Prokof'ev, Nikolai
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Professor, Physics Department
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Prokof'ev
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Nikolai
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Physics
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Publication Exact, complete, and universal continuous-time worldline Monte Carlo approach to the statistics of discrete quantum systems(1998) Prokof'ev, Nikolai; Svistunov, Boris; Tupitsyn,We show how the worldline quantum Monte Carlo procedure, which usually relies on an artificial time discretization, can be formulated directly in continuous time, rendering the scheme exact. For an arbitrary system with discrete Hilbert space, none of the configuration update procedures contain small parameters. We find that the most effective update strategy involves the motion of worldline discontinuities (both in space and time), i.e., the evaluation of the Green’s function. Being based on local updates only, our method nevertheless allows one to work with the grand canonical ensemble and nonzero winding numbers, and to calculate any dynamical correlation function as easily as expectation values of, e.g., total energy. The principles found for the update in continuous time generalize to any continuous variables in the space of discrete virtual transitions, and in principle also make it possible to simulate continuous systems exactly.Publication Exact quantum Monte Carlo process for the statistics of discrete systems(1996) Prokof'ev, Nikolai; Svistunov, Boris; Tupitsyn, IWe propose an exact Monte Carlo approach for the statistics of discrete quantum systems that does not employ the standard partition of the imaginary time into a mesh and does not contain small parameters. The method operates with discrete objects — kinks, describing virtual transitions at different moments in time. The global statistics of the kinks is reproduced by exact local procedures, the main one being based on the known solution for an asymmetric two-level system.Publication Effective Hamiltonian in the Problem of a "Central Spin" Coupled to a Spin Environment(1997) Tupitsyn, I; Prokof'ev, Nikolai; Stamp, PWe consider here the problem of a "giant spin", with spin quantum number S≫1, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model describes the low-energy properties of magnetic grains or magnetic macromolecules (ferromagnetically or antiferromagnetically ordered) interacting with a surrounding spin environment, such as nuclear spins. Our aim is to give a general method for truncating the model to another one, valid at low energies, in which a two-level system interacts with the environmental spins, and higher energy terms are absorbed into a new set of couplings. This is done using an instanton technique. We then study the accuracy of this technique, by comparing the results for the low energy effective Hamiltonian, with results derived for the original giant spin, coupled to a macroscopic spin, using exact diagonalization techniques. We find that the low energy central spin effective Hamiltonian gives very accurate results (with increasing accuracy for large S), provided the typical coupling energies between the giant spin and the microscopic spins are not too large, and provided temperature and external field are sufficiently low. The essential limitation to the applicability of the low-energy effective Hamiltonian is just the semiclassical WKB approximation itself, which inevitably fails for very small S. Our results thus justify previous use of this effective Hamiltonian in calculations of the effects of nuclear spins on the dynamics of nanomagnetic systems.Publication Effects of finite temperature on the Mott-insulator state(2006-01) Pupillo, G; Williams, C; Prokof'ev, NikolaiWe investigate the effects of finite temperature on ultracold Bose atoms confined in an optical lattice plus a parabolic potential in the Mott-insulator state. In particular, we analyze the temperature dependence of the density distribution of atomic pairs in the lattice, by means of exact Monte Carlo simulations. We introduce a simple model that quantitatively accounts for the computed pair density distributions at low enough temperatures. We suggest that the temperature dependence of the atomic pair statistics may be used to estimate the system’s temperature at energies of the order of the atoms’ interaction energy.Publication Phase diagram and thermodynamics of the three-dimensional Bose-Hubbard model(2007-01) Capogrosso-Sansone, B; Prokof'ev, Nikolai; Svistunov, BorisWe report results of quantum Monte Carlo simulations of the Bose-Hubbard model in three dimensions. Critical parameters for the superfluid-to-Mott-insulator transition are determined with significantly higher accuracy than has been done in the past. In particular, the position of the critical point at filling factor n=1 is found to be at (U∕t)c=29.34(2), and the insulating gap Δ is measured with accuracy of a few percent of the hopping amplitude t. We obtain the effective mass of particle and hole excitations in the insulating state—with explicit demonstration of the emerging particle-hole symmetry and relativistic dispersion law at the transition tip—along with the sound velocity in the strongly correlated superfluid phase. These parameters are the necessary ingredients to perform analytic estimates of the low temperature (T⪡Δ) thermodynamics in macroscopic samples. We present accurate thermodynamic curves, including these for specific heat and entropy, for typical insulating (U∕t=40) and superfluid (t∕U=0.0385) phases. Our data can serve as a basis for accurate experimental thermometry, and a guide for appropriate initial conditions if one attempts to use interacting bosons in quantum information processing.Publication Absence of a Direct Superfluid to Mott Insulator Transition in Disordered Bose Systems(2009-01) Pollet, L; Prokof'ev, N; Svistunov, B; Troyer,We prove the absence of a direct quantum phase transition between a superfluid and a Mott insulator in a bosonic system with generic, bounded disorder. We also prove the compressibility of the system on the superfluid–insulator critical line and in its neighborhood. These conclusions follow from a general theorem of inclusions, which states that for any transition in a disordered system, one can always find rare regions of the competing phase on either side of the transition line. Quantum Monte Carlo simulations for the disordered Bose-Hubbard model show an even stronger result, important for the nature of the Mott insulator to Bose glass phase transition: the critical disorder bound Δc corresponding to the onset of disorder-induced superfluidity, satisfies the relation Δc>Eg/2, with Eg/2 the half-width of the Mott gap in the pure system.Publication Fate of Vacancy-Induced Supersolidity in 4He(2006-01) Boninsegni, M; Kuklov, A; Pollet, L; Prokof'ev, Nikolai; Svistunov, Boris; Troyer, MThe supersolid state of matter, exhibiting nondissipative flow in solids, has been elusive for 35 years. The recent discovery of a nonclassical moment of inertia in solid 4He by Kim and Chan provided the first experimental evidence, although the interpretation in terms of supersolidity of the ideal crystal phase remains a subject to debate. Using quantum Monte Carlo methods we investigate the long-standing question of vacancy-induced superflow and find that vacancies in a 4He crystal phase separate instead of forming a supersolid. On the other hand, nonequilibrium vacancies relaxing on defects of polycrystalline samples could provide an explanation for the experimental observations.Publication Superfluid-insulator and roughening transitions in domain walls(2007-01) Söyler, S; Capogrosso-Sansone,; Prokof'ev, Nikolai; Svistunov, BorisWe have performed quantum Monte Carlo simulations to investigate the superfluid behavior of one- and two-dimensional interfaces separating checkerboard solid domains. The system is described by the hard-core Bose-Hubbard Hamiltonian with nearest-neighbor interaction. In accordance with Burovski et al. [Phys. Rev. Lett. 94, 165301 (2005)] we find that (i) the interface remains superfluid in a wide range of interaction strength before it undergoes a superfluid-insulator transition; (ii) in one dimension, the transition is of the Kosterlitz-Thouless type and is accompanied by the roughening transition, driven by proliferation of charge-1∕2 quasiparticles; (iii) in two dimensions, the transition belongs to the three-dimensional U(1) universality class and the interface remains smooth. Similar phenomena are expected for domain walls in quantum antiferromagnets.Publication Superglass Phase of 4He(2006-01) Boninsegni, M; Prokof'ev, Nikolai; Svistunov, BorisWe study different solid phases of 4He, by means of path integral Monte Carlo simulations based on a recently developed worm algorithm. Our study includes simulations that start off from a high-T gas phase, which is then “quenched” down to T=0.2 K. The low-T properties of the system crucially depend on the initial state. While an ideal hcp crystal is a clear-cut insulator, the disordered system freezes into a superglass, i.e., a metastable amorphous solid featuring off-diagonal long-range order and superfluidity.Publication The Fermi–Hubbard model at unitarity(2006-01) Bourovski, F; Prokof'ev, Nikolai; Svistunov, Boris; Troyer, MWe simulate the dilute attractive Fermi–Hubbard model in the unitarity regime using a diagrammatic determinant Monte Carlo (MC) algorithm with worm-type updates. We obtain the dependence of the critical temperature on the filling factor ν and, by extrapolating to ν → 0, determine the universal critical temperature of the continuum unitary Fermi gas in units of Fermi energy: Tc/εF = 0.152(7). We also determine the thermodynamic functions and show how the MC results can be used for accurate thermometry of a trapped unitary gas.