scholarly journals Stability of the Enhanced Area Law of the Entanglement Entropy

2020 ◽  
Vol 21 (11) ◽  
pp. 3639-3658
Author(s):  
Peter Müller ◽  
Ruth Schulte
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Ground State ◽  
Entanglement Entropy ◽  
Fermi Gas ◽  
Central Idea ◽  
Bipartite Entanglement ◽  
Free Fermi ◽  
Negative Laplacian ◽  
Area Law

Abstract We consider a multi-dimensional continuum Schrödinger operator which is given by a perturbation of the negative Laplacian by a compactly supported potential. We establish both an upper bound and a lower bound on the bipartite entanglement entropy of the ground state of the corresponding quasi-free Fermi gas. The bounds prove that the scaling behaviour of the entanglement entropy remains a logarithmically enhanced area law as in the unperturbed case of the free Fermi gas. The central idea for the upper bound is to use a limiting absorption principle for such kinds of Schrödinger operators.

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.

Energy bounds for the spiked harmonic oscillator

1995 ◽  
Vol 73 (7-8) ◽  
pp. 493-496 ◽  
Author(s):  
Richard L. Hall ◽  
Nasser Saad
Keyword(s):  
Lower Bound ◽  
Harmonic Oscillator ◽  
Ground State Energy ◽  
Upper Bound ◽  
Ground State ◽  
Trial Function ◽  
State Energy ◽  
Parameter Range ◽  
Complementary Energy ◽  
Energy Bounds

A three-parameter variational trial function is used to determine an upper bound to the ground-state energy of the spiked harmonic-oscillator Hamiltonian [Formula: see text]. The entire parameter range λ > 0 and α ≥ 1 is treated in a single elementary formulation. The method of potential envelopes is also employed to derive a complementary energy lower bound formula valid for all the discrete eigenvalues.

scholarly journals Power law corrections to BTZ black hole entropy

2014 ◽  
Vol 24 (01) ◽  
pp. 1550001 ◽  
Author(s):  
Dharm Veer Singh
Keyword(s):  
Black Hole ◽  
Excited State ◽  
Power Law ◽  
Ground State ◽  
Entanglement Entropy ◽  
Black Hole Entropy ◽  
Mixed States ◽  
Btz Black Hole ◽  
First Excited State ◽  
Area Law

We study the quantum scalar field in the background of BTZ black hole and evaluate the entanglement entropy of the nonvacuum states. The entropy is proportional to the area of event horizon for the ground state, but the area law is violated in the case of nonvacuum states (first excited state and mixed states) and the corrections scale as power law.

scholarly journals Edge States and Entanglement Entropy

1997 ◽  
Vol 12 (03) ◽  
pp. 625-641 ◽  
Author(s):  
A. P. Balachandran ◽  
Arshad Momen ◽  
L. Chandar
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Ground State ◽  
Entanglement Entropy ◽  
Quantum Hall ◽  
Coarse Graining ◽  
Gauge Fields ◽  
Edge States ◽  
Area Law

It is known that gauge fields defined on manifolds with spatial boundaries support states localized at the boundaries. In this paper, we demonstrate how coarse-graining over these states can lead to an entanglement entropy. In particular, we show that the entanglement entropy of the ground state for the quantum Hall effect on a disk exhibits an approximate "area" law.

scholarly journals TOPOLOGICAL ENTANGLEMENT ENTROPY IN THE SECOND LANDAU LEVEL

2010 ◽  
Vol 24 (24) ◽  
pp. 4707-4715 ◽  
Author(s):  
B. A. FRIEDMAN ◽  
G. C. LEVINE
Keyword(s):  
Landau Level ◽  
Coulomb Potential ◽  
Ground State ◽  
Entanglement Entropy ◽  
Finite Thickness ◽  
Quantum Hall ◽  
Topological Order ◽  
Quantum Hall System ◽  
Topological Entanglement Entropy ◽  
Area Law

The entanglement entropy of the incompressible states of a realistic quantum Hall system in the second Landau level is studied by direct diagonalization. The subdominant term of the area law, the topological entanglement entropy, which is believed to carry information about topological order in the ground state, was extracted for filling factors ν = 12/5 and ν = 7/3. While it is difficult to make strong conclusions about ν = 12/5, the ν = 7/3 state appears to be very consistent with the topological entanglement entropy for the k = 4 Read–Rezayi state. The effect of finite thickness corrections to the Coulomb potential used in the direct diagonalization is also systematically studied.

scholarly journals Entropy Area Law in Quantum Field Theories and Spin Systems

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 5
Author(s):  
Salvatore Mancani
Keyword(s):  
Shannon Entropy ◽  
Ground State ◽  
Entanglement Entropy ◽  
Quantum Correlations ◽  
Spatial Dimension ◽  
Quantum Field Theories ◽  
Adiabatic Evolution ◽  
Xxz Model ◽  
Conformally Invariant ◽  
Area Law

The entanglement entropy measures quantum correlations and it can be seen as the uncertainty on a quantum state. In one spatial dimension, the entanglement entropy scales as the boundary that divides two subsystems, so an area law has been proposed. However, the entanglement entropy diverges logarithmically at conformally invariant critical points, so the area law does not hold. The purpose of the work is to find a way to get more information about a critical state. The ground state of the Heisenberg XXZ model at criticality is analyzed by means of critical Ising eigenstates. Two ways of analysis are followed: a basis made of Ising eigenstates is built up and used to represent the XXZ ground state, then the Shannon entropy in the new basis is computed; the adiabatic evolution from the Ising ground state to the XXZ ground state. The result is that the Shannon entropy in the Ising basis scales linearly with the length of the system, while a phase transition is encountered during the adiabatic evolution. The conclusion is that there is no net gain in information after the procedure and possibly it is related to the fact the two systems stand in different phases.

Ground-State Properties of Superfluid Fermi Gas in Fourier-Synthesized Optical Lattices

2014 ◽  
Vol 31 (3) ◽  
pp. 030301 ◽  
Author(s):  
Yan Chen ◽  
Ke-Zhi Zhang ◽  
Xiao-Liang Wang ◽  
Yong Chen
Keyword(s):  
Ground State ◽  
Optical Lattices ◽  
Fermi Gas ◽  
Superfluid Fermi Gas ◽  
Ground State Properties ◽  
Superfluid Fermi
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