Worm Algorithm for Problems of Quantum and Classical Statistics

This is a chapter of the multi-author book "Understanding Quantum Phase Transitions," edited by Lincoln Carr and published by Taylor and Francis. In this chapter, we give a general introduction to the worm algorithm and present important results highlighting the power of the approachComment: 27 pages, 15 figures, chapter in a boo

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.Comment: Revtex, 4 pages, no figures; Submitted to Phys. Rev. A (Brief Reports

Criticality in Trapped Atomic Systems

We discuss generic limits posed by the trap in atomic systems on the accurate determination of critical parameters for second-order phase transitions, from which we deduce optimal protocols to extract them. We show that under current experimental conditions the in-situ density profiles are barely suitable for an accurate study of critical points in the strongly correlated regime. Contrary to recent claims, the proper analysis of time-of-fight images yields critical parameters accurately.Comment: 4 pages, 3 figures; added reference

Comment on "Direct Mapping of the Finite Temperature Phase Diagram of Strongly Correlated Quantum Models" by Q. Zhou, Y. Kato, N. Kawashima, and N. Trivedi, Phys. Rev. Lett. 103, 085701 (2009)

In their Letter, Zhou, Kato, Kawashima, and Trivedi claim that finite-temperature critical points of strongly correlated quantum models emulated by optical lattice experiments can generically be deduced from kinks in the derivative of the density profile of atoms in the trap with respect to the external potential, $\kappa = -dn(r)/dV(r)$. In this comment we demonstrate that the authors failed to achieve their goal: to show that under realistic experimental conditions critical densities $n_c(T,U)$ can be extracted from density profiles with controllable accuracy.Comment: 1 page, 1 figur

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.Comment: 11 pages, 13 figure

Polynomial complexity despite the fermionic sign

It is commonly believed that in quantum Monte Carlo approaches to fermionic many- body problems, the infamous sign problem generically implies prohibitively large computational times for obtaining thermodynamic-limit quantities. We point out that for convergent Feynman diagrammatic series evaluated with the Monte Carlo algorithm of [Rossi, arXiv:1612.05184], the computational time increases only polynomially with the inverse error on thermodynamic-limit quantities

Diagrammatic Monte Carlo algorithm for the resonant Fermi gas

We provide a description of a diagrammatic Monte Carlo algorithm for the resonant Fermi gas in the normal phase. Details are given on diagrammatic framework, Monte Carlo moves, and incorporation of ultraviolet asymptotics. Apart from the self-consistent bold scheme, we also describe a non-self-consistent scheme, for which the ultraviolet treatment is more involved.Comment: Revised and extended versio