70 research outputs found
Dissipative Symmetry-Protected Topological Order
In this work, we investigate the interplay between dissipation and
symmetry-protected topological order. We considered the one-dimensional spin-1
Affleck-Kennedy-Lieb-Tasaki model interacting with an environment where the
dissipative dynamics are described by the Lindladian master equation. The
Markovian dynamics is solved by the implementation of a tensor network
algorithm for mixed states in the thermodynamic limit. We observe that, for
time-reversal symmetric dissipation, the resulting steady state has topological
signatures even if being a mixed state. This is seen in finite string-order
parameters as well as in the degeneracy pattern of singular values in the
tensor network decomposition of the reduced density matrix. We also show that
such features do not appear for non-symmetric dissipation. Our work opens the
way toward a generalized and more practical definition of symmetry-protected
topological order for mixed states induced by dissipation.Comment: 5 pages, 5 figure, revised versio
Entanglement, subsystem particle numbers and topology in free fermion systems
We study the relationship between bipartite entanglement, subsystem particle
number and topology in a half-filled free fermion system. It is proposed that
the spin-projected particle numbers can distinguish the quantum spin Hall state
from other states, and can be used to establish a new topological index for the
system. Furthermore, we apply the new topological invariant to a disordered
system and show that a topological phase transition occurs when the disorder
strength is increased beyond a critical value. It is also shown that the
subsystem particle number fluctuation displays behavior very similar to that of
the entanglement entropy. This provides a lower-bound estimation for the
entanglement entropy, which can be utilized to obtain an estimate of the
entanglement entropy experimentally.Comment: 14 pages, 6 figure
Numerical study of the one-dimensional quantum compass model
The ground state magnetic phase diagram of the one-dimensional quantum
compass model (QCM) is studied using the numerical Lanczos method. A detailed
numerical analysis of the low energy excitation spectrum is presented. The
energy gap and the spin-spin correlation functions are calculated for finite
chains. Two kind of the magnetic long-range orders, the Neel and a type of the
stripe-antiferromagnet, in the ground state phase diagram are identified. Based
on the numerical analysis, the first and second order quantum phase transitions
in the ground state phase diagram are identified.Comment: 6 pages, 8 figures. arXiv admin note: text overlap with
arXiv:1105.211
Biogenesis and Ultrastructure of Carboxysomes from Wild Type and Mutants of Synechococcus sp. Strain PCC 7942
Entanglement and alpha entropies for a massive Dirac field in two dimensions
We present some exact results about universal quantities derived from the
local density matrix, for a free massive Dirac field in two dimensions. We
first find the trace of powers of the density matrix in a novel fashion, which
involves the correlators of suitable operators in the sine-Gordon model. These,
in turn, can be written exactly in terms of the solutions of non-linear
differential equations of the Painlev\'e V type. Equipped with the previous
results, we find the leading terms for the entanglement entropy, both for short
and long distances, and showing that in the intermediate regime it can be
expanded in a series of multiple integrals. The previous results have been
checked by direct numerical calculations on the lattice, finding perfect
agreement. Finally, we comment on a possible generalization of the entanglement
entropy c-theorem to the alpha-entropies.Comment: Clarification in section 2, one reference added. 15 pages, 3 figure
Geometrical entanglement of highly symmetric multipartite states and the Schmidt decomposition
In a previous paper we examined a geometric measure of entanglement based on
the minimum distance between the entangled target state of interest and the
space of unnormalized product states. Here we present a detailed study of this
entanglement measure for target states with a large degree of symmetry. We
obtain analytic solutions for the extrema of the distance function and solve
for the Hessian to show that, up to the action of trivial symmetries, the
solutions correspond to local minima of the distance function. In addition, we
show that the conditions that determine the extremal solutions for general
target states can be obtained directly by parametrizing the product states via
their Schmidt decomposition.Comment: 16 pages, references added and discussion expande
Block Spin Density Matrix of the Inhomogeneous AKLT Model
We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain
model. Spins at each lattice site could be different. Under certain conditions,
the ground state of this AKLT model is unique and is described by the
Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous
block of bulk spins in this ground state. The density matrix is independent of
spins outside the block. It is diagonalized and shown to be a projector onto a
subspace. We prove that for large block the density matrix behaves as the
identity in the subspace. The von Neumann entropy coincides with Renyi entropy
and is equal to the saturated value.Comment: 20 page
Current Issues in the Phenomenology of Particle Physics
The present status of the Standard Model and its experimental tests are
reviewed, including indications on the likely mass of the Higgs boson. Also
discussed are the motivations for supersymmetry and grand unification, searches
for sparticles at LEP, neutrino oscillations, and the prospects for physics at
the LHC.Comment: 32 pages, LaTeX, 10 figures (included), Invited plenary talk
presented at the Inaugural Conference of the APCTP, Seoul, June 199
Entanglement and Density Matrix of a Block of Spins in AKLT Model
We study a 1-dimensional AKLT spin chain, consisting of spins in the bulk
and at both ends. The unique ground state of this AKLT model is described
by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a
contiguous block of bulk spins in this ground state. It is shown that the
density matrix is a projector onto a subspace of dimension . This
subspace is described by non-zero eigenvalues and corresponding eigenvectors of
the density matrix. We prove that for large block the von Neumann entropy
coincides with Renyi entropy and is equal to .Comment: Revised version, typos corrected, references added, 31 page
Entanglement Entropy dynamics in Heisenberg chains
By means of the time-dependent density matrix renormalization group algorithm
we study the zero-temperature dynamics of the Von Neumann entropy of a block of
spins in a Heisenberg chain after a sudden quench in the anisotropy parameter.
In the absence of any disorder the block entropy increases linearly with time
and then saturates. We analyze the velocity of propagation of the entanglement
as a function of the initial and final anisotropies and compare, wherever
possible, our results with those obtained by means of Conformal Field Theory.
In the disordered case we find a slower (logarithmic) evolution which may
signals the onset of entanglement localization.Comment: 15 pages, 9 figure
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