Nikolay Prokof'ev

Critical temperature and thermodynamics of attractive fermions at unitarity

The unitarity regime of the BCS-BEC crossover can be realized by diluting a system of two-component lattice fermions with an on-site attractive interaction. We perform a systematic-error-free finite-temperature simulation of this system by diagrammatic determinant Monte Carlo method. The critical temperature in units of Fermi energy is found to be T(C)/epsilonF=0.152(7). We also report the behavior of the thermodynamic functions, and discuss the issues of thermometry of ultracold Fermi gases.

Monte Carlo study of the two-dimensional Bose-Hubbard model

One of the most promising applications of ultracold gases in optical lattices is the possibility to use them as quantum emulators of more complex condensed matter systems. We provide benchmark calculations, based on exact quantum Monte Carlo simulations, for the emulator to be tested against. We report results for the ground state phase diagram of the two-dimensional Bose-Hubbard model at unity filling factor. We precisely trace out the critical behavior of the system and resolve the region of small insulating gaps,

Worm Algorithm for Continuous-Space Path Integral Monte Carlo Simulations

\ensuremath{\Delta}⪡J

Critical Point of a Weakly Interacting Two-Dimensional Bose Gas

. The critical point is found to be

Fermi-polaron problem: Diagrammatic Monte Carlo method for divergent sign-alternating series

{(J/U)}_{c}=0.05974(3)

What makes a crystal supersolid

, in perfect agreement with the high-order strong-coupling expansion method of Elstner and Monien [Phys. Rev. B 59, 12184 (1999)]. In addition, we present data for the effective mass of particle and hole excitations inside the insulating phase and obtain the critical temperature for the superfluid-normal transition at unity filling factor.

“Worm” algorithm in quantum Monte Carlo simulations

We present a new approach to path integral Monte Carlo (PIMC) simulations based on the worm algorithm, originally developed for lattice models and extended here to continuous-space many-body systems. The scheme allows for efficient computation of thermodynamic properties, including winding numbers and off-diagonal correlations, for systems of much greater size than that accessible to conventional PIMC simulations. As an illustrative application of the method, we simulate the superfluid transition of 4He in two dimensions.

Fate of Vacancy-Induced Supersolidity in 4He

We study the Berezinskii-Kosterlitz-Thouless transition in a weakly interacting 2D quantum Bose gas using the concept of universality and numerical simulations of the classical absolute value psi(4) model on a lattice. The critical density and chemical potential are given by relations n(c) = (mT/2piPlancks(2))ln(xiPlancks(2)/mU) and mu(c) = (mTU/piPlancks(2))ln(xi(mu)Plancks(2)/mU), where T is the temperature, m is the mass, and U is the effective interaction. The dimensionless constant xi = 380+/-3 is very large and thus any quantitative analysis of the experimental data crucially depends on its value. For xi(mu) our result is xi(mu) = 13.2+/-0.4. We also report the study of the quasicondensate correlations at the critical point.

Absence of a Direct Superfluid to Mott Insulator Transition in Disordered Bose Systems

Diagrammatic Monte Carlo approach is applied to a problem of a single spin-down fermion resonantly interacting with the sea of ideal spin-up fermions. On one hand, we develop a generic, sign-problem tolerant, method of exact numerical solution of polaron-type models. On the other hand, our solution is important for understanding the phase diagram and properties of the BCS-BEC crossover in the strongly imbalanced regime. This is the first, and possibly characteristic, example of how the Monte Carlo approach can be applied to a divergent sign-alternating diagrammatic series.

Two-dimensional weakly interacting Bose gas in the fluctuation region

For nearly half a century the supersolid phase of matter has remained mysterious, not only eluding experimental observation, but also generating a great deal of controversy among theorists. The recent discovery of what is interpreted as a non-classical moment of inertia at low temperature in solid 4He [E. Kim and M.H.W. Chan, Nature 427 225 (2004a); E. Kim and M.H.W. Chan, Science 305 1941 (2004b); E. Kim and M.H.W. Chan, Phys. Rev. Lett. 97 115302 (2006); A.C. Clark and M.H.W. Chan, J. Low Temp. Phys. 138 853 (2005)] has elicited much excitement as a possible first observation of a supersolid phase. In the two years following the discovery, however, more puzzles than answers have been provided to the fundamental issue of whether the supersolid phase exists, in helium or any other naturally occurring condensed matter system. Presently, there is no established theoretical framework to understand the body of experimental data on 4He. Different microscopic mechanisms that have been suggested to underlie superfluidity in a perfect quantum crystal do not seem viable for 4He, for which a wealth of experimental and theoretical evidence points to an insulating crystalline ground state. This perspective addresses some of the outstanding problems with the interpretation of recent experimental observations of the apparent superfluid response in 4He (seen now by several groups, e.g. A.S. Rittner and J.D. Reppy 2006; M. Kondo, S. Takada, Y. Shibayama and K. Shirahama, Proceedings of QFS2006, Kyoto, Submitted to J. Low Temp. Phys.; A. Penzyev, Y. Yasuta and M. Kubota, Proceedings of QFS2006, Kyoto, Submitted to J. Low Temp. Phys., cond-mat/0702632.) and discusses various scenarios alternative to the homogeneous supersolid phase, such as superfluidity induced by extended defects of the crystalline structure, including grain boundaries, dislocations and anisotropic stresses. Can a metastable superfluid ‘glassy’ phase exist, and can it be relevant to some of the experimental observations? One of the most interesting and unsolved fundamental questions is what interatomic potentials, given the freedom to design one, can support an ideal supersolid phase in continuous space, and can they be found in Nature.