## Current research topics

Our group is interested in novel states of quantum matter, universal thermodynamic and dynamic properties of continuous phase transitions, ground-state and finite-temperature phase diagrams, as well as benchmark calculations of experimental systems. To deal with effects of strong correlations in bosonic and fermionic Hamiltonians we employ a combination of exact analytic considerations, path integral, and diagrammatic Monte Carlo methods. Some of the highlights include universal properties of weakly-interacting Bose gases in the fluctuation region, the BCS-BEC crossover curve for the resonant Fermi gas, quantum critical dynamics at the superfluid-to-Mott insulator phase transition, and ground-state phase diagrams for disordered bosons.

The Fermi polaron is an impurity interacting with a sea of fermions. Similar setups have been addressed in the context of electric conductance (electrons immersed in a bath of phonons -- the collective excitations of the dielectric medium) or mixtures of different helium isotopes. In atomic physics the Fermi polaron can also be understood as the limiting case of a population-imbalanced two-species system, where one species has been diluted so strongly that it now merely consists of one particle. The impurity exchanges momentum with particles in the Fermi sea, thus creating particle-hole pairs. If interactions are sufficiently strong, a molecular bound state forms between the impurity and a fermion from the environment. Diagrammatic Monte Carlo has proven very successful in calculating different properties of the Fermi polaron. It allows us to study the system in a controlled, systematically improvable way and with great precision. Currently we study the polaron spectral function, which is directly linked to many of its physical propertis and is the quantity probed in experiments.

A characteristic feature of all frustrated magnets is close competition among numerous spin configurations and absence of an obvious arrangement that gains the maximum amount of energy from all interaction terms. Frustration prevents the development of long-range magnetic orders and often leads to novel and exotic collective phenomena. One of the best known examples is the fluid-like states of magnets, so-called spin liquids, in which the constituent spins are highly correlated but still fluctuate strongly down to a temperature of absolute zero. The fluctuations of the spins in a spin liquid can be classical or quantum and show remarkable collective phenomena such as emergent gauge fields and fractionalized excitations. Unfortunately, in the strongly correlated regime of frustrated spin systems, conventional Monte Carlo methods suffer from the notorious sign problem, and variational methods are not applicable. Our approach is to employ the Diagrammatic Monte Carlo (DiagMC) method, which is based on Monte Carlo sampling of skeleton Feynman diagrams, within the fermionization framework of spin systems. The DiagMC method allows us to study the low temperature physics of strongly correlated quantum spin systems in a controlled way. The first successful application of DiagMC to spin systems is the study of the triangular lattice spin-1/2 Heisenberg model. We reveal a surprisingly accurate microscopic correspondence with its classical counterpart at all accessible temperatures in the correlated paramagnet regime. We can also obtain the zero temperature physics by extrapolation of this relation. In our recent work, we performed a DiagMC study of the SU(2)-symmetric spin-1/2 Heisenberg antiferromagnet on a pyrochlore lattice and found a "fingerprint" evidence for the thermal spin-ice state in a broad low temperature regime where degenerate states satisfy the "2-in/2-out" ice rule on each tetrahedron. The dynamics of the fractional excitations has also been revealed.

A quantum critical point is a continuous phase transition at zero temperatue. Due to the strong zero point quantum fluctuations associated with Heisenberg's uncertainty principle, quantum critical systems are strongly correlated and thus feature many novel emergent phenomena. The superfluid-to-Mott insulator quantum critical point (SF-MI QCP), which can be realized with ultracold atoms in an optical lattice, is one of the simplest examples of quantum criticality. Near the QCP, the system is described by the relativistic Φ4 theory with complex field, and thus has emergent Lorentz invariance. The "universe" near the SF-MI QCP mimics the standard model in particle physics, with bosonic atoms corresponding to the relativistic superfluid vacuum, the speed of sound to the speed of light, phonons to massless Goldstone modes and the amplitude mode to Higgs bosons. The emergent amplitude mode (also called massive Goldstone or Higgs mode) has strong decay into phonons in (2+1)-dimensions. Its visiblity in the relevant spectral functions has been controversial for decades. We caculate the spectral function for the kinetic energy using path-integral Monte Carlo simulations and numerical analytical continuation methods, and we find the amplitude mode survives as a well-defined universal finite-width resonance. The frequency dependent universal conductivity at SF-MI QCP received a lot of interest recently as a way of testing the AdS/CFT correspondence from string theory. We find that the AdS/CFT correspondence for transport properties can be made compatible with the data if temperature of the horizon of the black brane is different from the temperature of the conformal field theory. The requirements for measuring the universal conductivity in an ultacold atoms experiment are also determined by our calculation.

** Scratched XY universality class**

In 1987, Giamarchi and Schulz showed that in one-dimensional disordered and interacting boson systems there is a quantum phase transition from a superfluid to an insulating state in the weak-disorder limit. This phase transition is driven by the proliferation of vortex–anti-vortex pairs in the mapped 2D classical field. It belongs to the well-known Berezinskii-Kosterlitz-Thouless universality class that is ubiquitous in 1D quantum and 2D classical systems. However, the nature of the phase transition in the strong-disorder regime had been beyond the reach of physicists for nearly 30 years! Inspired by the special role played by potential barriers (weak links) in destroying superfluidity in 1D quantum systems, we developed an asymptotically exact renormalization group theory of superfluid-insulator transitions describing phase transitions in both the strong- and weak-disorder regimes, as well as the crossover between the two. We found that in the strong-disorder regime, weak links can cut the superfluid into disconnected pieces and thus destroy superfluidity, while the proliferation of vortex–anti-vortex pairs remains irrelevant. The new universality class is coined the "scratched XY universality class" since upon (1+1)D mapping, the 1D quantum system is mapped to a 2D classical system with correlated disorder in the form of parallel "scratches". Based on our theory, for the first time we are able to establish the ground-state phase diagram of the 1D disordered Bose-Hubbard model.