Abstract
An iterative scheme based on the kernel polynomial method is devised for the efficient computation of the one-body density matrix of weakly interacting Bose gases within Bogoliubov theory. This scheme is used to analyze the coherence properties of disordered bosons in one and two dimensions. In the one-dimensional geometry, we examine the quantum phase transition between superfluid and Bose glass at weak interactions, and we recover the scaling of the phase boundary that was characterized using a direct spectral approach by Fontanesi et al (2010 Phys. Rev. A 81 053603). The kernel polynomial scheme is also used to study the disorder-induced condensate depletion in the two-dimensional geometry. Our approach paves the way for an analysis of coherence properties of Bose gases across the superfluid–insulator transition in two and three dimensions.
Highlights
[42] Clement D, Bouyer P, Aspect A and Sanchez-Palencia L 2008 Density modulations in an elongated Bose-Einstein condensate released from a disordered potential Phys
[60] Allard B, Plisson T, Holzmann M, Salomon G, Aspect A, Bouyer P and Bourdel T 2012 Effect of disorder close to the superfluid transition in a two-dimensional Bose gas Phys
Summary
[25] Altman E, Kafri Y, Polkovnikov A and Refael G 2010 Superfluid-insulator transition of disordered bosons in one dimension Phys. [27] Ristivojevic Z, Petkovic A, Le Doussal P and Giamarchi T 2012 Phase transition of interacting disordered bosons in one dimension Phys. [28] Aleiner I L, Altshuler B L and Shlyapnikov G V 2010 A finite-temperature phase transition for disordered weakly interacting bosons in one dimension Nature Phys.
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