2,822 research outputs found
Computing quantum phase transitions
This article first gives a concise introduction to quantum phase transitions,
emphasizing similarities with and differences to classical thermal transitions.
After pointing out the computational challenges posed by quantum phase
transitions, a number of successful computational approaches is discussed. The
focus is on classical and quantum Monte Carlo methods, with the former being
based on the quantum-to classical mapping while the latter directly attack the
quantum problem. These methods are illustrated by several examples of quantum
phase transitions in clean and disordered systems.Comment: 99 pages, 15 figures, submitted to Reviews in Computational Chemistr
Rare region effects at classical, quantum, and non-equilibrium phase transitions
Rare regions, i.e., rare large spatial disorder fluctuations, can
dramatically change the properties of a phase transition in a quenched
disordered system. In generic classical equilibrium systems, they lead to an
essential singularity, the so-called Griffiths singularity, of the free energy
in the vicinity of the phase transition. Stronger effects can be observed at
zero-temperature quantum phase transitions, at nonequilibrium phase
transitions, and in systems with correlated disorder. In some cases, rare
regions can actually completely destroy the sharp phase transition by smearing.
This topical review presents a unifying framework for rare region effects at
weakly disordered classical, quantum, and nonequilibrium phase transitions
based on the effective dimensionality of the rare regions. Explicit examples
include disordered classical Ising and Heisenberg models, insulating and
metallic random quantum magnets, and the disordered contact process.Comment: Topical review, 68 pages, 14 figures, final version as publishe
Criticality and entanglement in random quantum systems
We review studies of entanglement entropy in systems with quenched
randomness, concentrating on universal behavior at strongly random quantum
critical points. The disorder-averaged entanglement entropy provides insight
into the quantum criticality of these systems and an understanding of their
relationship to non-random ("pure") quantum criticality. The entanglement near
many such critical points in one dimension shows a logarithmic divergence in
subsystem size, similar to that in the pure case but with a different universal
coefficient. Such universal coefficients are examples of universal critical
amplitudes in a random system. Possible measurements are reviewed along with
the one-particle entanglement scaling at certain Anderson localization
transitions. We also comment briefly on higher dimensions and challenges for
the future.Comment: Review article for the special issue "Entanglement entropy in
extended systems" in J. Phys.
Strong disorder RG approach of random systems
There is a large variety of quantum and classical systems in which the
quenched disorder plays a dominant r\^ole over quantum, thermal, or stochastic
fluctuations : these systems display strong spatial heterogeneities, and many
averaged observables are actually governed by rare regions. A unifying approach
to treat the dynamical and/or static singularities of these systems has emerged
recently, following the pioneering RG idea by Ma and Dasgupta and the detailed
analysis by Fisher who showed that the Ma-Dasgupta RG rules yield asymptotic
exact results if the broadness of the disorder grows indefinitely at large
scales. Here we report these new developments by starting with an introduction
of the main ingredients of the strong disorder RG method. We describe the basic
properties of infinite disorder fixed points, which are realized at critical
points, and of strong disorder fixed points, which control the singular
behaviors in the Griffiths-phases. We then review in detail applications of the
RG method to various disordered models, either (i) quantum models, such as
random spin chains, ladders and higher dimensional spin systems, or (ii)
classical models, such as diffusion in a random potential, equilibrium at low
temperature and coarsening dynamics of classical random spin chains, trap
models, delocalization transition of a random polymer from an interface, driven
lattice gases and reaction diffusion models in the presence of quenched
disorder. For several one-dimensional systems, the Ma-Dasgupta RG rules yields
very detailed analytical results, whereas for other, mainly higher dimensional
problems, the RG rules have to be implemented numerically. If available, the
strong disorder RG results are compared with another, exact or numerical
calculations.Comment: review article, 195 pages, 36 figures; final version to be published
in Physics Report
Phenomenological Renormalization Group Methods
Some renormalization group approaches have been proposed during the last few
years which are close in spirit to the Nightingale phenomenological procedure.
In essence, by exploiting the finite size scaling hypothesis, the approximate
critical behavior of the model on infinite lattice is obtained through the
exact computation of some thermal quantities of the model on finite clusters.
In this work some of these methods are reviewed, namely the mean field
renormalization group, the effective field renormalization group and the finite
size scaling renormalization group procedures. Although special emphasis is
given to the mean field renormalization group (since it has been, up to now,
much more applied an extended to study a wide variety of different systems) a
discussion of their potentialities and interrelations to other methods is also
addressed.Comment: Review Articl
Magnetic Cluster Excitations
Magnetic clusters, i.e., assemblies of a finite number (between two or three
and several hundred) of interacting spin centers which are magnetically
decoupled from their environment, can be found in many materials ranging from
inorganic compounds, magnetic molecules, artificial metal structures formed on
surfaces to metalloproteins. The magnetic excitation spectra in them are
determined by the nature of the spin centers, the nature of the magnetic
interactions, and the particular arrangement of the mutual interaction paths
between the spin centers. Small clusters of up to four magnetic ions are ideal
model systems to examine the fundamental magnetic interactions which are
usually dominated by Heisenberg exchange, but often complemented by anisotropic
and/or higher-order interactions. In large magnetic clusters which may
potentially deal with a dozen or more spin centers, the possibility of novel
many-body quantum states and quantum phenomena are in focus. In this review the
necessary theoretical concepts and experimental techniques to study the
magnetic cluster excitations and the resulting characteristic magnetic
properties are introduced, followed by examples of small clusters demonstrating
the enormous amount of detailed physical information which can be retrieved.
The current understanding of the excitations and their physical interpretation
in the molecular nanomagnets which represent large magnetic clusters is then
presented, with an own section devoted to the subclass of the single-molecule
magnets which are distinguished by displaying quantum tunneling of the
magnetization. Finally, some quantum many-body states are summarized which
evolve in magnetic insulators characterized by built-in or field-induced
magnetic clusters. The review concludes addressing future perspectives in the
field of magnetic cluster excitations.Comment: 59 pages, 64 figures, to appear in Rev. Mod. Phy
Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4
We analyze the effect of quenched disorder on spin-1/2 quantum magnets in
which magnetic frustration promotes the formation of local singlets. Our
results include a theory for 2d valence-bond solids subject to weak bond
randomness, as well as extensions to stronger disorder regimes where we make
connections with quantum spin liquids. We find, on various lattices, that the
destruction of a valence-bond solid phase by weak quenched disorder leads
inevitably to the nucleation of topological defects carrying spin-1/2 moments.
This renormalizes the lattice into a strongly random spin network with
interesting low-energy excitations. Similarly when short-ranged valence bonds
would be pinned by stronger disorder, we find that this putative glass is
unstable to defects that carry spin-1/2 magnetic moments, and whose residual
interactions decide the ultimate low energy fate. Motivated by these results we
conjecture Lieb-Schultz-Mattis-like restrictions on ground states for
disordered magnets with spin-1/2 per statistical unit cell. These conjectures
are supported by an argument for 1d spin chains. We apply insights from this
study to the phenomenology of YbMgGaO, a recently discovered triangular
lattice spin-1/2 insulator which was proposed to be a quantum spin liquid. We
instead explore a description based on the present theory. Experimental
signatures, including unusual specific heat, thermal conductivity, and
dynamical structure factor, and their behavior in a magnetic field, are
predicted from the theory, and compare favorably with existing measurements on
YbMgGaO and related materials.Comment: v2: Stylistic revisions to improve clarity. 22 pages, 8 figures, 2
tables main text; 13 pages, 3 figures appendice
Symmetry and Asymmetry in Quasicrystals or Amorphous Materials
About forty years after its discovery, it is still common to read in the literature that quasicrystals (QCs) occupy an intermediate position between amorphous materials and periodic crystals. However, QCs exhibit high-quality diffraction patterns containing a collection of discrete Bragg reflections at variance with amorphous phases. Accordingly, these materials must be properly regarded as long-range ordered materials with a symmetry incompatible with translation invariance. This misleading conceptual status can probably arise from the use of notions borrowed from the amorphous solids framework (such us tunneling states, weak interference effects, variable range hopping, or spin glass) in order to explain certain physical properties observed in QCs. On the other hand, the absence of a general, full-fledged theory of quasiperiodic systems certainly makes it difficult to clearly distinguish the features related to short-range order atomic arrangements from those stemming from long-range order correlations. The contributions collected in this book aim at gaining a deeper understanding on the relationship between the underlying structural order and the resulting physical properties in several illustrative aperiodic systems, including the border line between QCs and related complex metallic alloys, hierarchical superlattices, electrical transmission lines, nucleic acid sequences, photonic quasicrystals, and optical devices based on aperiodic order designs
Renormalized field theory for the static crossover in dipolar ferromagnets
A field theoretical description for the static crossover in dipolar ferromagnets is presented. New non leading critical exponents for the longitudinal static susceptibility are identified and the existence and magnitude of the dip in the effective critical exponent of the transverse susceptibility found by matching techniques is scrutinized
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