scholarly journals Entanglement entropy from charge statistics: Exact relations for noninteracting many-body systems

2011 ◽  
Vol 83 (16) ◽  
Author(s):  
H. Francis Song ◽  
Christian Flindt ◽  
Stephan Rachel ◽  
Israel Klich ◽  
Karyn Le Hur
Keyword(s):  
Entanglement Entropy ◽  
Many Body ◽  
Many Body Systems ◽  
Exact Relations

scholarly journals Probing phase transitions of holographic entanglement entropy with fixed area states

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Donald Marolf ◽  
Shannon Wang ◽  
Zhencheng Wang
Keyword(s):  
Phase Transitions ◽  
Entanglement Entropy ◽  
Many Body ◽  
Btz Black Hole ◽  
Holographic Entanglement Entropy ◽  
Volume Limit ◽  
Cutoff Dependence ◽  
Diagonal Approximation ◽  
Fixed Area ◽  
Many Body Systems

Abstract Recent results suggest that new corrections to holographic entanglement entropy should arise near phase transitions of the associated Ryu-Takayanagi (RT) surface. We study such corrections by decomposing the bulk state into fixed-area states and conjecturing that a certain ‘diagonal approximation’ will hold. In terms of the bulk Newton constant G, this yields a correction of order O(G−1/2) near such transitions, which is in particular larger than generic corrections from the entanglement of bulk quantum fields. However, the correction becomes exponentially suppressed away from the transition. The net effect is to make the entanglement a smooth function of all parameters, turning the RT ‘phase transition’ into a crossover already at this level of analysis.We illustrate this effect with explicit calculations (again assuming our diagonal approximation) for boundary regions given by a pair of disconnected intervals on the boundary of the AdS3 vacuum and for a single interval on the boundary of the BTZ black hole. In a natural large-volume limit where our diagonal approximation clearly holds, this second example verifies that our results agree with general predictions made by Murthy and Srednicki in the context of chaotic many-body systems. As a further check on our conjectured diagonal approximation, we show that it also reproduces the O(G−1/2) correction found Penington et al. for an analogous quantum RT transition. Our explicit computations also illustrate the cutoff-dependence of fluctuations in RT-areas.

scholarly journals Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain

Universe ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 33 ◽  
Author(s):  
Liron Levy ◽  
Moshe Goldstein
Keyword(s):  
Phase Diagram ◽  
Information Theory ◽  
Quantum Information ◽  
Critical Point ◽  
Entanglement Entropy ◽  
Quantum Information Theory ◽  
Topological Phase ◽  
Many Body ◽  
Zero Modes ◽  
Many Body Systems

In recent years, tools from quantum information theory have become indispensable in characterizing many-body systems. In this work, we employ measures of entanglement to study the interplay between disorder and the topological phase in 1D systems of the Kitaev type, which can host Majorana end modes at their edges. We find that the entanglement entropy may actually increase as a result of disorder, and identify the origin of this behavior in the appearance of an infinite-disorder critical point. We also employ the entanglement spectrum to accurately determine the phase diagram of the system, and find that disorder may enhance the topological phase, and lead to the appearance of Majorana zero modes in systems whose clean version is trivial.

scholarly journals REDUCED DENSITY MATRIX AND ENTANGLEMENT ENTROPY OF PERMUTATIONALLY INVARIANT QUANTUM MANY-BODY SYSTEMS

2012 ◽  
Vol 26 (27n28) ◽  
pp. 1243009 ◽  
Author(s):  
VLADISLAV POPKOV ◽  
MARIO SALERNO
Keyword(s):  
Density Matrix ◽  
Entanglement Entropy ◽  
Reduced Density Matrix ◽  
Diagonal Form ◽  
Temperature Phase ◽  
Many Body ◽  
Permutational Symmetry ◽  
Von Neumann ◽  
Many Body Systems ◽  
Reduced Density

In this paper we discuss the properties of the reduced density matrix of quantum many body systems with permutational symmetry and present basic quantification of the entanglement in terms of the von Neumann (VNE), Renyi and Tsallis entropies. In particular, we show, on the specific example of the spin 1/2 Heisenberg model, how the RDM acquires a block diagonal form with respect to the quantum number k fixing the polarization in the subsystem conservation of Sz and with respect to the irreducible representations of the Sn group. Analytical expression for the RDM elements and for the RDM spectrum are derived for states of arbitrary permutational symmetry and for arbitrary polarizations. The temperature dependence and scaling of the VNE across a finite temperature phase transition is discussed and the RDM moments and the Rényi and Tsallis entropies calculated both for symmetric ground states of the Heisenberg chain and for maximally mixed states.

scholarly journals Extensive Entropy from Unitary Evolution

2021 ◽  
Author(s):  
Yichen Huang
Keyword(s):  
Entanglement Entropy ◽  
Product State ◽  
Many Body ◽  
Unitary Evolution ◽  
Almost Everywhere ◽  
Random Product ◽  
Many Body Systems

In quantum many-body systems, a Hamiltonian is called an ``extensive entropy generator'' if starting from a random product state the entanglement entropy obeys a volume law at long times with overwhelming probability. We prove that (i) any Hamiltonian whose spectrum has non-degenerate gaps is an extensive entropy generator; (ii) in the space of (geometrically) local Hamiltonians, the non-degenerate gap condition is satisfied almost everywhere. Specializing to many-body localized systems, these results imply the observation stated in the title of Bardarson et al. [PRL 109, 017202 (2012)].

scholarly journals Coexistence of Different Scaling Laws for the Entanglement Entropy in a Periodically Driven System

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 6
Author(s):  
Tony J. G. Apollaro ◽  
Salvatore Lorenzo
Keyword(s):  
Ground State ◽  
Scaling Laws ◽  
Entanglement Entropy ◽  
Finite Size ◽  
Simultaneous Occurrence ◽  
Many Body ◽  
Periodically Driven ◽  
Quantum Ising Model ◽  
Long Time ◽  
Many Body Systems

The out-of-equilibrium dynamics of many body systems has recently received a burst of interest, also due to experimental implementations. The dynamics of observables, such as magnetization and susceptibilities, and quantum information related quantities, such as concurrence and entanglement entropy, have been investigated under different protocols bringing the system out of equilibrium. In this paper we focus on the entanglement entropy dynamics under a sinusoidal drive of the tranverse magnetic field in the 1D quantum Ising model. We find that the area and the volume law of the entanglement entropy coexist under periodic drive for an initial non-critical ground state. Furthermore, starting from a critical ground state, the entanglement entropy exhibits finite size scaling even under such a periodic drive. This critical-like behaviour of the out-of-equilibrium driven state can persist for arbitrarily long time, provided that the entanglement entropy is evaluated on increasingly subsytem sizes, whereas for smaller sizes a volume law holds. Finally, we give an interpretation of the simultaneous occurrence of critical and non-critical behaviour in terms of the propagation of Floquet quasi-particles.

scholarly journals Coexistence of Different Scaling Laws for the Entanglement Entropy in a Periodically Driven System

2018 ◽  
Author(s):  
Tony J. G. Apollaro ◽  
Salvatore Lorenzo
Keyword(s):  
Ground State ◽  
Scaling Laws ◽  
Entanglement Entropy ◽  
Finite Size ◽  
Simultaneous Occurrence ◽  
Many Body ◽  
Periodically Driven ◽  
Quantum Ising Model ◽  
Long Time ◽  
Many Body Systems

The out-of-equilibrium dynamics of many body systems has recently received a burst of interest, also due to experimental implementations. The dynamics of both observables, such as magnetization and susceptibilities, and quantum information related quantities, such as concurrence and entanglement entropy, have been investigated under different protocols bringing the system out of equilibrium. In this paper we focus on the entanglement entropy dynamics under a sinusoidal drive of the tranverse magnetic field in the 1D quantum Ising model. We find that the area and the volume law of the entanglement entropy coexist under periodic drive for an initial non-critical ground state. Furthermore, starting from a critical ground state, the entanglement entropy exhibits finite size scaling even under such a periodic drive. This critical-like behaviour of the out-of-equilibrium driven state can persist for arbitrarily long time, provided that the entanglement entropy is evaluated on increasingly subsytem sizes, whereas for smaller sizes a volume law holds. Finally, we give an interpretation of the simultaneous occurrence of critical and non-critical behaviour in terms of the propagation of Floquet quasi-particles.

scholarly journals Rényi entropy of highly entangled spin chains

2018 ◽  
Vol 32 (28) ◽  
pp. 1850306 ◽  
Author(s):  
Fumihiko Sugino ◽  
Vladimir Korepin
Keyword(s):  
Spin Chain ◽  
Information Science ◽  
Entanglement Entropy ◽  
Two Dimensions ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Many Body ◽  
Local Interactions ◽  
Many Body Systems ◽  
Area Law

Entanglement is one of the most intriguing features of quantum theory and a main resource in quantum information science. Ground states of quantum many-body systems with local interactions typically obey an “area law” which means that the entanglement entropy is proportional to the boundary length. It is exceptional when the system is gapless, and the area law had been believed to be violated by at most a logarithm over two decades. Recent discovery of Motzkin and Fredkin spin chain models is striking, since these models provide significant violation of the entanglement beyond the belief, growing as a square root of the volume in spite of local interactions. In this paper, we first analytically compute the Rényi entropy of the Motzkin and Fredkin models by careful treatment of asymptotic analysis. The Rényi entropy is an important quantity, since the whole spectrum of an entangled subsystem is reconstructed once the Rényi entropy is known as a function of its parameter. We find nonanalytic behavior of the Rényi entropy with respect to the parameter, which is a novel phase transition never seen in any other spin chain studied so far. Interestingly, similar behavior is seen in the Rényi entropy of Rokhsar–Kivelson states in two dimensions.

REGULAR STRUCTURE OF LOW-LYING STATES FOR ATOMIC NUCLEI UNDER RANDOM INTERACTIONS

2008 ◽  
Vol 17 (supp01) ◽  
pp. 304-317
Author(s):  
Y. M. ZHAO
Keyword(s):  
Ground State ◽  
Collective Motion ◽  
Regular Structure ◽  
Positive Parity ◽  
Many Body ◽  
Random Interactions ◽  
Atomic Nuclei ◽  
Many Body Systems

In this paper we review regularities of low-lying states for many-body systems, in particular, atomic nuclei, under random interactions. We shall discuss the famous problem of spin zero ground state dominance, positive parity dominance, collective motion, odd-even staggering, average energies, etc., in the presence of random interactions.

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