Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9609243 · Physical review. B, Condensed matter

Superfluid–Bose-glass transition in weakly disordered commensurate one-dimensional system

Boris V. Svistunov

Published Dec 1, 1996• 42 citations
arXivHTMLPDF

Abstract

We study the effect of commensurability (integer filling factor) on the superfluid (SF)--Bose-glass (BG) transition in a one-dimensional disordered system in the limit of weak disorder, when the effect is most pronounced and, on the other hand, may be traced via the renormalization-group analysis. The equation for the SF-BG phase boundary demonstrating the effect of disorder-stimulated superfluidity implies that the strength of disorder sufficient to restore superfluidity from Mott insulator (MI) is much larger than that enough to turn MI into BG. Thus we provide an explicit proof of the fact that at arbitrarily small disorder the SF and MI phases are always separated by BG. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.16131

Related papers

Superfluid-insulator transition of disordered bosons in one dimension

Ehud Altman, Yariv Kafri, Anatoli Polkovnikov +1 more

We study the superfluid-insulator transition in a one-dimensional system of interacting bosons, modeled as a disordered Josephson array, using a strong-randomness real-space renormalization-group technique. Unlike perturbative methods, this approach does not suffer from run-away flows and allows us to study the complete phase diagram. We show that the superfluid-insulator transition is always Kosterlitz-Thouless like in the way that length and time scales diverge at the critical point. Interestingly however, we find that the transition at strong disorder occurs at a nonuniversal value of the Luttinger parameter, which depends on the disorder strength. This result places the transition in a universality class different from the weak disorder transition first analyzed by Giamarchi and Schulz [Europhys. Lett. 3, 1287 (1987)]. While the details of the disorder potential are unimportant at the critical point, the type of disorder does influence the properties of the insulating phases. We find three classes of insulators which arise for different classes of disorder potential. For disorder only in the charging energies and Josephson coupling constants, at integer filling we find an incompressible but gapless Mott-glass phase. If both integer and half-integer filling factors are allowed then the corresponding phase is a random-singlet insulator, which has a divergent compressibility. Finally in a generic disorder potential the insulator is a Bose glass with a finite compressibility.

arXiv:0909.4096•Physical Review B•May 25, 2010•81 citations

Direct Mott insulator-to-superfluid transition in the presence of disorder

Ferenc Pázmándi, Gergely T. Zimányi

We use renormalization-group theory to examine the quantum phase transitions upon exiting the insulating phase of a disordered, strongly interacting boson system. For weak disorder we find a direct transition from this Mott insulator to the superfluid phase. In $d>4$ a finite region around the particle-hole symmetric point supports this direct transition, whereas for $2<~d<4$ perturbative arguments suggest that the direct transition survives only precisely at commensurate filling. For strong disorder the renormalization trajectories pass next to two fixed points, describing a pair of distinct transitions; first from the Mott insulator to the Bose glass, and then from the Bose glass to the superfluid. The latter fixed point possesses statistical particle-hole symmetry and a dynamical exponent $z$, equal to the dimension $d$.

arXiv:cond-mat/9702169•Physical review. B, Condensed matter•Mar 1, 1998•31 citations

Bose glass in a large- N commensurate dirty boson model

M. B. Hastings

The large-$N$ commensurate dirty boson model, in both the weakly and strongly commensurate cases, is considered via a perturbative renormalization-group treatment. In the weakly commensurate case, there exists a fixed line under renormalization-group flow, with varying amounts of disorder along the line. Including $1/N$ corrections causes the system to flow to strong disorder, indicating that the model does not have a phase transition perturbatively connected to the Mott insulator-superfluid (MI-SF) transition. I discuss the qualitative effects of instantons on the low-energy density of excitations. In the strongly commensurate case, a fixed point found previously is considered and results are obtained for higher moments of the correlation functions. To lowest order, correlation functions have a log-normal distribution. Finally, I prove two interesting theorems for large-$N$ vector models with disorder, relevant to the problem of replica symmetry breaking and frustration in such systems.

arXiv:cond-mat/9811121•Physical review. B, Condensed matter•Jun 20, 2001•7 citations

Real-space renormalization study of disordered interacting bosons

Kanwal G. Singh, Daniel S. Rokhsar

We study a real-space renormalization group for disordered, interacting bosons at zero temperature in one and two dimensions. In the absence of disorder at commensurate density we find a superfluid--Mott insulator transition that is unaffected by the addition of weak disorder, i.e., disorder is weakly irrelevant at the Mott-superfluid transition. Above a threshold disorder a gapless insulating phase---the ``Bose glass''---intervenes.

Physical review. B, Condensed matter•Aug 1, 1992•101 citations

Density matrix renormalization group for disordered bosons in one dimension

S Rapsch, U Schollwöck, W. Zwerger

We calculate the zero-temperature phase diagram of the disordered Bose-Hubbard model in one dimension using the density matrix renormalization group. For integer filling the Mott insulator is always separated from the superfluid by a Bose glass phase. There is a re-entrance of the Bose glass both as a function of the repulsive interaction and of disorder. At half-filling where no Mott insulator exists, the superfluid density has a maximum where the kinetic and repulsive energies are about the same. Superfluidity is suppressed both for small and very strong repulsion but is always monotonic in disorder.

arXiv:cond-mat/9901080•Europhysics Letters (EPL)•Jun 1, 1999•144 citations

Anomalous suppression of the Bose glass at commensurate fillings in the disordered Bose-Hubbard model

Frank Krüger, Jiansheng Wu, Philip Phillips

We study the weakly disordered Bose-Hubbard model on a cubic lattice through a one-loop renormalization-group analysis of the corresponding effective-field theory which is explicitly derived by combining a strong-coupling expansion with a replica average over the disorder. The method is applied not only to generic uncorrelated on-site disorder but also to simultaneous hopping-disorder correlated with the differences of adjacent disorder potentials. Such correlations are inherent in fine-grained optical speckle potentials used as a source of disorder in optical lattice experiments. As a result of strong coupling, the strength of the replica-mixing disorder vertex, responsible for the emergence of a Bose glass, crucially depends on the chemical potential and the Hubbard repulsion and vanishes to leading order in the disorder at commensurate boson fillings. As a consequence, at such fillings a direct transition between the Mott insulator and the superfluid in the presence of disorder cannot be excluded on the basis of a one-loop calculation. At incommensurate fillings, at a certain length scale, the Mott insulator will eventually become unstable toward the formation of a Bose glass. Phase diagrams as a function of the microscopic parameters are presented and the finite-size crossover between the Mott-insulating state and the Bose glass is analyzed.

arXiv:0904.4480•Physical Review B•Sep 25, 2009•20 citations
We study the effect of commensurability (integer filling factor) on the superfluid (SF)--Bose-glass (BG) transition in a one-dimensional disordered system in the limit of weak disorder, when the effect is most pronounced and, on the other hand, may be traced via the renormalization-group analysis. The equation for the SF-BG phase boundary demonstrating the effect of disorder-stimulated superfluidity implies that the strength of disorder sufficient to restore superfluidity from Mott insulator (MI) is much larger than that enough to turn MI into BG. Thus we provide an explicit proof of the fact that at arbitrarily small disorder the SF and MI phases are always separated by BG. \textcopyright{} 1996 The American Physical Society.
We study the superfluid-insulator transition in a one-dimensional system of interacting bosons, modeled as a disordered Josephson array, using a strong-randomness real-space renormalization-group technique. Unlike perturbative methods, this approach does not suffer from run-away flows and allows us to study the complete phase diagram. We show that the superfluid-insulator transition is always Kosterlitz-Thouless like in the way that length and time scales diverge at the critical point. Interestingly however, we find that the transition at strong disorder occurs at a nonuniversal value of the Luttinger parameter, which depends on the disorder strength. This result places the transition in a universality class different from the weak disorder transition first analyzed by Giamarchi and Schulz [Europhys. Lett. 3, 1287 (1987)]. While the details of the disorder potential are unimportant at the critical point, the type of disorder does influence the properties of the insulating phases. We find three classes of insulators which arise for different classes of disorder potential. For disorder only in the charging energies and Josephson coupling constants, at integer filling we find an incompressible but gapless Mott-glass phase. If both integer and half-integer filling factors are allowed then the corresponding phase is a random-singlet insulator, which has a divergent compressibility. Finally in a generic disorder potential the insulator is a Bose glass with a finite compressibility.
We use renormalization-group theory to examine the quantum phase transitions upon exiting the insulating phase of a disordered, strongly interacting boson system. For weak disorder we find a direct transition from this Mott insulator to the superfluid phase. In d>4d>4d>4 a finite region around the particle-hole symmetric point supports this direct transition, whereas for 2< d<42<~d<42< d<4 perturbative arguments suggest that the direct transition survives only precisely at commensurate filling. For strong disorder the renormalization trajectories pass next to two fixed points, describing a pair of distinct transitions; first from the Mott insulator to the Bose glass, and then from the Bose glass to the superfluid. The latter fixed point possesses statistical particle-hole symmetry and a dynamical exponent zzz, equal to the dimension ddd.
The large-NNN commensurate dirty boson model, in both the weakly and strongly commensurate cases, is considered via a perturbative renormalization-group treatment. In the weakly commensurate case, there exists a fixed line under renormalization-group flow, with varying amounts of disorder along the line. Including 1/N1/N1/N corrections causes the system to flow to strong disorder, indicating that the model does not have a phase transition perturbatively connected to the Mott insulator-superfluid (MI-SF) transition. I discuss the qualitative effects of instantons on the low-energy density of excitations. In the strongly commensurate case, a fixed point found previously is considered and results are obtained for higher moments of the correlation functions. To lowest order, correlation functions have a log-normal distribution. Finally, I prove two interesting theorems for large-NNN vector models with disorder, relevant to the problem of replica symmetry breaking and frustration in such systems.
We calculate the zero-temperature phase diagram of the disordered Bose-Hubbard model in one dimension using the density matrix renormalization group. For integer filling the Mott insulator is always separated from the superfluid by a Bose glass phase. There is a re-entrance of the Bose glass both as a function of the repulsive interaction and of disorder. At half-filling where no Mott insulator exists, the superfluid density has a maximum where the kinetic and repulsive energies are about the same. Superfluidity is suppressed both for small and very strong repulsion but is always monotonic in disorder.
We study the weakly disordered Bose-Hubbard model on a cubic lattice through a one-loop renormalization-group analysis of the corresponding effective-field theory which is explicitly derived by combining a strong-coupling expansion with a replica average over the disorder. The method is applied not only to generic uncorrelated on-site disorder but also to simultaneous hopping-disorder correlated with the differences of adjacent disorder potentials. Such correlations are inherent in fine-grained optical speckle potentials used as a source of disorder in optical lattice experiments. As a result of strong coupling, the strength of the replica-mixing disorder vertex, responsible for the emergence of a Bose glass, crucially depends on the chemical potential and the Hubbard repulsion and vanishes to leading order in the disorder at commensurate boson fillings. As a consequence, at such fillings a direct transition between the Mott insulator and the superfluid in the presence of disorder cannot be excluded on the basis of a one-loop calculation. At incommensurate fillings, at a certain length scale, the Mott insulator will eventually become unstable toward the formation of a Bose glass. Phase diagrams as a function of the microscopic parameters are presented and the finite-size crossover between the Mott-insulating state and the Bose glass is analyzed.