4 research outputs found
SPT extension of quantum Ising model's ferromagnetic phase
This paper focuses on creation of a model with explicitly defined symmetry
protected topological (SPT) phases on a triangular lattice, based on
Ising model's ferromagnetic phase. It results in emergence of massless edge
states in non-trivial SPT phases. The Hamiltonian for these edge states
contains four-point spin interactions between next-to-next nearest neighbors. A
generic technique for creating SPT models is developed, allowing for the
construction of translation-invariant edge models
Geometry of random potentials: Induction of 2D gravity in Quantum Hall plateau transitions
In the context of the Integer Quantum Hall plateau transitions, we formulate
a specific map from random landscape potentials onto 2D discrete random
surfaces. Critical points of the potential, namely maxima, minima and saddle
points uniquely define a discrete surface and its dual made of
quadrangular and gonal faces, respectively, thereby linking the geometry of
the potential with the geometry of discrete surfaces. The map is
parameter-dependent on the Fermi level. Edge states of Fermi lakes moving along
equipotential contours between neighbour saddle points form a network of
scatterings, which define the geometric basis, in the fermionic model, for the
plateau transitions. The replacement probability characterizing the network
model with geometric disorder recently proposed by Gruzberg, Kl\"umper, Nuding
and Sedrakyan, is physically interpreted within the current framework as a
parameter connected with the Fermi level
and symmetry protected topological paramagnets
We identify two-dimensional three-state Potts paramagnets with gapless edge
modes on a triangular lattice protected by symmetry and smaller symmetry. We derive microscopic
models for the gapless edge, uncover their symmetries and analyze the conformal
properties. We study the properties of the gapless edge by employing the
numerical density-matrix renormalization group (DMRG) simulation and exact
diagonalization. We discuss the corresponding conformal field theory, its
central charge, and the scaling dimension of the corresponding primary field.
The discussed two-dimensional models realize a variety of symmetry-protected
topological phases, opening a window for studies of the unconventional quantum
criticalities between them.Comment: 33 pages, 9 figure
Deep Lake: a Lakehouse for Deep Learning
Traditional data lakes provide critical data infrastructure for analytical
workloads by enabling time travel, running SQL queries, ingesting data with
ACID transactions, and visualizing petabyte-scale datasets on cloud storage.
They allow organizations to break down data silos, unlock data-driven
decision-making, improve operational efficiency, and reduce costs. However, as
deep learning takes over common analytical workflows, traditional data lakes
become less useful for applications such as natural language processing (NLP),
audio processing, computer vision, and applications involving non-tabular
datasets. This paper presents Deep Lake, an open-source lakehouse for deep
learning applications developed at Activeloop. Deep Lake maintains the benefits
of a vanilla data lake with one key difference: it stores complex data, such as
images, videos, annotations, as well as tabular data, in the form of tensors
and rapidly streams the data over the network to (a) Tensor Query Language, (b)
in-browser visualization engine, or (c) deep learning frameworks without
sacrificing GPU utilization. Datasets stored in Deep Lake can be accessed from
PyTorch, TensorFlow, JAX, and integrate with numerous MLOps tools