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/0005220

Disordered Quantum Solids

Thierry Giamarchi, E. Orignac

Published May 12, 2000• 0 citations
arXivHTMLPDF

Abstract

Due to the peculiar non-fermi liquid of one dimensional systems, disorder has particularly strong effects. We show that such systems belong to the more general class of disordered quantum solids. We discuss the physics of such disordered interacting systems and the methods that allows to treat them. In addition to, by now standard renormalization group methods, We explain how a simple variational approach allows to treat these problems even in case when the RG fails. We discuss various physical realizations of such disordered quantum solids both in one and higher dimensions (Wigner crystal, Bose glass). We investigate in details the interesting example of a disordered Mott insulator and argue that intermediate disorder can lead to a novel phase, the Mott glass, intermediate between a Mott and and Anderson insulator.

DOI
10.48550/arxiv.cond-mat/0005220

Related papers

Strong disorder renormalization group primer and the superfluid–insulator transition

Gil Refael, Ehud Altman

This brief review introduces the method and application of real-space renormalization group to strongly disordered quantum systems. The focus is on recent applications of the strong disorder renormalization group to the physics of disordered-boson systems and the superfluid–insulator transition in one dimension. The fact that there is also a well-understood weak disorder theory for this problem allows us to illustrate what aspects of the physics change at strong disorder. In particular, the strong disorder RG analysis suggests that the transitions at weak disorder and strong disorder belong to distinct universality classes, but this question remains under debate and is not fully resolved to date. Further applications of the strong disorder renormalization group to higher-dimensional Bose systems and to bosons coupled to dissipation are also briefly reviewed.

arXiv:1402.6008•Comptes Rendus Physique•Oct 1, 2013•37 citations

Disordered One-Dimensional Bose-Fermi Mixtures: The Bose-Fermi Glass

François Crépin, Gergely Zaránd, Pascal Simon

We analyze an interacting Bose-Fermi mixture in a 1D disordered potential by using a combination of renormalization group and variational methods. We obtain the complete phase diagram in the incommensurate case as a function of bosonic and interspecies interaction strengths, in the weak disorder limit. We find that the system is characterized by several phase transitions between superfluid and various glassy insulating states, including a new Bose-Fermi glass phase, where both species are coupled and localized. We show that the dynamical structure factor, as measured through Bragg scattering experiments, can distinguish between the various localized phases and probe their dynamics.

arXiv:1005.2483•Physical Review Letters•Sep 8, 2010•21 citations

Strong Correlations in Low Dimensional Systems

Thierry Giamarchi

I describe in these notes the physical properties of one dimensional interacting quantum particles. In one dimension the combined effects of interactions and quantum fluctuations lead to a radically new physics quite different from the one existing in the higher dimensional world. Although the general physics and concepts are presented, I focuss in these notes on the properties of interacting bosons, with a special emphasis on cold atomic physics in optical lattices. The method of bosonization used to tackle such problems is presented. It is then used to solve two fundamental problems. The first one is the action of a periodic potential, leading to a superfluid to (Mott)-Insulator transition. The second is the action of a random potential that transforms the superfluid in phase localized by disorder, the Bose glass. Some discussion of other interesting extensions of these studies is given.

arXiv:cond-mat/0605472•AIP conference proceedings•Jan 1, 2006•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

The Anderson-Mott transition

D. Belitz, T. R. Kirkpatrick

The interacting disordered electron problem is reviewed with emphasis on the quantum phase transitions that occur in a model system and on the field-theoretic methods used to describe them. An elementary discussion of conservation laws and diffusive dynamics is followed by a detailed derivation of the extended nonlinear sigma model, which serves as an effective field theory for the problem. A general scaling theory of metal-insulator and related transitions is developed, and explicit renormalization-group calculations for the various universality classes are reviewed and compared with experimental results. A discussion of pertinent physical ideas and phenomenological approaches to the metal-insulator transition not contained in the sigma-model approach is given, and phase-transition aspects of related problems, like disordered superconductors and the quantum Hall effect, are discussed. The review concludes with a list of open problems.

Reviews of Modern Physics•Apr 1, 1994•988 citations

Strong Correlations in Low Dimensional Systems

Thierry Giamarchi

Abstract. I describe in these notes the physical properties of one dimensional interacting quantum particles. In one dimension the combined effects of interactions and quantum fluctuations lead to a radically new physics quite different from the one existing in the higher dimensional world. Although the general physics and concepts are presented, I focuss in these notes on the properties of interacting bosons, with a special emphasis on cold atomic physics in optical lattices. The method of bosonization used to tackle such problems is presented. It is then used to solve two fundamental problems. The first one is the action of a periodic potential, leading to a superfluid to (Mott)-Insulator transition. The second is the action of a random potential that transforms the superfluid in phase localized by disorder, the Bose glass. Some discussion of other interesting extensions of these studies is given. INTRODUCTION AND CHOICE OF CONTENTS One-dimensional systems of interacting particles are particularly fascinating both from a theoretical and experimental point of view. Such systems have been extensively investigated theoretically for more than 40 years now. They are wonderful systems in which interactions play a very special role and whose physics is drastically different

•Jan 1, 2006•4 citations
Due to the peculiar non-fermi liquid of one dimensional systems, disorder has particularly strong effects. We show that such systems belong to the more general class of disordered quantum solids. We discuss the physics of such disordered interacting systems and the methods that allows to treat them. In addition to, by now standard renormalization group methods, We explain how a simple variational approach allows to treat these problems even in case when the RG fails. We discuss various physical realizations of such disordered quantum solids both in one and higher dimensions (Wigner crystal, Bose glass). We investigate in details the interesting example of a disordered Mott insulator and argue that intermediate disorder can lead to a novel phase, the Mott glass, intermediate between a Mott and and Anderson insulator.
This brief review introduces the method and application of real-space renormalization group to strongly disordered quantum systems. The focus is on recent applications of the strong disorder renormalization group to the physics of disordered-boson systems and the superfluid–insulator transition in one dimension. The fact that there is also a well-understood weak disorder theory for this problem allows us to illustrate what aspects of the physics change at strong disorder. In particular, the strong disorder RG analysis suggests that the transitions at weak disorder and strong disorder belong to distinct universality classes, but this question remains under debate and is not fully resolved to date. Further applications of the strong disorder renormalization group to higher-dimensional Bose systems and to bosons coupled to dissipation are also briefly reviewed.
We analyze an interacting Bose-Fermi mixture in a 1D disordered potential by using a combination of renormalization group and variational methods. We obtain the complete phase diagram in the incommensurate case as a function of bosonic and interspecies interaction strengths, in the weak disorder limit. We find that the system is characterized by several phase transitions between superfluid and various glassy insulating states, including a new Bose-Fermi glass phase, where both species are coupled and localized. We show that the dynamical structure factor, as measured through Bragg scattering experiments, can distinguish between the various localized phases and probe their dynamics.
I describe in these notes the physical properties of one dimensional interacting quantum particles. In one dimension the combined effects of interactions and quantum fluctuations lead to a radically new physics quite different from the one existing in the higher dimensional world. Although the general physics and concepts are presented, I focuss in these notes on the properties of interacting bosons, with a special emphasis on cold atomic physics in optical lattices. The method of bosonization used to tackle such problems is presented. It is then used to solve two fundamental problems. The first one is the action of a periodic potential, leading to a superfluid to (Mott)-Insulator transition. The second is the action of a random potential that transforms the superfluid in phase localized by disorder, the Bose glass. Some discussion of other interesting extensions of these studies is given.
The interacting disordered electron problem is reviewed with emphasis on the quantum phase transitions that occur in a model system and on the field-theoretic methods used to describe them. An elementary discussion of conservation laws and diffusive dynamics is followed by a detailed derivation of the extended nonlinear sigma model, which serves as an effective field theory for the problem. A general scaling theory of metal-insulator and related transitions is developed, and explicit renormalization-group calculations for the various universality classes are reviewed and compared with experimental results. A discussion of pertinent physical ideas and phenomenological approaches to the metal-insulator transition not contained in the sigma-model approach is given, and phase-transition aspects of related problems, like disordered superconductors and the quantum Hall effect, are discussed. The review concludes with a list of open problems.
Abstract. I describe in these notes the physical properties of one dimensional interacting quantum particles. In one dimension the combined effects of interactions and quantum fluctuations lead to a radically new physics quite different from the one existing in the higher dimensional world. Although the general physics and concepts are presented, I focuss in these notes on the properties of interacting bosons, with a special emphasis on cold atomic physics in optical lattices. The method of bosonization used to tackle such problems is presented. It is then used to solve two fundamental problems. The first one is the action of a periodic potential, leading to a superfluid to (Mott)-Insulator transition. The second is the action of a random potential that transforms the superfluid in phase localized by disorder, the Bose glass. Some discussion of other interesting extensions of these studies is given. INTRODUCTION AND CHOICE OF CONTENTS One-dimensional systems of interacting particles are particularly fascinating both from a theoretical and experimental point of view. Such systems have been extensively investigated theoretically for more than 40 years now. They are wonderful systems in which interactions play a very special role and whose physics is drastically different