relevance to the organic superconductors [Phys Rev B 91,045137].

3) for diagrammatic Monte Carlo (fermionic many-body systems), PhD student Peter Kroiss and the PI have been working on the Fermi polaron problem. This has progressed steadily and resulted in two papers published in PRB for the quasi-2d system and for the 3d system with mass imbalance, respectively [Phys Rev B 90,104510, Phys Rev B 91,144507]. The key new insight was the reordering of the series by counting the number of hole propagators. PhD student Sebastian Schultess is working on the main goal of the ERC project, namely the physics of screening for fermionic models with long-range interactions, in collaboration with Peter Kroiss and the PI. Finally, an existing collaboration centered around the Troyer group of ETH Zurich has resulted in two diagrammatic Monte Carlo papers for the two-dimensional Hubbard model. In the first one [Phys Rev Lett 113,195301], the spin-up particles preferentially hop along the x-direction and the spin-down particles preferentially along the y-direction. This breaks the spin SU(2) symmetry explicitly and was suggested as a model for an elusive Bose metal phase. However, it was found that the system will still order in the ground state by pairing atoms of the same spin at exponentially low temperatures. In the second paper [arXiv:1509.05050] , SU(2) symmetry is maintained but we investigate the case of population imbalance. It was shown that, for moderately attractive interactions, there exists a region in the phase diagram where the leading instability is towards the Fulde-Ferrel-Larkin-Ovchinnikov pairing, which is a superconducting instability towards a phase with non-zero center of mass pairing. Previous numerical studies could not unambiguously determine the existence of this controversial phase.