23 research outputs found
Orbital-selective Mott transitions: Heavy fermions and beyond
Quantum phase transitions in metals are often accompanied by violations of
Fermi liquid behavior in the quantum critical regime. Particularly fascinating
are transitions beyond the Landau-Ginzburg-Wilson concept of a local order
parameter. The breakdown of the Kondo effect in heavy-fermion metals
constitutes a prime example of such a transition. Here, the strongly correlated
f electrons become localized and disappear from the Fermi surface, implying
that the transition is equivalent to an orbital-selective Mott transition, as
has been discussed for multi-band transition-metal oxides. In this article,
available theoretical descriptions for orbital-selective Mott transitions will
be reviewed, with an emphasis on conceptual aspects like the distinction
between different low-temperature phases and the structure of the global phase
diagram. Selected results for quantum critical properties will be listed as
well. Finally, a brief overview is given on experiments which have been
interpreted in terms of orbital-selective Mott physics.Comment: 29 pages, 4 figs, mini-review prepared for a special issue of JLT
Strongly coupled quantum criticality with a Fermi surface in two dimensions: fractionalization of spin and charge collective modes
We describe two dimensional models with a metallic Fermi surface which
display quantum phase transitions controlled by strongly interacting critical
field theories below their upper critical dimension. The primary examples
involve transitions with a topological order parameter associated with
dislocations in collinear spin density wave ("stripe") correlations: the
gapping of the order parameter fluctuations leads to a fractionalization of
spin and charge collective modes, and this transition has been proposed as a
candidate for the cuprates near optimal doping. The coupling between the order
parameter and long-wavelength volume and shape deformations of the Fermi
surface is analyzed by the renormalization group, and a runaway flow to a
non-perturbative regime is found in most cases. A phenomenological scaling
analysis of simple observable properties of possible second order quantum
critical points is presented, with results quite similar to those near quantum
spin glass transitions and to phenomenological forms proposed by Schroeder et
al. (cond-mat/0011002).Comment: 16 pages, 4 figures; (v2) additional clarifying remark
Weak magnetism and non-Fermi liquids near heavy-fermion critical points
This paper is concerned with the weak-moment magnetism in heavy-fermion
materials and its relation to the non-Fermi liquid physics observed near the
transition to the Fermi liquid. We explore the hypothesis that the primary
fluctuations responsible for the non-Fermi liquid physics are those associated
with the destruction of the large Fermi surface of the Fermi liquid. Magnetism
is suggested to be a low-energy instability of the resulting small Fermi
surface state. A concrete realization of this picture is provided by a
fractionalized Fermi liquid state which has a small Fermi surface of conduction
electrons, but also has other exotic excitations with interactions described by
a gauge theory in its deconfined phase. Of particular interest is a
three-dimensional fractionalized Fermi liquid with a spinon Fermi surface and a
U(1) gauge structure. A direct second-order transition from this state to the
conventional Fermi liquid is possible and involves a jump in the electron Fermi
surface volume. The critical point displays non-Fermi liquid behavior. A
magnetic phase may develop from a spin density wave instability of the spinon
Fermi surface. This exotic magnetic metal may have a weak ordered moment
although the local moments do not participate in the Fermi surface.
Experimental signatures of this phase and implications for heavy-fermion
systems are discussed.Comment: 20 pages, 8 figures; (v2) includes expanded discussion and solution
of quantum Boltzmann equatio
Order and quantum phase transitions in the cuprate superconductors
It is now widely accepted that the cuprate superconductors are characterized
by the same long-range order as that present in the Bardeen-Cooper-Schrieffer
(BCS) theory: that associated with the condensation of Cooper pairs. We argue
that many physical properties of the cuprates require interplay with additional
order parameters associated with a proximate Mott insulator. We review a
classification of Mott insulators in two dimensions, and contend that the
experimental evidence so far shows that the class appropriate to the cuprates
has collinear spin correlations, bond order, and confinement of neutral, spin
S=1/2 excitations. Proximity to second-order quantum phase transitions
associated with these orders, and with the pairing order of BCS, has led to
systematic predictions for many physical properties. We use this context to
review the results of recent neutron scattering, fluxoid detection, nuclear
magnetic resonance, and scanning tunnelling microscopy experiments.Comment: 20 pages, 13 figures, non-technical review article; some technical
details in the companion review cond-mat/0211027; (v3) added refs; (v4)
numerous improvements thanks to the referees, to appear in Reviews of Modern
Physics; (v6) final version as publishe
Competing orders and quantum criticality in doped antiferromagnets
We use a number of large-N limits to explore the competition between ground
states of square lattice doped antiferromagnets which break electromagnetic
U(1), time-reversal, or square lattice space group symmetries. Among the states
we find are d-, (s+id)-, and (d+id)-wave superconductors, Wigner crystals,
Wigner crystals of hole pairs, orbital antiferromagnets (or staggered-flux
states), and states with spin-Peierls and bond-centered charge stripe order. In
the vicinity of second-order quantum phase transitions between the states, we
go beyond the large-N limit by identifying the universal quantum field theories
for the critical points, and computing the finite temperature, quantum-critical
damping of fermion spectral functions. We identify candidate critical points
for the recently observed quantum-critical behavior in photoemission
experiments on BSCCO by Valla et al. (Science 285, 2110 (1999)). These involve
onset of a charge density wave, or of broken time-reversal symmetry with (d+id)
or (s+id) pairing, in a d-wave superconductor. It is not required (although it
is allowed) that the stable state in the doped cuprates to be anything other
than the d-wave superconductor--the other states need only be stable nearby in
parameter space. At finite temperatures, fluctuations associated with these
nearby states lead to the observed fermion damping in the vicinity of the nodal
points in the Brillouin zone. The cases with broken time-reversal symmetry are
appealing because the order parameter is not required to satisfy any special
commensurability conditions. The observed absence of inelastic damping of
quasiparticles with momenta (pi,k), (k,pi) (with 0 < k < pi) also appears very
naturally for the case of a transition to (d+id) order.Comment: 26 pages, 13 figures; added references, clarifications, and a new
figur
Competing orders in a magnetic field: spin and charge order in the cuprate superconductors
We describe two-dimensional quantum spin fluctuations in a superconducting
Abrikosov flux lattice induced by a magnetic field applied to a doped Mott
insulator. Complete numerical solutions of a self-consistent large N theory
provide detailed information on the phase diagram and on the spatial structure
of the dynamic spin spectrum. Our results apply to phases with and without
long-range spin density wave order and to the magnetic quantum critical point
separating these phases. We discuss the relationship of our results to a number
of recent neutron scattering measurements on the cuprate superconductors in the
presence of an applied field. We compute the pinning of static charge order by
the vortex cores in the `spin gap' phase where the spin order remains
dynamically fluctuating, and argue that these results apply to recent scanning
tunnelling microscopy (STM) measurements. We show that with a single typical
set of values for the coupling constants, our model describes the field
dependence of the elastic neutron scattering intensities, the absence of
satellite Bragg peaks associated with the vortex lattice in existing neutron
scattering observations, and the spatial extent of charge order in STM
observations. We mention implications of our theory for NMR experiments. We
also present a theoretical discussion of more exotic states that can be built
out of the spin and charge order parameters, including spin nematics and phases
with `exciton fractionalization'.Comment: 36 pages, 33 figures; for a popular introduction, see
http://onsager.physics.yale.edu/superflow.html; (v2) Added reference to new
work of Chen and Ting; (v3) reorganized presentation for improved clarity,
and added new appendix on microscopic origin; (v4) final published version
with minor change
Condensed matter and AdS/CFT
I review two classes of strong coupling problems in condensed matter physics,
and describe insights gained by application of the AdS/CFT correspondence. The
first class concerns non-zero temperature dynamics and transport in the
vicinity of quantum critical points described by relativistic field theories. I
describe how relativistic structures arise in models of physical interest,
present results for their quantum critical crossover functions and
magneto-thermoelectric hydrodynamics. The second class concerns symmetry
breaking transitions of two-dimensional systems in the presence of gapless
electronic excitations at isolated points or along lines (i.e. Fermi surfaces)
in the Brillouin zone. I describe the scaling structure of a recent theory of
the Ising-nematic transition in metals, and discuss its possible connection to
theories of Fermi surfaces obtained from simple AdS duals.Comment: 39 pages, 12 figures; Lectures at the 5th Aegean summer school, "From
gravity to thermal gauge theories: the AdS/CFT correspondence", and the De
Sitter Lecture Series in Theoretical Physics 2009, University of Groninge
Quantum phase transitions
In recent years, quantum phase transitions have attracted the interest of
both theorists and experimentalists in condensed matter physics. These
transitions, which are accessed at zero temperature by variation of a
non-thermal control parameter, can influence the behavior of electronic systems
over a wide range of the phase diagram. Quantum phase transitions occur as a
result of competing ground state phases. The cuprate superconductors which can
be tuned from a Mott insulating to a d-wave superconducting phase by carrier
doping are a paradigmatic example. This review introduces important concepts of
phase transitions and discusses the interplay of quantum and classical
fluctuations near criticality. The main part of the article is devoted to bulk
quantum phase transitions in condensed matter systems. Several classes of
transitions will be briefly reviewed, pointing out, e.g., conceptual
differences between ordering transitions in metallic and insulating systems. An
interesting separate class of transitions are boundary phase transitions where
only degrees of freedom of a subsystem become critical; this will be
illustrated in a few examples. The article is aimed on bridging the gap between
high-level theoretical presentations and research papers specialized in certain
classes of materials. It will give an overview over a variety of different
quantum transitions, critically discuss open theoretical questions, and
frequently make contact with recent experiments in condensed matter physics.Comment: 50 pages, 7 figs; (v2) final version as publishe
Quantum phases and phase transitions of Mott insulators
This article contains a theoretical overview of the physical properties of
antiferromagnetic Mott insulators in spatial dimensions greater than one. Many
such materials have been experimentally studied in the past decade and a half,
and we make contact with these studies. The simplest class of Mott insulators
have an even number of S=1/2 spins per unit cell, and these can be described
with quantitative accuracy by the bond operator method: we discuss their spin
gap and magnetically ordered states, and the transitions between them driven by
pressure or an applied magnetic field. The case of an odd number of S=1/2 spins
per unit cell is more subtle: here the spin gap state can spontaneously develop
bond order (so the ground state again has an even number of S=1/2 spins per
unit cell), and/or acquire topological order and fractionalized excitations. We
describe the conditions under which such spin gap states can form, and survey
recent theories (T. Senthil et al., cond-mat/0312617) of the quantum phase
transitions among these states and magnetically ordered states. We describe the
breakdown of the Landau-Ginzburg-Wilson paradigm at these quantum critical
points, accompanied by the appearance of emergent gauge excitations.Comment: 51 pages, 13 figure
Dimensional reduction at a quantum critical point
Competition between electronic ground states near a quantum critical point
(QCP) - the location of a zero-temperature phase transition driven solely by
quantum-mechanical fluctuations - is expected to lead to unconventional
behaviour in low-dimensional systems. New electronic phases of matter have been
predicted to occur in the vicinity of a QCP by two-dimensional theories, and
explanations based on these ideas have been proposed for significant unsolved
problems in condensed-matter physics, such as non-Fermi-liquid behaviour and
high-temperature superconductivity. But the real materials to which these ideas
have been applied are usually rendered three-dimensional by a finite electronic
coupling between their component layers; a two-dimensional QCP has not been
experimentally observed in any bulk three-dimensional system, and mechanisms
for dimensional reduction have remained the subject of theoretical conjecture.
Here we show evidence that the Bose-Einstein condensate of spin triplets in the
three-dimensional Mott insulator BaCuSi2O6 provides an experimentally
verifiable example of dimensional reduction at a QCP. The interplay of
correlations on a geometrically frustrated lattice causes the individual
two-dimensional layers of spin-1/2 Cu2+ pairs (spin dimers) to become decoupled
at the QCP, giving rise to a two-dimensional QCP characterized by power law
scaling distinctly different from that of its three-dimensional counterpart.
Thus the very notion of dimensionality can be said to acquire an 'emergent'
nature: although the individual particles move on a three-dimensional lattice,
their collective behaviour occurs in lower-dimensional space.Comment: 14 pages, 4 figure