13,058 research outputs found
Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems
In these lecture notes, we present a pedagogical review of a number of
related {\it numerically exact} approaches to quantum many-body problems. In
particular, we focus on methods based on the exact diagonalization of the
Hamiltonian matrix and on methods extending exact diagonalization using
renormalization group ideas, i.e., Wilson's Numerical Renormalization Group
(NRG) and White's Density Matrix Renormalization Group (DMRG). These methods
are standard tools for the investigation of a variety of interacting quantum
systems, especially low-dimensional quantum lattice models. We also survey
extensions to the methods to calculate properties such as dynamical quantities
and behavior at finite temperature, and discuss generalizations of the DMRG
method to a wider variety of systems, such as classical models and quantum
chemical problems. Finally, we briefly review some recent developments for
obtaining a more general formulation of the DMRG in the context of matrix
product states as well as recent progress in calculating the time evolution of
quantum systems using the DMRG and the relationship of the foundations of the
method with quantum information theory.Comment: 51 pages; lecture notes on numerically exact methods. Pedagogical
review appearing in the proceedings of the "IX. Training Course in the
Physics of Correlated Electron Systems and High-Tc Superconductors", Vietri
sul Mare (Salerno, Italy, October 2004
Time evolution of one-dimensional Quantum Many Body Systems
The level of current understanding of the physics of time-dependent strongly
correlated quantum systems is far from complete, principally due to the lack of
effective controlled approaches. Recently, there has been progress in the
development of approaches for one-dimensional systems. We describe recent
developments in the construction of numerical schemes for general
(one-dimensional) Hamiltonians: in particular, schemes based on exact
diagonalization techniques and on the density matrix renormalization group
method (DMRG). We present preliminary results for spinless fermions with
nearest-neighbor-interaction and investigate their accuracy by comparing with
exact results.Comment: Contribution for the conference proceedings of the "IX. Training
Course in the Physics of Correlated Electron Systems and High-Tc
Superconductors" held in Vietri sul Mare (Salerno, Italy) in October 200
Time evolution of correlations in strongly interacting fermions after a quantum quench
Using the adaptive time-dependent density matrix renormalization group, we
study the time evolution of density correlations of interacting spinless
fermions on a one-dimensional lattice after a sudden change in the interaction
strength. Over a broad range of model parameters, the correlation function
exhibits a characteristic light-cone-like time evolution representative of a
ballistic transport of information. Such behavior is observed both when
quenching an insulator into the metallic region and also when quenching within
the insulating region. However, when a metallic state beyond the quantum
critical point is quenched deep into the insulating regime, no indication for
ballistic transport is observed. Instead, stable domain walls in the density
correlations emerge during the time evolution, consistent with the predictions
of the Kibble-Zurek mechanism.Comment: Published version; minor changes, references adde
Entanglement Complexity in Quantum Many-Body Dynamics, Thermalization and Localization
Entanglement is usually quantified by von Neumann entropy, but its properties
are much more complex than what can be expressed with a single number. We show
that the three distinct dynamical phases known as thermalization, Anderson
localization, and many-body localization are marked by different patterns of
the spectrum of the reduced density matrix for a state evolved after a quantum
quench. While the entanglement spectrum displays Poisson statistics for the
case of Anderson localization, it displays universal Wigner-Dyson statistics
for both the cases of many-body localization and thermalization, albeit the
universal distribution is asymptotically reached within very different time
scales in these two cases. We further show that the complexity of entanglement,
revealed by the possibility of disentangling the state through a
Metropolis-like algorithm, is signaled by whether the entanglement spectrum
level spacing is Poisson or Wigner-Dyson distributed.Comment: Minor revision
Dzyaloshinskii-Moriya anisotropy and non-magnetic impurities in the kagome system ZnCu_3(OH)_6Cl_2
Motivated by recent nuclear magnetic resonance experiments on
ZnCu(OH)Cl, we present an exact-diagonalization study of the
combined effects of non-magnetic impurities and Dzyaloshinskii-Moriya (DM)
interactions in the kagome antiferromagnet. The local response to an
applied field and correlation-matrix data reveal that the dimer freezing which
occurs around each impurity for persists at least up to , where and denote respectively the exchange and DM interaction
energies. The phase transition to the () semiclassical, 120
state favored at large takes place at . However, the dimers
next to the impurity sites remain strong up to values , far above
this critical point, and thus do not participate fully in the ordered state. We
discuss the implications of our results for experiments on
ZnCu(OH)Cl.Comment: 11 pages, submitted to PR
Flavour-conserving oscillations of Dirac-Majorana neutrinos
We analyze both chirality-changing and chirality-preserving transitions of
Dirac-Majorana neutrinos. In vacuum, the first ones are suppressed with respect
to the others due to helicity conservation and the interactions with a
(``normal'') medium practically does not affect the expressions of the
probabilities for these transitions, even if the amplitudes of oscillations
slightly change. For usual situations involving relativistic neutrinos we find
no resonant enhancement for all flavour-conserving transitions. However, for
very light neutrinos propagating in superdense media, the pattern of
oscillations is dramatically altered with respect to the
vacuum case, the transition probability practically vanishing. An application
of this result is envisaged.Comment: 14 pages, latex 2E, no figure
Hypoconstrained Jammed Packings of Nonspherical Hard Particles: Ellipses and Ellipsoids
Continuing on recent computational and experimental work on jammed packings
of hard ellipsoids [Donev et al., Science, vol. 303, 990-993] we consider
jamming in packings of smooth strictly convex nonspherical hard particles. We
explain why the isocounting conjecture, which states that for large disordered
jammed packings the average contact number per particle is twice the number of
degrees of freedom per particle (\bar{Z}=2d_{f}), does not apply to
nonspherical particles. We develop first- and second-order conditions for
jamming, and demonstrate that packings of nonspherical particles can be jammed
even though they are hypoconstrained (\bar{Z}<2d_{f}). We apply an algorithm
using these conditions to computer-generated hypoconstrained ellipsoid and
ellipse packings and demonstrate that our algorithm does produce jammed
packings, even close to the sphere point. We also consider packings that are
nearly jammed and draw connections to packings of deformable (but stiff)
particles. Finally, we consider the jamming conditions for nearly spherical
particles and explain quantitatively the behavior we observe in the vicinity of
the sphere point.Comment: 33 pages, third revisio
Densest local packing diversity. II. Application to three dimensions
The densest local packings of N three-dimensional identical nonoverlapping
spheres within a radius Rmin(N) of a fixed central sphere of the same size are
obtained for selected values of N up to N = 1054. In the predecessor to this
paper [A.B. Hopkins, F.H. Stillinger and S. Torquato, Phys. Rev. E 81 041305
(2010)], we described our method for finding the putative densest packings of N
spheres in d-dimensional Euclidean space Rd and presented those packings in R2
for values of N up to N = 348. We analyze the properties and characteristics of
the densest local packings in R3 and employ knowledge of the Rmin(N), using
methods applicable in any d, to construct both a realizability condition for
pair correlation functions of sphere packings and an upper bound on the maximal
density of infinite sphere packings. In R3, we find wide variability in the
densest local packings, including a multitude of packing symmetries such as
perfect tetrahedral and imperfect icosahedral symmetry. We compare the densest
local packings of N spheres near a central sphere to minimal-energy
configurations of N+1 points interacting with short-range repulsive and
long-range attractive pair potentials, e.g., 12-6 Lennard-Jones, and find that
they are in general completely different, a result that has possible
implications for nucleation theory. We also compare the densest local packings
to finite subsets of stacking variants of the densest infinite packings in R3
(the Barlow packings) and find that the densest local packings are almost
always most similar, as measured by a similarity metric, to the subsets of
Barlow packings with the smallest number of coordination shells measured about
a single central sphere, e.g., a subset of the FCC Barlow packing. We
additionally observe that the densest local packings are dominated by the
spheres arranged with centers at precisely distance Rmin(N) from the fixed
sphere's center.Comment: 45 pages, 18 figures, 2 table
Self-assembly of the simple cubic lattice with an isotropic potential
Conventional wisdom presumes that low-coordinated crystal ground states
require directional interactions. Using our recently introduced optimization
procedure to achieve self-assembly of targeted structures (Phys. Rev. Lett. 95,
228301 (2005), Phys. Rev. E 73, 011406 (2006)), we present an isotropic pair
potential for a three-dimensional many-particle system whose classical
ground state is the low-coordinated simple cubic (SC) lattice. This result is
part of an ongoing pursuit by the authors to develop analytical and
computational tools to solve statistical-mechanical inverse problems for the
purpose of achieving targeted self-assembly. The purpose of these methods is to
design interparticle interactions that cause self-assembly of technologically
important target structures for applications in photonics, catalysis,
separation, sensors and electronics. We also show that standard approximate
integral-equation theories of the liquid state that utilize pair correlation
function information cannot be used in the reverse mode to predict the correct
simple cubic potential. We report in passing optimized isotropic potentials
that yield the body-centered cubic and simple hexagonal lattices, which provide
other examples of non-close-packed structures that can be assembled using
isotropic pair interactions.Comment: 16 pages, 12 figures. Accepted for publication in Physical Review
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