1,804 research outputs found
Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions
It is an open question how well tensor network states in the form of an
infinite projected entangled pair states (iPEPS) tensor network can approximate
gapless quantum states of matter. Here we address this issue for two different
physical scenarios: i) a conformally invariant quantum critical point
in the incarnation of the transverse field Ising model on the square lattice
and ii) spontaneously broken continuous symmetries with gapless Goldstone modes
exemplified by the antiferromagnetic Heisenberg and XY models on the
square lattice. We find that the energetically best wave functions display {\em
finite} correlation lengths and we introduce a powerful finite correlation
length scaling framework for the analysis of such finite- iPEPS states. The
framework is important i) to understand the mild limitations of the finite-
iPEPS manifold in representing Lorentz-invariant, gapless many body quantum
states and ii) to put forward a practical scheme in which the finite
correlation length combined with field theory inspired formulae can be
used to extrapolate the data to infinite correlation length, i.e. to the
thermodynamic limit. The finite correlation length scaling framework opens the
way for further exploration of quantum matter with an (expected)
Lorentz-invariant, massless low-energy description, with many applications
ranging from condensed matter to high-energy physics.Comment: 16 pages, 11 figure
Entanglement Structure of Deconfined Quantum Critical Points
We study the entanglement properties of deconfined quantum critical points.
We show not only that these critical points may be distinguished by their
entanglement structure but also that they are in general more highly entangled
that conventional critical points. We primarily focus on computations of the
entanglement entropy of deconfined critical points in 2+1 dimensions, drawing
connections to topological entanglement entropy and a recent conjecture on the
monotonicity under RG flow of universal terms in the entanglement entropy. We
also consider in some detail a variety of issues surrounding the extraction of
universal terms in the entanglement entropy. Finally, we compare some of our
results to recent numerical simulations.Comment: 12 pages, 4 figure
Entanglement negativity and conformal field theory: a Monte Carlo study
We investigate the behavior of the moments of the partially transposed
reduced density matrix \rho^{T_2}_A in critical quantum spin chains. Given
subsystem A as union of two blocks, this is the (matrix) transposed of \rho_A
with respect to the degrees of freedom of one of the two. This is also the main
ingredient for constructing the logarithmic negativity. We provide a new
numerical scheme for calculating efficiently all the moments of \rho_A^{T_2}
using classical Monte Carlo simulations. In particular we study several
combinations of the moments which are scale invariant at a critical point.
Their behavior is fully characterized in both the critical Ising and the
anisotropic Heisenberg XXZ chains. For two adjacent blocks we find, in both
models, full agreement with recent CFT calculations. For disjoint ones, in the
Ising chain finite size corrections are non negligible. We demonstrate that
their exponent is the same governing the unusual scaling corrections of the
mutual information between the two blocks. Monte Carlo data fully match the
theoretical CFT prediction only in the asymptotic limit of infinite intervals.
Oppositely, in the Heisenberg chain scaling corrections are smaller and,
already at finite (moderately large) block sizes, Monte Carlo data are in
excellent agreement with the asymptotic CFT result.Comment: 31 pages, 10 figures. Minor changes, published versio
A variational method based on weighted graph states
In a recent article [Phys. Rev. Lett. 97 (2006), 107206], we have presented a
class of states which is suitable as a variational set to find ground states in
spin systems of arbitrary spatial dimension and with long-range entanglement.
Here, we continue the exposition of our technique, extend from spin 1/2 to
higher spins and use the boson Hubbard model as a non-trivial example to
demonstrate our scheme.Comment: 36 pages, 13 figure
Unusual Corrections to Scaling in Entanglement Entropy
We present a general theory of the corrections to the asymptotic behaviour of
the Renyi entropies which measure the entanglement of an interval A of length L
with the rest of an infinite one-dimensional system, in the case when this is
described by a conformal field theory of central charge c. These can be due to
bulk irrelevant operators of scaling dimension x>2, in which case the leading
corrections are of the expected form L^{-2(x-2)} for values of n close to 1.
However for n>x/(x-2) corrections of the form L^{2-x-x/n} and L^{-2x/n} arise
and dominate the conventional terms. We also point out that the last type of
corrections can also occur with x less than 2. They arise from relevant
operators induced by the conical space-time singularities necessary to describe
the reduced density matrix. These agree with recent analytic and numerical
results for quantum spin chains. We also compute the effect of marginally
irrelevant bulk operators, which give a correction (log L)^{-2}, with a
universal amplitude. We present analogous results for the case when the
interval lies at the end of a semi-infinite system.Comment: 15 pages, no figure
Instantons and Entanglement Entropy
We would like to put the area law -- believed to by obeyed by entanglement
entropies in the ground state of a local field theory -- to scrutiny in the
presence of non-perturbative effects. We study instanton corrections to
entanglement entropy in various models whose instanton effects are well
understood, including gauge theory in 2+1 dimensions and false vacuum
decay in theory, and we demonstrate that the area law is indeed obeyed
in these models. We also perform numerical computations for toy wavefunctions
mimicking the theta vacuum of the (1+1)-dimensional Schwinger model. Our
results indicate that such superpositions exhibit no more violation of the area
law than the logarithmic behavior of a single Fermi surface.Comment: 29 pages, 4 figures, typos corrected, substantially revised,
published versio
Holographic coherent states from random tensor networks
Random tensor networks provide useful models that incorporate various
important features of holographic duality. A tensor network is usually defined
for a fixed graph geometry specified by the connection of tensors. In this
paper, we generalize the random tensor network approach to allow quantum
superposition of different spatial geometries. We set up a framework in which
all possible bulk spatial geometries, characterized by weighted adjacent
matrices of all possible graphs, are mapped to the boundary Hilbert space and
form an overcomplete basis of the boundary. We name such an overcomplete basis
as holographic coherent states. A generic boundary state can be expanded on
this basis, which describes the state as a superposition of different spatial
geometries in the bulk. We discuss how to define distinct classical geometries
and small fluctuations around them. We show that small fluctuations around
classical geometries define "code subspaces" which are mapped to the boundary
Hilbert space isometrically with quantum error correction properties. In
addition, we also show that the overlap between different geometries is
suppressed exponentially as a function of the geometrical difference between
the two geometries. The geometrical difference is measured in an area law
fashion, which is a manifestation of the holographic nature of the states
considered.Comment: 33 pages, 8 figures. An error corrected on page 14. Reference update
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