scholarly journals Volume law for the entanglement entropy in non-local QFTs

2014 ◽  
Vol 2014 (2) ◽  
Author(s):  
Noburo Shiba ◽  
Tadashi Takayanagi
Keyword(s):  
Entanglement Entropy ◽  
Non Local

scholarly journals Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model

2020 ◽  
Vol 3 (2) ◽  
Author(s):  
Tommaso Micallo ◽  
Vittorio Vitale ◽  
Marcello Dalmonte ◽  
Pierre Fromholz
Keyword(s):  
Entanglement Entropy ◽  
Finite Size ◽  
Topological Invariant ◽  
Topological Invariants ◽  
Finite Size Scaling ◽  
Bipartite Entanglement ◽  
Non Local ◽  
Two Phases ◽  
Area And Volume ◽  
Second Order Phase Transition

We study the disconnected entanglement entropy, S^\mathrm{D}SD, of the Su-Schrieffer-Heeger model. S^\mathrm{D}SD is a combination of both connected and disconnected bipartite entanglement entropies that removes all area and volume law contributions and is thus only sensitive to the non-local entanglement stored within the ground state manifold. Using analytical and numerical computations, we show that S^\mathrm{D}SD behaves like a topological invariant, i.e., it is quantized to either 00 or 2\log(2)2log(2) in the topologically trivial and non-trivial phases, respectively. These results also hold in the presence of symmetry-preserving disorder. At the second-order phase transition separating the two phases, S^\mathrm{D}SD displays a finite-size scaling behavior akin to those of conventional order parameters, that allows us to compute entanglement critical exponents. To corroborate the topological origin of the quantized values of S^\mathrm{D}SD, we show how the latter remain quantized after applying unitary time evolution in the form of a quantum quench, a characteristic feature of topological invariants associated with particle-hole symmetry.

scholarly journals High temperature behavior of non-local observables in boosted strongly coupled plasma: a holographic study

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Atanu Bhatta ◽  
Shankhadeep Chakrabortty ◽  
Suat Dengiz ◽  
Ercan Kilicarslan
Keyword(s):  
High Temperature ◽  
Thermal Plasma ◽  
Rotational Symmetry ◽  
Entanglement Entropy ◽  
Region Of Interest ◽  
Boundary Theory ◽  
Strongly Coupled ◽  
Non Local ◽  
Local Observables ◽  
Strip Geometry

Abstract In this work, we perform a holographic analysis to study non local observables associated to a uniformly boosted strongly coupled large N thermal plasma in d-dimensions. In order to accomplish the holographic analysis, the appropriate dual bulk theory turns out to be $$d+1$$d+1 dimensional boosted AdS-Schwarzschild blackhole background. In particular, we compute entanglement entropy of the boosted plasma at high temperature living inside a strip geometry with entangling width l in the boundary at a particular instant of time. We also study the two-point correlators in the boundary by following geodesic approximation method. For analyzing the effect of boosting on the thermal plasma and correspondingly on both non local observables, we keep the alignment of the width of region of interest both parallel and perpendicular to the direction of the boost. We find our results significantly modified compared to those in un-boosted plasma up to the quadratic order of the boost velocity v. More interestingly, the relative orientation of the boost and the entangling width play a crucial role to quantify the holographic entanglement entropy in the boundary theory. The breaking of rotational symmetry in the boundary theory due to the boosting of the plasma along a specific flat direction causes this interesting feature.

ENTANGLEMENT ENTROPY AND STRONGLY CORRELATED TOPOLOGICAL MATTER

2013 ◽  
Vol 28 (05) ◽  
pp. 1330001 ◽  
Author(s):  
TARUN GROVER
Keyword(s):  
Entanglement Entropy ◽  
Local Order ◽  
Strongly Correlated ◽  
Edge States ◽  
Ordered Phases ◽  
Local Order Parameter ◽  
Topological States ◽  
Non Local ◽  
Topological Entanglement Entropy ◽  
Entanglement Structure

Topological ordered phases are gapped states of matter that are characterized by non-local entanglement in their ground state wave functions instead of a local order parameter. In this paper, we review some of the basic results on the entanglement structure of topologically ordered phases. In particular, we focus on the notion and uses of "topological entanglement entropy" in two and higher dimensions, and also briefly review the relation between entanglement spectrum and the spectrum of the physical edge states for chiral topological states. Furthermore, we discuss a curvature expansion for the entanglement entropy which sharpens the nonlocality of topological entanglement entropy.

scholarly journals Non-local probes of entanglement in the scale-invariant gravity

2021 ◽  
Vol 18 (12) ◽  
Author(s):  
R. Pirmoradian ◽  
M. Reza Tanhayi
Keyword(s):  
Mutual Information ◽  
Invariant Theory ◽  
Entanglement Entropy ◽  
Scale Invariant ◽  
Non Local ◽  
Theory Of Gravity

In this paper, we study the generic action for the scale-invariant theory of gravity and then by making use of the holographic methods, we compute some specific holographic measures of entanglement. Precisely, we calculate the entanglement entropy, mutual and tripartite information and show that the mutual information is always positive while the tripartite information becomes negative. This indeed recovers the monogamy property of mutual information in this context.

Toward High-Resolution Low-Voltage SEM

1988 ◽  
Vol 46 ◽  
pp. 218-219
Author(s):  
Zhifeng Shao
Keyword(s):  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Limiting Factor ◽  
Operating Voltage ◽  
Probe Radius ◽  
Non Local ◽  
Electron Microscopes ◽  
Image Position ◽  
Scanning Electron Microscopes

Recently, low voltage (≤5kV) scanning electron microscopes have become popular because of their unprecedented advantages, such as minimized charging effects and smaller specimen damage, etc. Perhaps the most important advantage of LVSEM is that they may be able to provide ultrahigh resolution since the interaction volume decreases when electron energy is reduced. It is obvious that no matter how low the operating voltage is, the resolution is always poorer than the probe radius. To achieve 10Å resolution at 5kV (including non-local effects), we would require a probe radius of 5∽6 Å. At low voltages, we can no longer ignore the effects of chromatic aberration because of the increased ratio δV/V. The 3rd order spherical aberration is another major limiting factor. The optimized aperture should be calculated as

Chromatic aberration and low-voltage SEM

1987 ◽  
Vol 45 ◽  
pp. 546-547
Author(s):  
Zhifeng Shao ◽  
A.V. Crewe
Keyword(s):  
Electron Energy ◽  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Primary Electron ◽  
Probe Size ◽  
Non Local ◽  
Optical Treatment ◽  
Electron Microscopes ◽  
Scanning Electron Microscopes

For scanning electron microscopes, it is plausible that by lowering the primary electron energy, one can decrease the volume of interaction and improve resolution. As shown by Crewe /1/, at V0 =5kV a 10Å resolution (including non-local effects) is possible. To achieve this, we would need a probe size about 5Å. However, at low voltages, the chromatic aberration becomes the major concern even for field emission sources. In this case, δV/V = 0.1 V/5kV = 2x10-5. As a rough estimate, it has been shown that /2/ the chromatic aberration δC should be less than ⅓ of δ0 the probe size determined by diffraction and spherical aberration in order to neglect its effect. But this did not take into account the distribution of electron energy. We will show that by using a wave optical treatment, the tolerance on the chromatic aberration is much larger than we expected.

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