SPT extension of Z2Z_2 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 $Z_2$ 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 $S$ and its dual $S^*$ made of quadrangular and $n-$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

Z3Z_3 and (×Z3)3(\times Z_3)^3 symmetry protected topological paramagnets

We identify two-dimensional three-state Potts paramagnets with gapless edge modes on a triangular lattice protected by $(\times Z_3)^3\equiv Z_3\times Z_3\times Z_3$ symmetry and smaller $Z_3$ 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