1,285 research outputs found
Comb entanglement in quantum spin chains
Bipartite entanglement in the ground state of a chain of quantum spins
can be quantified either by computing pairwise concurrence or by dividing the
chain into two complementary subsystems. In the latter case the smaller
subsystem is usually a single spin or a block of adjacent spins and the
entanglement differentiates between critical and non-critical regimes. Here we
extend this approach by considering a more general setting: our smaller
subsystem consists of a {\it comb} of spins, spaced sites apart.
Our results are thus not restricted to a simple `area law', but contain
non-local information, parameterized by the spacing . For the XX model we
calculate the von-Neumann entropy analytically when and
investigate its dependence on and . We find that an external magnetic
field induces an unexpected length scale for entanglement in this case.Comment: 6 pages, 4 figure
On relations between one-dimensional quantum and two-dimensional classical spin systems
We exploit mappings between quantum and classical systems in order to obtain
a class of two-dimensional classical systems with critical properties
equivalent to those of the class of one-dimensional quantum systems discussed
in a companion paper (J. Hutchinson, J. P. Keating, and F. Mezzadri,
arXiv:1503.05732). In particular, we use three approaches: the Trotter-Suzuki
mapping; the method of coherent states; and a calculation based on commuting
the quantum Hamiltonian with the transfer matrix of a classical system. This
enables us to establish universality of certain critical phenomena by extension
from the results in our previous article for the classical systems identified.Comment: 36 page
Relaxation due to random collisions with a many-qudit environment
We analyze the dynamics of a system qudit of dimension mu sequentially
interacting with the nu-dimensional qudits of a chain playing the ore of an
environment. Each pairwise collision has been modeled as a random unitary
transformation. The relaxation to equilibrium of the purity of the system
qudit, averaged over random collisions, is analytically computed by means of a
Markov chain approach. In particular, we show that the steady state is the one
corresponding to the steady state for random collisions with a single
environment qudit of effective dimension nu_e=nu*mu. Finally, we numerically
investigate aspects of the entanglement dynamics for qubits (mu=nu=2) and show
that random unitary collisions can create multipartite entanglement between the
system qudit and the qudits of the chain.Comment: 7 pages, 6 figure
Evolution of magneto-orbital order upon B-site electron doping in Na1-xCaxMn7O12 quadruple perovskite manganites
We present the discovery and refinement by neutron powder diffraction of a
new magnetic phase in the Na1-xCaxMn7O12 quadruple perovskite phase diagram,
which is the incommensurate analogue of the well-known pseudo-CE phase of the
simple perovskite manganites. We demonstrate that incommensurate magnetic order
arises in quadruple perovskites due to the exchange interactions between A and
B sites. Furthermore, by constructing a simple mean field Heisenberg exchange
model that generically describes both simple and quadruple perovskite systems,
we show that this new magnetic phase unifies a picture of the interplay between
charge, magnetic and orbital ordering across a wide range of compounds.Comment: Accepted for publication in Physical Review Letter
A new correlator in quantum spin chains
We propose a new correlator in one-dimensional quantum spin chains, the
Emptiness Formation Probability (EFP). This is a natural generalization
of the Emptiness Formation Probability (EFP), which is the probability that the
first spins of the chain are all aligned downwards. In the EFP we let
the spins in question be separated by sites. The usual EFP corresponds to
the special case when , and taking allows us to quantify non-local
correlations. We express the EFP for the anisotropic XY model in a
transverse magnetic field, a system with both critical and non-critical
regimes, in terms of a Toeplitz determinant. For the isotropic XY model we find
that the magnetic field induces an interesting length scale.Comment: 6 pages, 1 figur
Optical study of the vibrational and dielectric properties of BiMnO3
BiMnO3 (BMO), ferromagnetic (FM) below Tc = 100 K, was believed to be also
ferroelectric (FE) due to a non-centro-symmetric C2 structure, until
diffraction data indicated that its space group is the centro-symmetric C2/c.
Here we present infrared phonon spectra of BMO, taken on a mosaic of single
crystals, which are consistent with C2/c at any T > 10 K, as well as
room-temperature Raman data which strongly support this conclusion. We also
find that the infrared intensity of several phonons increases steadily for
decreasing T, causing the relative permittivity of BMO to vary from 18.5 at 300
K to 45 at 10 K. At variance with FE materials of displacive type, no
appreciable softening has been found in the infrared phonons. Both their
frequencies and intensities, moreover, appear insensitive to the FM transition
at Tc
A spin-glass model for the loss surfaces of generative adversarial networks
We present a novel mathematical model that seeks to capture the key design
feature of generative adversarial networks (GANs). Our model consists of two
interacting spin glasses, and we conduct an extensive theoretical analysis of
the complexity of the model's critical points using techniques from Random
Matrix Theory. The result is insights into the loss surfaces of large GANs that
build upon prior insights for simpler networks, but also reveal new structure
unique to this setting.Comment: 26 pages, 9 figure
Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory
We compute the entropy of entanglement between the first spins and the
rest of the system in the ground states of a general class of quantum
spin-chains. We show that under certain conditions the entropy can be expressed
in terms of averages over ensembles of random matrices. These averages can be
evaluated, allowing us to prove that at critical points the entropy grows like
as , where and are determined explicitly. In an important class of systems,
is equal to one-third of the central charge of an associated Virasoro algebra.
Our expression for therefore provides an explicit formula for the
central charge.Comment: 4 page
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