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.

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 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 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 Entanglement entropy: non-Gaussian states and strong coupling

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
José J. Fernández-Melgarejo ◽  
Javier Molina-Vilaplana
Keyword(s):  
Ground State ◽  
Entanglement Entropy ◽  
Energy Functional ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Gaussian States ◽  
Strong Subadditivity ◽  
Point Correlation ◽  
Non Gaussian

Abstract In this work we provide a method to study the entanglement entropy for non-Gaussian states that minimize the energy functional of interacting quantum field theories at arbitrary coupling. To this end, we build a class of non-Gaussian variational trial wavefunctionals with the help of exact nonlinear canonical transformations. The calculability bonanza shown by these variational ansatze allows us to compute the entanglement entropy using the prescription for the ground state of free theories. In free theories, the entanglement entropy is determined by the two-point correlation functions. For the interacting case, we show that these two-point correlators can be replaced by their nonperturbatively corrected counterparts. Upon giving some general formulae for general interacting models we calculate the entanglement entropy of half space and compact regions for the ϕ4 scalar field theory in 2D. Finally, we analyze the rôle played by higher order correlators in our results and show that strong subadditivity is satisfied.

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.

Thermodynamics of $T \Tbar$ perturbations of some single particle field theories

2021 ◽  
Author(s):  
Andre LeClair
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Chemical Potential ◽  
Central Charge ◽  
Liouville Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Conformally Invariant ◽  
Massless Boson

Abstract We study the Thermodynamic Bethe Ansatz (TBA) equations for pure $T\Tbar$ perturbations of some simple integrable quantum field theories with a single bosonic or fermionic particle, in particular the massive sinh-Gordon model and its ultraviolet (UV) limit which is a deformation of the conformally invariant free massless boson. Whereas the TBA equations for $T\Tbar$ deformations of massive theories are in principle known, the TBA equations we propose for the deformations of conformal field theories (CFT's) are relatively new and require a special factorization in rapidity variables of the CDD factor for the scattering of the massless particles. The latter TBA equations can be solved exactly and reproduce the known results for the ground state energy on a cylinder of circumference $R$ which were previously obtained using different methods based for instance on the Burgers differential equation. Special attention is paid to the c-theorem in this context which is discussed in some detail. For positive infra-red (IR) central charge $c_{IR}$, for flows consistent with the c-theorem the ground state energy develops a (previously known) square-root singularity towards the UV, which strongly suggests the theories are UV incomplete in these physically important cases. We suggest that the singularity indicates a tachyonic vacuum instability. Other cases with $c_{IR} < 0$ do not have this singularity are interpreted as being UV complete with $c_{UV} = 0$. We extend our results to a continuously variable $c_{IR}$ by introducing a chemical potential and suggest this as a possible toy model for the $T\Tbar$ perturbed Liouville theory.

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 Entanglement time in the primordial universe

2015 ◽  
Vol 24 (12) ◽  
pp. 1544006 ◽  
Author(s):  
Eugenio Bianchi ◽  
Lucas Hackl ◽  
N. Yokomizo
Keyword(s):  
Quantum Gravity ◽  
Entanglement Entropy ◽  
Quantum Correlations ◽  
Arrow Of Time ◽  
Cosmological Singularity ◽  
Cosmic Inflation ◽  
Inflationary Phase ◽  
Quantum Version ◽  
The Universe ◽  
Area Law

We investigate the behavior of the entanglement entropy of space in the primordial phase of the universe before the beginning of the cosmic inflation. We argue that in this phase the entanglement entropy of a region of space grows from a zero-law to an area-law. This behavior provides a quantum version of the classical Belinsky–Khalatnikov–Lifshitz (BKL) conjecture that spatially separated points decouple in the approach to a cosmological singularity. We show that the relational growth of the entanglement entropy with the scale factor provides a new statistical notion of arrow of time in quantum gravity. The growth of entanglement in the pre-inflationary phase provides a mechanism for the production of the quantum correlations present at the beginning of inflation and imprinted in the CMB sky.

Ground-state fidelity and entanglement entropy for the quantum three-state Potts model in one spatial dimension

2010 ◽  
Vol 43 (37) ◽  
pp. 372001 ◽  
Author(s):  
Yan-Wei Dai ◽  
Bing-Quan Hu ◽  
Jian-Hui Zhao ◽  
Huan-Qiang Zhou
Keyword(s):  
Potts Model ◽  
Ground State ◽  
Entanglement Entropy ◽  
Spatial Dimension

scholarly journals Spread of Entanglement in Non-Relativistic Theories

2018 ◽  
Vol 2018 ◽  
pp. 1-27
Author(s):  
Sagar F. Lokhande
Keyword(s):  
Broad Class ◽  
Entanglement Entropy ◽  
Time Dependent ◽  
Quantum Field Theories ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Instantaneous Power ◽  
Holographic Entanglement Entropy ◽  
Quantum Quenches ◽  
Good Order

We use a simple holographic toy model to study global quantum quenches in strongly coupled, hyperscaling-violating-Lifshitz quantum field theories using entanglement entropy as a probe. Generalizing our conformal field theory results, we show that the holographic entanglement entropy of small subsystems can be written as a simple linear response relation. We use this relation to derive a time-dependent first law of entanglement entropy. In general, this law has a time-dependent term resembling relative entropy which we propose as a good order parameter to characterize out-of-equilibrium states in the post-quench evolution. We use these tools to study a broad class of quantum quenches in detail: instantaneous, power law, and periodic.

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