Condensed matter physics, area laws & LQG?

In summary, tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. Symmetric tensors decompose into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they
  • #386
https://arxiv.org/abs/1809.01197v1
Building up spacetime with quantum entanglement II: It from BC-bit
Mark Van Raamsdonk
(Submitted on 4 Sep 2018)
In this note, we describe how collections of arbitrary numbers of "BC-bits," distinct non-interacting quantum systems each consisting of a holographic boundary conformal field theory (BCFT), can be placed in multipartite entangled states in order to encode single connected bulk spacetimes that approximate geometries dual to holographic CFT states. The BC-bit version of a holographic CFT state corresponds to a geometry that can be made arbitrarily similar to the associated CFT-state geometry within a "causal diamond" region defined by points that are spacelike separated from the boundary time slice at which the state is defined. These holographic multi BC-bit states can be well-represented by tensor networks in which the individual tensors are associated with states of small numbers of BC-bits
 
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  • #387
Demystifier said:
@atyy something for you:
http://lanl.arxiv.org/abs/1807.05998
A solution to the chiral fermion problem: 1+1D U(1) chiral fermion theory realized by a truly local lattice model with U(1) on-site symmetry
Juven Wang, Xiao-Gang Wen

I clicked on the above link and got a warning from Google Chrome.

upload_2018-9-9_22-32-22.png


The paper above is also at, https://arxiv.org/abs/1807.05998

which Google tells me is a safe connection.
 

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  • #388
https://arxiv.org/abs/1902.10157
Holographic Tensor Networks in Full AdS/CFT
Ning Bao, Geoffrey Penington, Jonathan Sorce, Aron C. Wall
(Submitted on 26 Feb 2019)
We present a general procedure for constructing tensor networks for geometric states in the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. Given a state in a large-N CFT with a static, semiclassical gravitational dual, our procedure produces a tensor network for the boundary state whose internal geometry matches (a discretization of) the bulk spacetime geometry. By invoking the "holographic entanglement of purification" conjecture, our construction can be made to capture the structure of the bulk spacetime at sub-AdS scales.
 
  • #389
https://arxiv.org/abs/1905.08255Entanglement Wedge Reconstruction and the Information Paradox
Geoffrey Penington
When absorbing boundary conditions are used to evaporate a black hole in AdS/CFT, we show that there is a phase transition in the location of the quantum Ryu-Takayanagi surface, at precisely the Page time. The new RT surface lies slightly inside the event horizon, at an infalling time approximately the scrambling time β/2πlogSBH into the past. We can immediately derive the Page curve, using the Ryu-Takayanagi formula, and the Hayden-Preskill decoding criterion, using entanglement wedge reconstruction. Because part of the interior is now encoded in the early Hawking radiation, the decreasing entanglement entropy of the black hole is exactly consistent with the semiclassical bulk entanglement of the late-time Hawking modes, despite the absence of a firewall.
By studying the entanglement wedge of highly mixed states, we can understand the state dependence of the interior reconstructions. A crucial role is played by the existence of tiny, non-perturbative errors in entanglement wedge reconstruction. Directly after the Page time, interior operators can only be reconstructed from the Hawking radiation if the initial state of the black hole is known. As the black hole continues to evaporate, reconstructions become possible that simultaneously work for a large class of initial states. Using similar techniques, we generalise Hayden-Preskill to show how the amount of Hawking radiation required to reconstruct a large diary, thrown into the black hole, depends on both the energy and the entropy of the diary. Finally we argue that, before the evaporation begins, a single, state-independent interior reconstruction exists for any code space of microstates with entropy strictly less than the Bekenstein-Hawking entropy, and show that this is sufficient state dependence to avoid the AMPSS typical-state firewall paradox.
 
<H2>1. What is condensed matter physics?</H2><p>Condensed matter physics is a branch of physics that studies the physical properties of materials in their solid or liquid form. It deals with the behavior of large numbers of particles, such as atoms or molecules, and how they interact with each other to create different states of matter.</p><H2>2. What are area laws in condensed matter physics?</H2><p>Area laws in condensed matter physics refer to the mathematical relationships between the size and shape of a material and its physical properties. These laws help us understand how the arrangement of particles in a material affects its behavior and properties.</p><H2>3. What is LQG in condensed matter physics?</H2><p>LQG, or loop quantum gravity, is a theoretical framework that attempts to reconcile the principles of quantum mechanics with those of general relativity. It has applications in condensed matter physics as it can help us understand the behavior of materials at the smallest scales, such as the atomic and subatomic levels.</p><H2>4. How do area laws and LQG relate to each other?</H2><p>Area laws and LQG are closely related as both deal with understanding the structure and behavior of materials at the smallest scales. LQG provides a theoretical framework for understanding the fundamental building blocks of matter, while area laws help us understand how these building blocks interact and give rise to the properties of different materials.</p><H2>5. What are some real-world applications of condensed matter physics, area laws, and LQG?</H2><p>Condensed matter physics, area laws, and LQG have numerous real-world applications, including the development of new materials for use in technology and medicine, the creation of more efficient energy storage and conversion systems, and the study of exotic states of matter such as superconductors and superfluids. They also have implications in fields such as cosmology and astrophysics, where understanding the fundamental properties of matter is crucial in explaining the behavior of the universe.</p>

1. What is condensed matter physics?

Condensed matter physics is a branch of physics that studies the physical properties of materials in their solid or liquid form. It deals with the behavior of large numbers of particles, such as atoms or molecules, and how they interact with each other to create different states of matter.

2. What are area laws in condensed matter physics?

Area laws in condensed matter physics refer to the mathematical relationships between the size and shape of a material and its physical properties. These laws help us understand how the arrangement of particles in a material affects its behavior and properties.

3. What is LQG in condensed matter physics?

LQG, or loop quantum gravity, is a theoretical framework that attempts to reconcile the principles of quantum mechanics with those of general relativity. It has applications in condensed matter physics as it can help us understand the behavior of materials at the smallest scales, such as the atomic and subatomic levels.

4. How do area laws and LQG relate to each other?

Area laws and LQG are closely related as both deal with understanding the structure and behavior of materials at the smallest scales. LQG provides a theoretical framework for understanding the fundamental building blocks of matter, while area laws help us understand how these building blocks interact and give rise to the properties of different materials.

5. What are some real-world applications of condensed matter physics, area laws, and LQG?

Condensed matter physics, area laws, and LQG have numerous real-world applications, including the development of new materials for use in technology and medicine, the creation of more efficient energy storage and conversion systems, and the study of exotic states of matter such as superconductors and superfluids. They also have implications in fields such as cosmology and astrophysics, where understanding the fundamental properties of matter is crucial in explaining the behavior of the universe.

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