scholarly journals Algebraic QFT and the area law for entropy of localized quantum matter

2007 ◽  
Author(s):  
Bert Schroer
Keyword(s):  
Quantum Matter ◽  
Algebraic Qft ◽  
Area Law

scholarly journals Supercritical entanglement in local systems: Counterexample to the area law for quantum matter

2016 ◽  
Vol 113 (47) ◽  
pp. 13278-13282 ◽  
Author(s):  
Ramis Movassagh ◽  
Peter W. Shor
Keyword(s):  
Physical Models ◽  
Matching Theory ◽  
Many Body ◽  
Quantum Matter ◽  
Condensed Matter Theory ◽  
Simple Quantum ◽  
Matter Theory ◽  
Many Body Systems ◽  
Classical Computer ◽  
Area Law

Quantum entanglement is the most surprising feature of quantum mechanics. Entanglement is simultaneously responsible for the difficulty of simulating quantum matter on a classical computer and the exponential speedups afforded by quantum computers. Ground states of quantum many-body systems typically satisfy an “area law”: The amount of entanglement between a subsystem and the rest of the system is proportional to the area of the boundary. A system that obeys an area law has less entanglement and can be simulated more efficiently than a generic quantum state whose entanglement could be proportional to the total system’s size. Moreover, an area law provides useful information about the low-energy physics of the system. It is widely believed that for physically reasonable quantum systems, the area law cannot be violated by more than a logarithmic factor in the system’s size. We introduce a class of exactly solvable one-dimensional physical models which we can prove have exponentially more entanglement than suggested by the area law, and violate the area law by a square-root factor. This work suggests that simple quantum matter is richer and can provide much more quantum resources (i.e., entanglement) than expected. In addition to using recent advances in quantum information and condensed matter theory, we have drawn upon various branches of mathematics such as combinatorics of random walks, Brownian excursions, and fractional matching theory. We hope that the techniques developed herein may be useful for other problems in physics as well.

NEW PHASES OF QUANTUM MATTER AND TOPOLOGY

2016 ◽  
pp. 63-73
Author(s):  
I.V. Krive ◽  
◽  
S.I. Shevchenko ◽  
Keyword(s):  
Quantum Matter ◽  
And Topology

scholarly journals Weyl, Dirac and high-fold chiral fermions in topological quantum matter

2021 ◽  
Author(s):  
M. Zahid Hasan ◽  
Guoqing Chang ◽  
Ilya Belopolski ◽  
Guang Bian ◽  
Su-Yang Xu ◽  
...  
Keyword(s):  
Quantum Matter ◽  
Topological Quantum

scholarly journals Improved Thermal Area Law and Quasilinear Time Algorithm for Quantum Gibbs States

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tomotaka Kuwahara ◽  
Álvaro M. Alhambra ◽  
Anurag Anshu
Keyword(s):  
Time Algorithm ◽  
Gibbs States ◽  
Area Law

scholarly journals Target space entanglement in quantum mechanics of fermions and matrices

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Sotaro Sugishita
Keyword(s):  
Mutual Information ◽  
Ground State ◽  
Entanglement Entropy ◽  
Algebraic Approach ◽  
Upper Bounds ◽  
Wave Functions ◽  
Target Space ◽  
Single Interval ◽  
Area Law ◽  
Formula Expression

Abstract We consider entanglement of first-quantized identical particles by adopting an algebraic approach. In particular, we investigate fermions whose wave functions are given by the Slater determinants, as for singlet sectors of one-matrix models. We show that the upper bounds of the general Rényi entropies are N log 2 for N particles or an N × N matrix. We compute the target space entanglement entropy and the mutual information in a free one-matrix model. We confirm the area law: the single-interval entropy for the ground state scales as $$ \frac{1}{3} $$ 1 3 log N in the large N model. We obtain an analytical $$ \mathcal{O}\left({N}^0\right) $$ O N 0 expression of the mutual information for two intervals in the large N expansion.

scholarly journals Refinement of the Bousso-Engelhardt area law

2016 ◽  
Vol 94 (2) ◽  
Author(s):  
Fabio Sanches ◽  
Sean J. Weinberg
Keyword(s):  
Area Law
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