Continuous quantum phase transitions

Sondhi, S. L.; Girvin, S. M.; Carini, J. P.; Shahar, D.

doi:10.1103/revmodphys.69.315

Cited by 1,259 publications

(1,512 citation statements)

References 60 publications

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“…In this case, the quantum critical point is then also the end point of a T = 0 ordered state. However, sometimes the "ordered" state really only exists at T = 0, for example in metal-insulator transitions and in quantum Hall e ect transitions [247,212]. A well-known example of this case in spin models is in two-dimensional antiferromagnetic quantum Heisenberg models with "quantumness" as a parameter g [56], which do not order at any ÿnite temperature, but which show genuine ordered phases at T = 0 below some value g ¡ g c .…”

Section: Quantum Critical Points In Fermionic Systemsmentioning

confidence: 99%

“…The standard more modern formulation now, which we will follow, is due to Hertz [123]. A nice introduction can be found in the article by Sondhi et al [247], and for a detailed expose, we refer to the book by Sachdev [225]. See also the review by Continento [67].…”

Section: Quantum Critical Points In Fermionic Systemsmentioning

confidence: 99%

“…Interesting new developments in this problem with references to substantial earlier work may be found in [176,177,247]. The problem of transitions in Josephson arrays [247] is a variant of such problems.…”

Section: Aim and Scope Of This Papermentioning

confidence: 99%

“…[124,227,259]). Likewise, for a discussion of the application of quantum critical scaling ideas to Josephson arrays or quantum Hall e ects, we refer to the nice introduction by Sondhi et al [247].…”

Section: Aim and Scope Of This Papermentioning

confidence: 99%

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Singular or non-Fermi liquids

2002

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Section: Quantum Critical Points In Fermionic Systemsmentioning

confidence: 99%

Section: Quantum Critical Points In Fermionic Systemsmentioning

confidence: 99%

Section: Aim and Scope Of This Papermentioning

confidence: 99%

Section: Aim and Scope Of This Papermentioning

confidence: 99%

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Singular or non-Fermi liquids

2002

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“…Quantum phase transitions occur at absolute zero; they are induced by the change of an external parameter or coupling constant [2], and are driven by fluctuations. Examples include transitions in quantum Hall systems [3], localization in Si-MOSFETs (metal oxide silicon field-effect transistors; Ref. [4]) and the superconductor-insulator transition in two-dimensional systems [5,6].…”

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confidence: 99%

Scaling of entanglement close to a quantum phase transition

Osterloh¹,

Amico

Falci

et al. 2002

Nature

1,846

2,051

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In this Letter we discuss the entanglement near a quantum phase transition by analyzing the properties of the concurrence for a class of exactly solvable models in one dimension. We find that entanglement can be classified in the framework of scaling theory. Further, we reveal a profound difference between classical correlations and the non-local quantum correlation, entanglement: the correlation length diverges at the phase transition, whereas entanglement in general remains short ranged.Classical phase transitions occur when a physical system reaches a state below a critical temperature characterized by a macroscopic order [1]. Quantum phase transitions occur at absolute zero; they are induced by the change of an external parameter or coupling constant [2], and are driven by fluctuations. Examples include transitions in quantum Hall systems [3], localization in Si-MOSFETs (metal oxide silicon field-effect transistors; Ref. [4]) and the superconductor-insulator transition in two-dimensional systems [5,6]. Both classical and quantum critical points are governed by a diverging correlation length, although quantum systems possess additional correlations that do not have a classical counterpart. This phenomenon, known as entanglement [7], is the resource that enables quantum computation and communication [8]. The role of the entanglement at a phase transition is not captured by statistical mechanics -a complete classification of the critical many-body state requires the introduction of concepts from quantum information theory [9]. Here we connect the theory of critical phenomena with quantum information by exploring the entangling resources of a system close to its quantum critical point. We demonstrate, for a class of one-dimensional magnetic systems, that entanglement shows scaling behaviour in the vicinity of the transition point.There are various questions that emerge in the study of this problem. Since the ground state wave-function undergoes qualitative changes at a quantum phase transition, it is important to understand how its genuine quantum aspects evolve throughout the transition. Will entanglement between distant subsystems be extended over macroscopic regions, as correlations are? Will it carry distinct features of the transition itself and show scaling behaviour? Answering these questions is important for a deeper understanding of quantum phase transitions and also from the perspective of quantum information theory. So results that bridge these two areas of research are of great relevance. We study a set of localized spins coupled through exchange interaction and subject to an external magnetic field (we consider only spin-1/2 particles), a model central both to condensed matter and information theory and subject to intense study [10]. FIG. 1. The change in the ground state wave-function in the critical region is analyzed considering ∂ λ C(1) as a function of the reduced coupling strength λ. The curves correspond to different lattice sizes N = 11, 41, 101, 251, 401, ∞. We choose N odd to avoid the sub...

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Superconductor–Insulator Transitions in 2D: The Experimental Situation

Marković¹,

Christiansen²,

Mack³

et al. 2000

phys. stat. sol. (b)

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Superconductor±insulator (SI) transitions in ultrathin films have attracted significant attention over the last decade because of the possibility that they are quantum phase transitions. Magnetic field, film thickness, or carrier concentration can be used as control parameters. The bosonic pictures of these transitions proposed some years ago are only in qualitative agreement with experiment. In particular, the critical resistance appears not to be universal, and there are variations in the values of critical exponents. It has been concluded that in real films fermionic degrees of freedom must be taken into account. There are also indications that the phase diagram may include a significant metallic phase separating the superconducting and insulating phases, and that the transition may have a significant percolative aspect. The experimental situation will be broadly reviewed with attention paid to issues relating to materials and measurements.Introduction The investigation of superconductivity in the presence of disorder began 60 years ago with the work of Shalnikov [1]. The subject has played an on-going role in contemporary condensed matter physics. Anderson [2] showed that nonmagnetic impurities have no significant effect on the superconducting transition by pointing out that Cooper pairs form from time-reversed eigenstates, which are not strongly affected by disorder. This idea is only relevant to weakly disordered systems where electronic states are extended. One anticipates that as states become localized, superconductivity will vanish [3].The case of very thin films is of particular interest as two dimensions (2D) is quite special. The superconducting transition in 2D, occurs as a topological, or KosterlitzThouless-Berezinskii transition [4]. Weakly interacting 2D electron systems are always localized, even for arbitrarily weak disorder [5]. Bosonic models, which involve a quantum phase tansition have ben proposed as an explanation of 2D superconductor±insula-tor transitions [6].

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Continuous quantum phase transitions

Cited by 1,259 publications

References 60 publications

Singular or non-Fermi liquids

Singular or non-Fermi liquids

Scaling of entanglement close to a quantum phase transition

Superconductor–Insulator Transitions in 2D: The Experimental Situation

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