Effects of Dissipation on a Quantum Critical Point with Disorder

Hoyos, José A.; Kotabage, Chetan; Vojta, Thomas

doi:10.1103/physrevlett.99.230601

Cited by 80 publications

(129 citation statements)

References 41 publications

(67 reference statements)

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“…[13,14], where the scaling and renormalization group (RG) picture of the 1d superfluid-insulator transition at weak disorder was also established. Recently, much theoretical progress was afforded through real-space RG approaches in the case of dissipative [15] and closed [16,17] bosonic chains, where the properties of the SF-insulator transition at strong disorder were established.In this paper, we study the excitations of the superfluid phase in a bosonic chain with a strongly random potential and interactions, near the SF-insulator transition. Capitalizing on the real-space RG understanding of this transition [16,17], we analyze the localization length of phonons (i.e., Bogoliubov quasiparticles) as a function of their frequency and wave number.…”

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Excitations of One-Dimensional Bose-Einstein Condensates in a Random Potential

2008

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We examine bosons hopping on a one-dimensional lattice in the presence of a random potential at zero temperature. Bogoliubov excitations of the Bose-Einstein condensate formed under such conditions are localized, with the localization length diverging at low frequency as (ω) ∼ 1/ω α . We show that the well known result α = 2 applies only for sufficiently weak random potential. As the random potential is increased beyond a certain strength, α starts decreasing. At a critical strength of the potential, when the system of bosons is at the transition from a superfluid to an insulator, α = 1. This result is relevant for understanding the behavior of the atomic Bose-Einstein condensates in the presence of random potential, and of the disordered Josephson junction arrays. One of the most challenging problems of quantum many body physics is the behavior of stongly interacting matter in a disordered environment. In this paper we investigate the universal properties of superfluids in such systems, near the superfluid insulator transition. Interest in this problem arises in many independent contexts, in work on granular superconducting films and wires [1, 2,3], Helium condensates in vycor [4], and recent experiments on Bose condensates in optical traps. In particular, issues such as the expansion of a noninteracting Bose condensate through a random potential [5], excitations in an interacting Bose Einstein condensate in a random potential [6,7], and the possibility of the observation of the Bose glass phase [8,9] were explored in very recent theoretical and experimental papers. As important is the possibility of investigating the behavior of disordered superconductors in a controlled fashion using Josephson junction arrays, as in Refs. [10,11,12]. In low dimensional quantum systems, where symmetry broken phases are very fragile, we expect the most dramatic manifestations of the interplay of disorder and interactions. The existence of the Bose-glass phase was established in Refs. [13,14], where the scaling and renormalization group (RG) picture of the 1d superfluid-insulator transition at weak disorder was also established. Recently, much theoretical progress was afforded through real-space RG approaches in the case of dissipative [15] and closed [16,17] bosonic chains, where the properties of the SF-insulator transition at strong disorder were established.In this paper, we study the excitations of the superfluid phase in a bosonic chain with a strongly random potential and interactions, near the SF-insulator transition. Capitalizing on the real-space RG understanding of this transition [16,17], we analyze the localization length of phonons (i.e., Bogoliubov quasiparticles) as a function of their frequency and wave number. Deep in the superfluid phase, when the random potential is weak, the phonon localization length (ω) at small ω diverges as [6,18,19]

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Excitations of One-Dimensional Bose-Einstein Condensates in a Random Potential

2008

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“…We therefore expect the cost of our method to scale as N y+3/2 s or N 3/2 s in the quantum Griffiths and quantum paramagnetic phases, respectively. For three dimensional systems, sparse matrices can be inverted in O(N 2 s ) operations [27], correspondingly the cost of our method is expected to behave as N A possible application of our method in three dimensions is the disordered itinerant antiferromagnetic quantum phase transitions [21,22]. The clean transition is described by a Landau-Ginzburg-Wilson theory which is generalization of the action (1) to d = 3 space dimensions and N = 3 order parameter components [18,19].…”

Section: Discussionmentioning

confidence: 99%

Numerical method for disordered quantum phase transitions in the large‐N limit

Nozadze

Vojta

2013

Physica Status Solidi (b)

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We develop an efficient numerical method to study the quantum critical behavior of disordered systems with O(N ) order-parameter symmetry in the large−N limit. It is based on the iterative solution of the large−N saddle-point equations combined with a fast algorithm for inverting the arising large sparse random matrices. As an example, we consider the superconductor-metal quantum phase transition in disordered nanowires. We study the behavior of various observables near the quantum phase transition. Our results agree with recent renormalization group predictions, i.e., the transition is governed by an infinite-randomness critical point, accompanied by quantum Griffiths singularities. In contrast to the existing numerical approach to this problem, our method gives direct access to the temperature dependencies of observables. Moreover, our algorithm is highly efficient because the numerical effort for each iteration scales linearly with the system size. This allows us to study larger systems, with up to 1024 sites, than previous methods. We also discuss generalizations to higher dimensions and other systems including the itinerant antiferromagnetic transitions in disordered metals.Copyright line will be provided by the publisher 1 Introduction Randomness can have much more dramatic effects at quantum phase transitions than at classical phase transitions because quenched disorder is perfectly correlated in the imaginary time direction which needs to be included at quantum phase transitions. Imaginary time acts as an additional coordinate with infinite extension at absolute zero temperature. Therefore, the impurities and defects are effectively very large which leads to strong-disorder phenomena including power-law quantum Griffiths singularities [1,2,3], infinite-randomness critical points characterized by exponential scaling [4,5], and smeared phase transitions [6]. For example, the zero-temperature quantum phase transition in the random transverse-field Ising model is governed by an infiniterandomness critical point [5] featuring slow activated (exponential) rather than power-law dynamical scaling. It is accompanied by quantum Griffiths singularities. This means, observables are expected to be singular not just at criticality but in a whole parameter region near the quan-

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“…This has been well established in systems with both Ising and continuous symmetry (Fisher, 1992(Fisher, , 1994(Fisher, , 1995Fisher and Young, 1998;Guo et al, 1996;Hyman and Yang, 1997;Hyman et al, 1996;Motrunich et al, 2001;Narayanan et al, 1999a,b;Pich et al, 1998;Refael et al, 2002;Yang et al, 1996). More recently, a symmetry-based classification scheme of these Griffiths phases has been proposed and applied to several different systems with great success (Hoyos et al, 2007;Vojta, 2006, 2008;Vojta, 2003Vojta, , 2006Vojta et al, 2009;Vojta and Schmalian, 2005a,b). The Mott transition, however, poses a problem of a different nature, as it is not described by an order parameter in an obvious way.…”

Section: The Disordered Mott-hubbard Transitionmentioning

confidence: 97%

Dynamical Mean-field Theories of Correlation and Disorder

Miranda¹,

Dobrosavljević²

2012

Conductor-Insulator Quantum Phase Transitions

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Dynamical mean-field theories of correlation and disorder 1.1 Mott transitions in clean and disordered systems 1.2 Mott-Anderson transitions: Typical Medium Theory 1.3 Mott-Anderson transitions: Statistical DMFT 1.4 Glassy behavior of correlated electrons 1.5 Beyond DMFT: loop expansion and diffusion modes 1.6 Acknowledgments References 1 Dynamical mean-field theories of correlation and disorder 1.1 Mott transitions in clean and disordered systems It is this fascination with the local and with the failures, not successes, of band theory, which... contradicted the assumptions of the time...

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Effects of Dissipation on a Quantum Critical Point with Disorder

Cited by 80 publications

References 41 publications

Excitations of One-Dimensional Bose-Einstein Condensates in a Random Potential

Excitations of One-Dimensional Bose-Einstein Condensates in a Random Potential

Numerical method for disordered quantum phase transitions in the large‐N limit

Dynamical Mean-field Theories of Correlation and Disorder

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