Related papers: Geometric entanglement in integer quantum Hall sta…
In a recent publication, we have discussed the effects of boundary conditions in finite quantum systems and their connection with symmetries. Focusing on the one-dimensional Hubbard Hamiltonian under twisted boundary conditions, we have…
The simulation of quantum Hall physics with rotating quantum gases is witnessing a revival due to recent experimental advances that enabled the observation of a Bose-Einstein condensate entirely contained in its lowest kinetic energy state,…
Protected edge modes are the cornerstone of topological states of matter. The simplest example is provided by the integer quantum Hall state at Landau level filling unity, which should feature a single chiral mode carrying electronic…
The entanglement spectroscopy, initially introduced by Li and Haldane in the context of the fractional quantum Hall effects, has stimulated an extensive range of studies. The entanglement spectrum is the spectrum of the reduced density…
Entanglement entropy for a spatial partition of a quantum system is studied in theories which admit a dual description in terms of the anti-de Sitter (AdS) gravity one dimension higher. A general proof of the holographic formula which…
Quantum geometry, which encompasses both Berry curvature and the quantum metric, plays a key role in multi-band interacting electron systems. We study the entanglement entropy of a region of linear size $\ell$ in fermion systems with…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement is explored for bi-partite and multi-partite pure and mixed states.…
Quantum entanglement does not necessarily imply Einstein-Podolsky-Rosen steering. We identify a \emph{boundary mechanism} that closes this gap when an entangled state meets the boundary of the trusted state space in a nondegenerate way. The…
Here we investigate the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of…
We introduce a novel class of phase transitions separating quantum states with different entanglement features. An example of such an "entanglement phase transition" is provided by the many-body localization transition in disordered quantum…
We perform an exact diagonalization study of the topological order in topological flat band models through calculating entanglement entropy and spectra of low energy states. We identify multiple independent minimal entangled states, which…
In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum…
The entanglement entropy of a distinguished region of a quantum many-body system reflects the entanglement present in its pure ground state. In this work, we establish scaling laws for this entanglement for critical quasi-free fermionic and…
This article is an expository account aimed at viewing entanglement in finite-dimensional quantum many-body systems as a phenomenon of global geometry. While the mathematics of general quantum states has been studied extensively, this…
We propose a framework for preparing quantum states with a holographic entanglement structure, in the sense that the entanglement entropies are governed by minimal surfaces in a chosen bulk geometry. We refer to such entropies as…
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…
Some quantum field theories show, in a fundamental or an effective manner, an alternative between a loss of duality for algebras of operators corresponding to complementary regions, or a loss of additivity. In this latter case, the algebra…
The bootstrap method aims to solve problems by imposing constraints on the space of physical observables, which often follow from physical assumptions such as positivity and symmetry. Here, we employ a bootstrap approach to study…
Entanglement entropy first arose from attempts to understand the entropy of black holes, and is believed to play a crucial role in a complete description of quantum gravity. This thesis explores some proposed connections between…
The entanglement entropy of the incompressible states of a realistic quantum Hall system in the second Landau level are studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy, which is…