Related papers: Symmetries in topological tensor network states: c…
Projected Entangled Pair States (PEPS) are recognized as a potent tool for exploring two-dimensional quantum many-body systems. However, a significant challenge emerges when applying conventional PEPS methodologies to systems with periodic…
We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…
We construct parametrized isometric tensor network states -- referred to as skeletons -- that allow us to explore phases of abelian topological order and can be efficiently implemented on quantum processors. We obtain stable finite…
In continuous quantum field theories, the entanglement entropy of a subsystem with sharp corners on its boundary exhibits a universal corner-dependent contribution. We study this contribution through the lens of lattice discretization, and…
Infinite projected entangled pair states (iPEPS) have emerged as a powerful tool for studying interacting two-dimensional fermionic systems. In this review, we discuss the iPEPS construction and some basic properties of this tensor network…
Topological phases of matter offer a promising platform for quantum computation and quantum error correction. Nevertheless, unlike its counterpart in pure states, descriptions of topological order in mixed states remain relatively…
We consider symmetry-protected topological (SPT) phases in 2D protected by linear subsystem symmetries, i.e. those that act along rigid lines. There is a distinction between a "strong" subsystem SPT phase, and a "weak" one, which is…
We study the classification of two-dimensional (2D) topological orders enriched by point-group symmetries, by generalizing the folding appraoch which was previously developed for mirror-symmetry-enriched topological orders. We fold the 2D…
We discuss entanglement entropy of gapped ground states in different dimensions, obtained on partitioning space into two regions. For trivial phases without topological order, we argue that the entanglement entropy may be obtained by…
Gutzwiller projections of non-interacting chiral topological phases are known to give rise to fractional, topologically ordered chiral phases. Here, we carry out a similar construction using two copies of non-interacting Euler insulators to…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
The Lattice Gauge Theory Hilbert space is divided into gauge-invariant sectors selected by the background charges. Such a projector can be directly embedded in a tensor network ansatz for gauge-invariant states as originally discussed in…
Many topologically nontrivial states of matter possess gapless degrees of freedom on the boundary, and when these boundary states delocalize into the bulk, a phase transition occurs and the system becomes topologically trivial. We show that…
The Minimally Entangled Typical Thermal States (METTS) are an ensemble of pure states, equivalent to the Gibbs thermal state, that can be efficiently represented by tensor networks. In this article, we use the Projected Entangled Pair…
We show how to accurately study 2D quantum critical phenomena using infinite projected entangled-pair states (iPEPS). We identify the presence of a finite correlation length in the optimal iPEPS approximation to Lorentz-invariant critical…
We present a construction of highly entangled states defined on the topology of a platonic solid using tensor networks based on ancillary Absolute Maximally Entangled (AME) states. We illustrate the idea using the example of a quantum state…
Symmetry-protected topological phases (SPTs) characterized by short-range entanglement include many states essential to understanding of topological condensed matter physics, and the extension to gapless SPTs provides essential…
We construct an algorithm to simulate imaginary time evolution of translationally invariant spin systems with local interactions on an infinite, symmetric tree. We describe the state by symmetric iPEPS and use translation-invariant…
Infinite projected entangled-pair states (iPEPS) provide a powerful tool for studying strongly correlated systems directly in the thermodynamic limit. A core component of the algorithm is the approximate contraction of the iPEPS, where the…
The norms or expectation values of infinite projected entangled-pair states (PEPS) cannot be computed exactly, and approximation algorithms have to be applied. In the last years, many efficient algorithms have been devised -- the corner…