title: Locating the quantum critical point of the Bose-Hubbard model through singularities of simple observables.
abstract: We show that the critical point of the two-dimensional Bose-Hubbard model can be easily found through studies of either on-site atom number fluctuations or the nearest-neighbor two-point correlation function (the expectation value of the tunnelling operator). Our strategy to locate the critical point is based on the observation that the derivatives of these observables with respect to the parameter that drives the superfluid-Mott insulator transition are singular at the critical point in the thermodynamic limit. Performing the quantum Monte Carlo simulations of the two-dimensional Bose-Hubbard model, we show that this technique leads to the accurate determination of the position of its critical point. Our results can be easily extended to the three-dimensional Bose-Hubbard model and different Hubbard-like models. They provide a simple experimentally-relevant way of locating critical points in various cold atomic lattice systems.
authors.affiliation: Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagielloński, ulica Łojasiewicza 11, 30-348 Kraków, Poland.|Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria.|Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria.
authors.forename: Mateusz
authors.initials: M
authors.lastname: Łącki
authors.affiliation: Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagielloński, ulica Łojasiewicza 11, 30-348 Kraków, Poland.
authors.forename: Bogdan
authors.initials: B
authors.lastname: Damski
authors.affiliation: Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagielloński, ulica Łojasiewicza 11, 30-348 Kraków, Poland.
authors.forename: Jakub
authors.initials: J
authors.lastname: Zakrzewski