Ultra-cold gases

- Our research is focusing on novel phases, vortex matter, phase transitions, and  other properties of cold bosons
in optical lattices.  The most recent efforts are on multi-component systems.

- We are the first group to calculate the BCS-BEC crossover curve for the  resonant Fermi gas  with controlled error bars.
Recently we developed a Diagrammatic Monte Carlo technique for numerically exact solution of the fermi-polaron problem
(resonant gas near 100% polarization) and work on  generalizing it to the many body case.

-We found new complex states of three-dimensional vortex matter in binary mixtures of Bose Condensates

- Our calculations established universal properties of weakly-interacting Bose gases in the fluctuation region (including the
critical temperature dependence on interactions). We are now working on the generic approach to the thermodynamics of
the system at all temperatures.

- We participate in the Optical Lattice Emulator project as part of the MIT-Harvard-Amherst-Innsbrouck-Paris-Mainz
collaboration to  perform high accuracy benchmark simulations of bosonic systems "as is''.

- We also work on the phase diagram and excitation spectrum Dipole gases.


Projected new states of matter and metallization of hydrogen

We work on the proposal of possible metallic quantum ordered states of hydrogen at ultrahigh compressions and low temperatures
which we predict are projected new states of matter endowed with exotic properties. Our works on this topic introduced the notion
of metallic superfluid and received front page billing in Nature and Nature Physics magazines.


Type-1.5 superconductivity
 
In multicomponent systems there could be a new type superconductivity falling outside the usual type-I/type-II dichotomy

Supersolidity in Helium

After we proved that ideal crystals of He-4 are not supersolid we discovered that disordered crystals are. Grain boundaries, ridges,
screw, and some edge dislocations have complex structural and superfluid properties in quantum crystlas. Most of the issues have
 never been explored before.

Monte Carlo methods

We have pioneered several key techniques in the field: Worm Algorithm, Diagrammatic Monte Carlo, and Bold Diagrammatic
Monte carlo. They have broad applications across all fields in physics and statistical mechanics.  Currently, we actively work
on the method for stochastic summation of all relevent Feyman diagrams (up to  some high order) for many-body systems,
including self-consistency conditions for efficient treatment of geometrical series and parquet.

New topological defects in condensed matter Knotted Solitons:

We study properties and condensed matter realizations of novel type of complex topological defects: the knotted solitons.
We also study collective propertis, aggregate states and phase transitions in the systems of  exotic topological defects such
as fractionally quantized quantum vortices.

Statistical models
We are interested in performing high precision tests of the hyperscaling relation, fractional dimensions for vortex lines at
criticality in neutral and charged XY-models in 3D, the phase diagram of the deconfined critical action with SU(2) symmetry,
superfluidity in structured networks, etc.

Atom tunneling