166 research outputs found
Entanglement Entropy From Tensor Network States for Stabilizer Codes
In this paper, we present the construction of tensor network states (TNS) for
some of the degenerate ground states of 3D stabilizer codes. We then use the
TNS formalism to obtain the entanglement spectrum and entropy of these
ground-states for some special cuts. In particular, we work out the examples of
the 3D toric code, the X-cube model and the Haah code. The latter two models
belong to the category of "fracton" models proposed recently, while the first
one belongs to the conventional topological phases. We mention the cases for
which the entanglement entropy and spectrum can be calculated exactly: for
these, the constructed TNS is the singular value decomposition (SVD) of the
ground states with respect to particular entanglement cuts. Apart from the area
law, the entanglement entropies also have constant and linear corrections for
the fracton models, while the entanglement entropies for the toric code models
only have constant corrections. For the cuts we consider, the entanglement
spectra of these three models are completely flat. We also conjecture that the
negative linear correction to the area law is a signature of extensive ground
state degeneracy. Moreover, the transfer matrices of these TNS can be
constructed. We show that the transfer matrices are projectors whose
eigenvalues are either 1 or 0. The number of nonzero eigenvalues is tightly
related to the ground state degeneracy.Comment: 33+9 pages. 16+3 figure
Entanglement entropy of (3+1)D topological orders with excitations
Excitations in (3+1)D topologically ordered phases have very rich structures.
(3+1)D topological phases support both point-like and string-like excitations,
and in particular the loop (closed string) excitations may admit knotted and
linked structures. In this work, we ask the question how different types of
topological excitations contribute to the entanglement entropy, or
alternatively, can we use the entanglement entropy to detect the structure of
excitations, and further obtain the information of the underlying topological
orders? We are mainly interested in (3+1)D topological orders that can be
realized in Dijkgraaf-Witten gauge theories, which are labeled by a finite
group and its group 4-cocycle up to group
automorphisms. We find that each topological excitation contributes a universal
constant to the entanglement entropy, where is the quantum
dimension that depends on both the structure of the excitation and the data
. The entanglement entropy of the excitations of the
linked/unlinked topology can capture different information of the DW theory
. In particular, the entanglement entropy introduced by Hopf-link
loop excitations can distinguish certain group 4-cocycles from the
others.Comment: 12 pages, 4 figures; v2: minor changes, published versio
Towards Graph-Aware Diffusion Modeling for Collaborative Filtering
Recovering masked feedback with neural models is a popular paradigm in
recommender systems. Seeing the success of diffusion models in solving
ill-posed inverse problems, we introduce a conditional diffusion framework for
collaborative filtering that iteratively reconstructs a user's hidden
preferences guided by its historical interactions. To better align with the
intrinsic characteristics of implicit feedback data, we implement forward
diffusion by applying synthetic smoothing filters to interaction signals on an
item-item graph. The resulting reverse diffusion can be interpreted as a
personalized process that gradually refines preference scores. Through graph
Fourier transform, we equivalently characterize this model as an anisotropic
Gaussian diffusion in the graph spectral domain, establishing both forward and
reverse formulations. Our model outperforms state-of-the-art methods by a large
margin on one dataset and yields competitive results on the others.Comment: 13 pages, 6 figure
Intrinsically/Purely Gapless-SPT from Non-Invertible Duality Transformations
The Kennedy-Tasaki (KT) transformation was used to construct the gapped
symmetry protected topological (SPT) phase from the symmetry breaking phase
with open boundary condition, and was generalized in our proceeding work [L. Li
et al. arXiv:2301.07899] on a ring by sacrificing the unitarity, and should be
understood as a non-invertible duality transformation. In this work, we further
apply the KT transformation to systematically construct gapless symmetry
protected topological phases. This construction reproduces the known examples
of (intrinsically) gapless SPT where the non-trivial topological features come
from the gapped sectors by means of decorated defect constructions. We also
construct new (intrinsically) purely gapless SPTs where there are no gapped
sectors, hence are beyond the decorated defect construction. This construction
elucidates the field theory description of the various gapless SPTs, and can
also be applied to analytically study the stability of various gapless SPT
models on the lattice under certain symmetric perturbations
Structure of the Entanglement Entropy of (3+1)D Gapped Phases of Matter
We study the entanglement entropy of gapped phases of matter in three spatial
dimensions. We focus in particular on size-independent contributions to the
entropy across entanglement surfaces of arbitrary topologies. We show that for
low energy fixed-point theories, the constant part of the entanglement entropy
across any surface can be reduced to a linear combination of the entropies
across a sphere and a torus. We first derive our results using strong
sub-additivity inequalities along with assumptions about the entanglement
entropy of fixed-point models, and identify the topological contribution by
considering the renormalization group flow; in this way we give an explicit
definition of topological entanglement entropy in (3+1)D,
which sharpens previous results. We illustrate our results using several
concrete examples and independent calculations, and show adding "twist" terms
to the Lagrangian can change in (3+1)D. For the generalized
Walker-Wang models, we find that the ground state degeneracy on a 3-torus is
given by in terms of the topological
entanglement entropy across a 2-torus. We conjecture that a similar
relationship holds for Abelian theories in dimensional spacetime, with
the ground state degeneracy on the -torus given by
.Comment: 34 pages, 16 figure
Symmetry TFTs for Non-Invertible Defects
Given any symmetry acting on a -dimensional quantum field theory, there is
an associated -dimensional topological field theory known as the
Symmetry TFT (SymTFT). The SymTFT is useful for decoupling the universal
quantities of quantum field theories, such as their generalized global
symmetries and 't Hooft anomalies, from their dynamics. In this work, we
explore the SymTFT for theories with Kramers-Wannier-like duality symmetry in
both d and d quantum field theories. After constructing the
SymTFT, we use it to reproduce the non-invertible fusion rules of duality
defects, and along the way we generalize the concept of duality defects to
\textit{higher} duality defects. We also apply the SymTFT to the problem of
distinguishing intrinsically versus non-intrinsically non-invertible duality
defects in d.Comment: 119 pages, 46 figures; v2: references added, typos corrected; v3:
publication versio
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