We prove that previous claims of observing a direct superfluid-Mott insulator
transition in the disordered J-current model are in error because numerical
simulations were done for too small system sizes and the authors ignored the
rigorous theorem.Comment: 1 page, Latex, 1 figur

Prokof'ev, Nikolay

Svistunov, Boris

English

arXiv

In a recent Letter [1] (see also [2]) the authors presented numerical evidence supporting an idea of a direct transition between the superfluid (SF) and Mott insulating (MI) phases in the disordered Bosonic system, and even studied non-trivial properties of the multicritical line where SF, MI and the Bose Glass (BG) phases meet. The results were obtained from Monte Carlo simulations of the (2+1)-dimensional classical loop-current model [3] with the lattice action S = 1 2K ÞE ~ J=0 XrƒÑ ~ J2(r, ƒÑ) . 2(ƒÊ + v(r)) ~ JƒÑ (r, ƒÑ) . (1) where r, ƒÑ are spatial and imaginary time coordinates, and ~ J(r, ƒÑ) are integer current vectors with zero divergence. The spatial disorder potential v(r) is uniformly distributed on the interval (.,)

Prokof’ev, N

Svistunov, B

ScholarWorks@UMass Amherst

University of Massachusetts AmherstScholarWorks@UMass AmherstPhysics Department Faculty Publication Series Physics2003Comment on “Phase Diagram of a DisorderedBoson Hubbard Model in Two Dimensions”N Prokof ’evUniversity of Massachusetts - Amherst, prokofev@physics.umass.eduB SvistunovUniversity of Massachusetts - Amherst, svistunov@physics.umass.eduFollow this and additional works at: https://scholarworks.umass.edu/physics_faculty_pubsPart of the Physics CommonsThis Article is brought to you for free and open access by the Physics at ScholarWorks@UMass Amherst. It has been accepted for inclusion in PhysicsDepartment Faculty Publication Series by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contactscholarworks@library.umass.edu.Recommended CitationProkof ’ev, N and Svistunov, B, "Comment on “Phase Diagram of a Disordered Boson Hubbard Model in Two Dimensions”" (2003).Physics Department Faculty Publication Series. 1121.Retrieved from https://scholarworks.umass.edu/physics_faculty_pubs/1121arXiv:cond-mat/0310251v1  [cond-mat.dis-nn]  10 Oct 2003Comment on “Phase Diagram of a Disordered Bo-son Hubbard Model in Two Dimensions”In a recent Letter [1] (see also [2]) the authors pre-sented numerical evidence supporting an idea of a directtransition between the superfluid (SF) and Mott insulat-ing (MI) phases in the disordered Bosonic system, andeven studied non-trivial properties of the multicriticalline where SF, MI and the Bose Glass (BG) phases meet.The results were obtained from Monte Carlo simulationsof the (2+1)-dimensional classical loop-current model [3]with the lattice actionS =12K∇· ~J=0∑rτ[~J2(r, τ) − 2(µ+ v(r)) ~Jτ (r, τ)]. (1)where r, τ are spatial and imaginary time coordinates,and ~J(r, τ) are integer current vectors with zero diver-gence. The spatial disorder potential v(r) is uniformlydistributed on the interval (−∆,∆).Here we prove that all of the above mentioned con-clusions are incorrect and originate from doing simula-tions for too small system sizes (the maximum systemsize considered in [1] was Lx × Ly × Lτ = 14× 14× 20),and ignoring the rigorous theorem of [4, 5] saying thatfor disorder ∆ larger than the half-width of the energygap in the ideal Mott insulator (we denote it as Eg) thesystem state is compressible, i.e. it is BG. Indeed, in theinfinite system one can always find arbitrary large regionswith the chemical potential being nearly homogeneouslyshifted downwards or upwards by ∆. There is no energygap then for the particle transfer between such regions,and they can be doped with particles/holes. [The con-jecture is that the MI-BG transition is exactly at theupper boundary of the theorem, ∆ = Eg(K).] We note,that the theorem is based on rare statistical fluctuations,and for ∆ → 0 the distance between regions contribut-ing to non-zero but exponentially small compressibility isdiverging exponentially.In Fig. 1 we plot our data for Eg(K) [6] along withthe critical values of disorder for the superfluid-insulatortransition. Since ∆ is always larger than Eg(Kc), thetransition is always from SF to the compressible insu-lating phase, or BG. Accordingly, the multicritical linewhere SF, MI, and BG phases meet does not exists fornon-zero ∆.The diverging distance between rare statistical real-izations of disorder is the major problem in interpretingMonte Carlo data for small system sizes. Recently devel-oped Worm algorithms [6, 7] allow simulations of systemsizes as large as 160×160×1000, but for ∆ = 0.4 even thisis barely enough to resolve very small but finite compress-ibility at the critical point [6]. Clearly, for smaller systemsizes and smaller values of disorder the short length-scalebehavior will mimic a direct SF-MI transition observedin Refs. [1, 2]. Similar arguments were used previouslyin the criticism of the direct SF-MI transition in one di-mensional systems [8].0 0.1 0.2 0.300.10.20.30.4K∆MISFBGFIG. 1: The phase diagram of the disordered, commensurateloop-current model (1). All error bars are of order 10−3 andsmaller than point sizes; data points for the SF-BG line weretaken from: ∆ = 0.4 [1, 2, 6], ∆ = 0.2 [2] ∆ = 0.1, 0.5 [thiswork].This work was supported by the National ScienceFoundation under Grant DMR-0071767.Nikolay Prokof’ev and Boris SvistunovDepartment of Physics,University of Massachusetts, Amherst, MA 01003,Russian Research Center “Kurchatov Institute”,123182 Moscow, RussiaPACS numbers: 74.20.De, 73.43.Nq, 74.40.+k[1] J.-W. Lee, M.-C. Cha, and D. Kim, Phys. Rev. Lett. 87,247006 (2001); ibid, 88, 049901 (2002)[2] J. Kisker and H. Rieger, Phys. Rev. B 55, R11981 (1997).[3] M. Wallin, et al., Phys. Rev. B 49, 12115 (1994).[4] M.P.A. Fisher, et al., Phys. Rev. B, 40, 546 (1989);[5] J.K. Freericks and H. Monien, Phys. Rev. B 53, 2691(1996).[6] N.V. Prokof’ev and B.V. Svistunov, cond-mat/0301205.[7] F. Alet and E.S. Sørensen, Phys. Rev. E 67, 015701(2003); ibid, 68, 026702 (2003).[8] N.V. Prokof’ev and B.V. Svistunov, Phys. Rev. Lett. 80,4355 (1998);

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