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Quantum phase transitions: introduction and some open problems

Achim Rosch

in Quantum Theory from Small to Large Scales: Lecture Notes of the Les Houches Summer School: Volume 95, August 2010

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199652495
eISBN:
9780191741203
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199652495.003.0005
Subject:
Physics, Atomic, Laser, and Optical Physics

At a quantum critical point the ground state of a many-particle quantum system undergoes a phase transition when some control parameters such as pressure, magnetic field, or chemical composition is ... More


Quantum phase transitions

G. G. Batrouni and R. T. Scalettar

in Ultracold Gases and Quantum Information: Lecture Notes of the Les Houches Summer School in Singapore: Volume 91, July 2009

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199603657
eISBN:
9780191729515
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199603657.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses quantum phase transitions (QPT). It starts with a brief review of thermal phase transitions, critical exponents and scaling laws. The scaling laws are then generalized to the ... More


Scaling Analysis of Direct Superconductor-Insulator Transitions in Disordered Ultrathin Films of Metals

A.M. Goldman

in Conductor-Insulator Quantum Phase Transitions

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199592593
eISBN:
9780191741050
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199592593.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Superconductor-insulator (SI) transitions of homogeneously disordered ultrathin quench-condensed films in many instances appear to be direct, without any intervening metallic regime. This is in ... More


FLUCTUATIONS NEAR SUPERCONDUCTOR-INSULATOR TRANSITION

Anatoly Larkin and Andrei Varlamov

in Theory of Fluctuations in Superconductors

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528159
eISBN:
9780191713521
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528159.003.0016
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses the quantum phase transition using the example of superconductor-insulator transition. For the 3D case, a version of the Ginzburg-Landau formalism is formulated from both ... More


Phase Transitions, Critical Phenomena, and Finite-Size Scaling

Hans-Peter Eckle

in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

Published in print:
2019
Published Online:
September 2019
ISBN:
9780199678839
eISBN:
9780191878589
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199678839.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

Interacting many-particle systems may undergo phase transitions and exhibit critical phenomena in the limit of infinite system size, while the precursors of these phenomena are studied in the theory ... More


FLUCTUATIONS IN NANOGRAINS, NANODROPS AND GRANULAR SUPERCONDUCTORS

Anatoly Larkin and Andrei Varlamov

in Theory of Fluctuations in Superconductors

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528159
eISBN:
9780191713521
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528159.003.0012
Subject:
Physics, Condensed Matter Physics / Materials

This chapter starts off with a discussion of the specifics of superconductivity in ultrasmall superconducting grains. The method of optimal fluctuations in the vicinity of Tc is then introduced, and ... More


Conductor-Insulator Quantum Phase Transitions

Vladimir Dobrosavljevic, Nandini Trivedi, and James M. Valles, Jr. (eds)

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199592593
eISBN:
9780191741050
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199592593.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Quantum phase transitions describe the violent rearrangement of electrons or atoms as they evolve from well defined excitations in one phase to a completely different set of excitations in another. ... More


Optical lattice emulators: Bose– and Fermi–Hubbard models

E. Duchon, Y. L. Loh, and N. Trivedi

in Novel Superfluids: Volume 2

Published in print:
2014
Published Online:
March 2015
ISBN:
9780198719267
eISBN:
9780191788529
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198719267.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

The equilibrium thermodynamics of bosons and fermions in optical lattices are considered in the single-band Hubbard regime, with an emphasis on interesting magnetic, superfluid, and spin liquid ... More


Statistical physics of condensed matter: basic concepts

Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger

in Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199573127
eISBN:
9780191775048
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573127.003.0002
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter explains the basic ideas and concepts of the modern quantum theory of condensed matter. It starts by discussing phase transition in classical systems, scaling, and renormalisation ... More


Superconductor-Insulator Transitions: Present Status and Open Questions

Nandini Trivedi

in Conductor-Insulator Quantum Phase Transitions

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199592593
eISBN:
9780191741050
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199592593.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A superconductor is a remarkable emergent state of matter in which electrons pair up and develop long range phase coherence resulting in zero resistance and perfect diamagnetism. How can a ... More


Theoretical Studies of Superconductor–Insulator Transitions

Yen Loh Lee and Nandini Trivedi

in Conductor-Insulator Quantum Phase Transitions

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199592593
eISBN:
9780191741050
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199592593.003.0017
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents a theoretical treatment of two types of superconductor-insulator transitions — the disorder-tuned transition and the parallel-magnetic-field-tuned transition. This is performed ... More


Momentum Space Topology of 2 + 1 Systems

VOLOVIK GRIGORY E.

in The Universe in a Helium Droplet

Published in print:
2009
Published Online:
January 2010
ISBN:
9780199564842
eISBN:
9780191709906
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199564842.003.0011
Subject:
Physics, Condensed Matter Physics / Materials, Particle Physics / Astrophysics / Cosmology

This chapter discusses the momentum space topology of 2+1 systems. In the D = 2 space the possible manifolds of gap nodes in the quasiparticle energy are point nodes and nodal lines. The nodal lines ... More


SCALING HYPOTHESIS

V.F. Gantmakher

in Electrons and Disorder in Solids

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198567561
eISBN:
9780191718267
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567561.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

This chapter presents phenomenological scaling theory of quantum metal-insulator transition of non-interacting electrons. It confirms the existence of the transition in 3D-system; and elucidates the ... More


Landau Critical Velocity

VOLOVIK GRIGORY E.

in The Universe in a Helium Droplet

Published in print:
2009
Published Online:
January 2010
ISBN:
9780199564842
eISBN:
9780191709906
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199564842.003.0026
Subject:
Physics, Condensed Matter Physics / Materials, Particle Physics / Astrophysics / Cosmology

This chapter opens the part of the book devoted to the nucleation of excitation of the vacuum — quasiparticles and topological defects. The superfluid vacuum flows with respect to environment (the ... More


Implementation of the renormalization group

Hidetoshi Nishimori and Gerardo Ortiz

in Elements of Phase Transitions and Critical Phenomena

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577224
eISBN:
9780191722943
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577224.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Actual computations of fixed points and eigenvalues usually involve approximations, often crude ones, except for a very limited number of simple cases such as the one-dimensional Ising model of the ... More


Magnetic Field-Induced Novel Insulating Phase in 2D Superconductors

G Sambandamurthy and N. Peter Armitage

in Conductor-Insulator Quantum Phase Transitions

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199592593
eISBN:
9780191741050
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199592593.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

DC and finite frequency transport measurements of thin films of amorphous indium oxide that were driven through the critical point of superconductor-insulator transition by the application of ... More


Heavy fermion superconductors

A.V. Narlikar

in Superconductors

Published in print:
2014
Published Online:
June 2014
ISBN:
9780199584116
eISBN:
9780191747496
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199584116.003.0013
Subject:
Physics, Condensed Matter Physics / Materials

This chapter describes advances made with a variety of heavy fermion (HF) superconducting systems, adding new challenges to the physics of this growing field. Much of the understanding has evolved ... More


Strongly Correlated Systems

J. B. Ketterson

in The Physics of Solids

Published in print:
2016
Published Online:
December 2016
ISBN:
9780198742906
eISBN:
9780191821523
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198742906.003.0045
Subject:
Physics, Condensed Matter Physics / Materials

This chapter examines strongly correlated systems. The discussions of the quantum mechanics of electrons in solids up to this point have largely involved properties that can be treated within the ... More


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