1,795 research outputs found
Protecting clean critical points by local disorder correlations
We show that a broad class of quantum critical points can be stable against
locally correlated disorder even if they are unstable against uncorrelated
disorder. Although this result seemingly contradicts the Harris criterion, it
follows naturally from the absence of a random-mass term in the associated
order-parameter field theory. We illustrate the general concept with explicit
calculations for quantum spin-chain models. Instead of the infinite-randomness
physics induced by uncorrelated disorder, we find that weak locally correlated
disorder is irrelevant. For larger disorder, we find a line of critical points
with unusual properties such as an increase of the entanglement entropy with
the disorder strength. We also propose experimental realizations in the context
of quantum magnetism and cold-atom physics.Comment: 5 pages, 3 figures; published versio
Small volume expansion of almost supersymmetric large N theories
We consider the small-volume dynamics of nonsupersymmetric orbifold and
orientifold field theories defined on a three-torus, in a test of the claimed
planar equivalence between these models and appropriate supersymmetric ``parent
models". We study one-loop effective potentials over the moduli space of flat
connections and find that planar equivalence is preserved for suitable averages
over the moduli space. On the other hand, strong nonlinear effects produce
local violations of planar equivalence at special points of moduli space. In
the case of orbifold models, these effects show that the "twisted" sector
dominates the low-energy dynamics.Comment: 20 pages, 3 figures; added references, minor change
Multi-component symmetry-projected approach for molecular ground state correlations
The symmetry-projected Hartree--Fock ansatz for the electronic structure
problem can efficiently account for static correlation in molecules, yet it is
often unable to describe dynamic correlation in a balanced manner. Here, we
consider a multi-component, systematically-improvable approach, that accounts
for all ground state correlations. Our approach is based on linear combinations
of symmetry-projected configurations built out of a set of non-orthogonal,
variationally optimized determinants. The resulting wavefunction preserves the
symmetries of the original Hamiltonian even though it is written as a
superposition of deformed (broken-symmetry) determinants. We show how short
expansions of this kind can provide a very accurate description of the
electronic structure of simple chemical systems such as the nitrogen and the
water molecules, along the entire dissociation profile. In addition, we apply
this multi-component symmetry-projected approach to provide an accurate
interconversion profile among the peroxo and bis(-oxo) forms of
[CuO], comparable to other state-of-the-art quantum chemical
methods
Correlation amplitude and entanglement entropy in random spin chains
Using strong-disorder renormalization group, numerical exact diagonalization,
and quantum Monte Carlo methods, we revisit the random antiferromagnetic XXZ
spin-1/2 chain focusing on the long-length and ground-state behavior of the
average time-independent spin-spin correlation function C(l)=\upsilon
l^{-\eta}. In addition to the well-known universal (disorder-independent)
power-law exponent \eta=2, we find interesting universal features displayed by
the prefactor \upsilon=\upsilon_o/3, if l is odd, and \upsilon=\upsilon_e/3,
otherwise. Although \upsilon_o and \upsilon_e are nonuniversal (disorder
dependent) and distinct in magnitude, the combination \upsilon_o + \upsilon_e =
-1/4 is universal if C is computed along the symmetric (longitudinal) axis. The
origin of the nonuniversalities of the prefactors is discussed in the
renormalization-group framework where a solvable toy model is considered.
Moreover, we relate the average correlation function with the average
entanglement entropy, whose amplitude has been recently shown to be universal.
The nonuniversalities of the prefactors are shown to contribute only to surface
terms of the entropy. Finally, we discuss the experimental relevance of our
results by computing the structure factor whose scaling properties,
interestingly, depend on the correlation prefactors.Comment: v1: 16 pages, 15 figures; v2: 17 pages, improved discussions and
statistics, references added, published versio
Cómo determinar los Parámetros de la Ecuación General de una Cuádrica a través de la Visualización
Las ecuaciones generales de las cuádricas en su forma general presentan un grado de dificultad al momento de determinar a qué tipo de cuádrica pertenece. En este sentido, la visualización juega un papel importante en la determinación y relación de la ecuación con su respectiva gráfica, dado que, al realizar una manipulación algebraica sobre la ecuación canónica de la superficie para transformarla a su forma general, se puede determinar por medio de la simple inspección de la ecuación general, no solamente a qué tipo de cuádrica pertenece, sino también se pueden determinar sus parámetros principale
Excited electronic states from a variational approach based on symmetry-projected Hartree--Fock configurations
Recent work from our research group has demonstrated that symmetry-projected
Hartree--Fock (HF) methods provide a compact representation of molecular ground
state wavefunctions based on a superposition of non-orthogonal Slater
determinants. The symmetry-projected ansatz can account for static correlations
in a computationally efficient way. Here we present a variational extension of
this methodology applicable to excited states of the same symmetry as the
ground state. Benchmark calculations on the C dimer with a modest basis
set, which allows comparison with full configuration interaction results,
indicate that this extension provides a high quality description of the
low-lying spectrum for the entire dissociation profile. We apply the same
methodology to obtain the full low-lying vertical excitation spectrum of
formaldehyde, in good agreement with available theoretical and experimental
data, as well as to a challenging model insertion pathway for BeH.
The variational excited state methodology developed in this work has two
remarkable traits: it is fully black-box and will be applicable to fairly large
systems thanks to its mean-field computational cost
Valence-bond theory of highly disordered quantum antiferromagnets
We present a large-N variational approach to describe the magnetism of
insulating doped semiconductors based on a disorder-generalization of the
resonating-valence-bond theory for quantum antiferromagnets. This method
captures all the qualitative and even quantitative predictions of the
strong-disorder renormalization group approach over the entire experimentally
relevant temperature range. Finally, by mapping the problem on a hard-sphere
fluid, we could provide an essentially exact analytic solution without any
adjustable parameters.Comment: 5 pages, 3 eps figure
Proper and improper zero energy modes in Hartree-Fock theory and their relevance for symmetry breaking and restoration
We study the spectra of the molecular orbital Hessian (stability matrix) and
random-phase approximation Hamiltonian of broken-symmetry Hartree-Fock
solutions, focusing on zero eigenvalue modes. After all negative eigenvalues
are removed from the Hessian by following their eigenvectors downhill, one is
left with only positive and zero eigenvalues. Zero modes correspond to orbital
rotations with no restoring force. These rotations determine states in the
Goldstone manifold, which originates from a spontaneously broken continuous
symmetry in the wave function. Zero modes can be classified as improper or
proper according to their different mathematical and physical properties.
Improper modes arise from symmetry breaking and their restoration always lowers
the energy. Proper modes, on the other hand, correspond to degeneracies of the
wave function, and their symmetry restoration does not necessarily lower the
energy. We discuss how the RPA Hamiltonian distinguishes between proper and
improper modes by doubling the number of zero eigenvalues associated with the
latter. Proper modes in the Hessian always appear in pairs which do not double
in RPA. We present several pedagogical cases exemplifying the above statements.
The relevance of these results for projected Hartree-Fock methods is also
addressed
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