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N. V. Prokof'ev

Publications and source records attributed to N. V. Prokof'ev.

At least 55 records · Page 3Linked to original sources
arXiv2007

Phase diagram and thermodynamics of the three-dimensional Bose-Hubbard model

We 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 it 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 Delta 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 << Delta) 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.

cond-mat.other↗
arXiv2006

Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations

A detailed description is provided of a new Worm Algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the general Path Integral Monte Carlo (PIMC) scheme, but also allows one to perform quantum simulations in the grand canonical ensemble, as well as to compute off-diagonal imaginary-time correlation functions, such as the Matsubara Green function, simultaneously with diagonal observables. Another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary (diagrammatic) contributions, which are then statistically sampled. This affords a complete microscopic account of the long-range part of the potential energy, while keeping the computational complexity of all updates independent of the size of the simulated system. The computational scheme allows for efficient calculations of the superfluid fraction and off-diagonal correlations in space-time, for system sizes which are orders of magnitude larger than those accessible to conventional PIMC. We present illustrative results for the superfluid transition in bulk liquid helium-four in two and three dimensions, as well as the calculation of the chemical potential of solid helium-four.

physics.comp-ph↗
arXiv2003

Optical conductivity of the Frohlich polaron

We present accurate results for optical conductivity of the three dimensional Frohlich polaron in all coupling regimes. The systematic-error free diagrammatic quantum Monte Carlo method is employed where the Feynman graphs for the momentum-momentum correlation function in imaginary time are summed up. The real-frequency optical conductivity is obtained by the analytic continuation with stochastic optimization. We compare numerical data with available perturbative and non-perturbative approaches to the optical conductivity and show that the picture of sharp resonances due to relaxed excited states in the strong coupling regime is ``washed out''by large broadening of these states. As a result, the spectrum contains only a single-maximum broad peak with peculiar shape and a shoulder.

cond-mat.str-el↗
arXiv2003

'Hole-digging' in ensembles of tunneling Molecular Magnets

The nuclear spin-mediated quantum relaxation of ensembles of tunneling magnetic molecules causes a 'hole' to appear in the distribution of internal fields in the system. The form of this hole, and its time evolution, are studied using Monte Carlo simulations. It is shown that the line-shape of the tunneling hole in a weakly polarised sample must have a Lorentzian lineshape- the short-time half-width $ξ_o$ in all experiments done so far should be $\sim E_0$, the half-width of the nuclear spin multiplet. After a time $τ_o$, the single molecule tunneling relaxation time, the hole width begins to increase rapidly. In initially polarised samples the disintegration of resonant tunneling surfaces is found to be very fast.

cond-mat.mes-hall↗
arXiv2002

Self-Trapping of Polarons in the Rashba-Pekar Model

We performed quantum Monte Carlo study of the exciton-polaron model which features the self-trapping phenomenon when the coupling strength and/or particle momentum is varied. For the first time accurate data for energy, effective mass, the structure of the polaronic cloud, dispersion law, and spectral function are available throughout the crossover region. We observed that self-trapping can not be reduced to hybridization of two states with different lattice deformation, and that at least three states are involved in the crossover from light- to heavy-mass regimes.

cond-mat.str-el↗
arXiv2002

Revealing Superfluid--Mott-Insulator Transition in an Optical Lattice

We study (by an exact numerical scheme) the single-particle density matrix of $\sim 10^3$ ultracold atoms in an optical lattice with a parabolic confining potential. Our simulation is directly relevant to the interpretation and further development of the recent pioneering experiment by Greiner et al. In particular, we show that restructuring of the spatial distribution of the superfluid component when a domain of Mott-insulator phase appears in the system, results in a fine structure of the particle momentum distribution. This feature may be used to locate the point of the superfluid--Mott-insulator transition.

cond-mat↗
arXiv2001

Diagrammatic Quantum Monte Carlo for Two-Body Problem: Exciton

We present a novel method for precise numerical solution of the irreducible two-body problem and apply it to excitons in solids. The approach is based on the Monte Carlo simulation of the two-body Green function specified by Feynman's diagrammatic expansion. Our method does not rely on the specific form of the electron and hole dispersion laws and is valid for any attractive electron-hole potential. We establish limits of validity of the Wannier (large radius) and Frenkel (small radius) approximations, present accurate data for the intermediate radius excitons, and give evidence for the charge transfer nature of the monopolar exciton in mixed valence materials.

cond-mat.str-el↗
arXiv2001

Single hole spectral function and spin-charge separation in the t-J model

Worm algorithm quantum Monte Carlo simulations of the hole Green function with subsequent spectral analysis were performed for J/t 0.1, 0.2, 0.4 on lattices with up to LxL=32x32 sites at temperatures as low as T=J/40, and present, apparently, the hole spectral function in the thermodynamic limit. Spectral analysis reveals a delta-function-sharp quasiparticle peak at the lower edge of the spectrum which is incompatible with the power-law singularity and thus rules out the possibility of spin-charge separation in this parameter range. Spectral continuum features two peaks separated by a gap ~4t.

cond-mat↗
arXiv1999

Comprehensive study of Frohlich polaron

A detailed study of the Frohlich polaron model is performed on the basis of diagrammatic quantum Monte Carlo method. The method is further developed both quantitatively (performance) and qualitatively (new estimators), and is enhanced by spectral analysis of the polaron Green function, within a novel approach. We present the best up to date results for the binding energy, and for the first time make available precise data for the effective mass, including the region of intermediate and strong couplings. We look at the structure of the polaron cloud and answer such questions as the average number of phonons in the cloud and their number/momentum distribution. The spectral analysis reveals non-trivial structure of the spectral density at intermediate and large coupling: the spectral continuum features pronounced peaks that we attribute to unstable excited states of the polaron.

cond-mat.stat-mech↗
arXiv1999

Supercurrent Stability in a Quasi-1D Weakly Interacting Bose Gas

We discuss a possibility of observing superfluid phenomena in a quasi-1D weakly interacting Bose gas at finite temperatures. The weakness of interaction in combination with generic properties of 1D liquids can result in a situation when relaxational time of supercurrent is essentially larger than the time of experimental observation, and the behavior of the system is indistinguishable from that of a genuine superfluid.

cond-mat↗
arXiv1999

Two Definitions of Superfluid Density

We point out that two different definitions of the superfluid density - through statistical response to static gauge phase and through dynamic response to altering gauge phase - yield, generally speaking, different quantities in $d<3$. The physics leading to this difference is associated with the equilibrium statistics of supercurrent states. Some experimentally observable consequences of this fact are discussed.

cond-mat↗
arXiv1998

Effect of the Tunneling Conductance on the Coulomb Staircase

Quantum fluctuations of the charge in the single electron box are investigated. The rounding of the Coulomb staircase caused by virtual electron tunneling is determined by perturbation theory up to third order in the tunneling conductance and compared with precise Monte Carlo data computed with a new algorithm. The remarkable agreement for large conductance indicates that presently available experimental data on Coulomb charging effects in metallic nanostructures can be well explained by finite order perturbative results.

cond-mat.mes-hall↗
arXiv1998

Quasicondensation in 2D Interacting Bose Gas: Quantum Monte Carlo Study

We present a detailed Monte Carlo study of correlations in an interacting two-dimensional Bose gas. The data for one-particle density matrix in coordinate representation are compared to the results for the local many-particle density correlators, which are responsible for the recombination rate in real experiments. We found that the appearance and growth of quasicondensate fluctuations changes local correlations between the particles well before the Kosterlitz-Thouless transition point. The amplitude of the $1/m!$-effect is very sensitive even to a rather moderate interaction, and is considerably smaller than its limiting value.

cond-mat↗
arXiv1998

Quantum Relaxation of Ensembles of Nanomagnets

Recent theory and experiment in crystals of molecular magnets suggest that fundamental tests of the decoherence mechanisms of macroscopic quantum phenomena may be feasible in these systems (which are almost ideal quantum spin glasses). We review the results, and suggest new experiments.

cond-mat↗
arXiv1998

Exact, Complete, and Universal Continuous-Time Worldline Monte Carlo Approach to the Statistics of Discrete Quantum Systems

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 non-zero winding numbers, and to calculate any dynamic 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.

cond-mat↗
arXiv1998

Quantum spin chains in a magnetic field

We demonstrate that the ``worm'' algorithm allows very effective and precise quantum Monte Carlo (QMC) simulations of spin systems in a magnetic field, and its auto-correlation time is rather insensitive to the value of H at low temperature. Magnetization curves for the $s=1/2$ and $s=1$ chains are presented and compared with existing Bethe ansatz and exact diagonalization results. From the Green function analysis we deduce the magnon spectra in the s=1 system, and directly establish the "relativistic" form E(p)=(Δ^2 +v^2 p^2)^{1/2} of the dispersion law.

cond-mat.str-el↗
arXiv1997

Effective Hamiltonian in the Problem of a "Central Spin" Coupled to a Spin Environment

We 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 interacting with a surrounding spin environment, such as nuclear spins. We describe 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 verify 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 microscopic spin, using exact diagonalisation techniques.

cond-mat↗