Entanglement entropy for singular surfaces

Myers, Robert C.; Singh, Ajay Pratap

doi:10.1007/jhep09(2012)013

Cited by 74 publications

(141 citation statements)

References 80 publications

(166 reference statements)

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“…In addition to non-universal, sub-leading terms, different parts of the entanglement may be universal for different critical points; identifying an appropriate scaling form is not straightforward. For example, in onedimensional conformal field theories one needs to consider ∂S/∂ log x in the limit x, L 1 [56,57]. By performing scaling collapses of S(x, L) for fixed x/L and various W [45], we find evidence that the volume law coefficient is a universal scaling function…”

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confidence: 99%

Scaling Theory of Entanglement at the Many-Body Localization Transition

2017

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We study the universal properties of eigenstate entanglement entropy across the transition between many-body localized (MBL) and thermal phases. We develop an improved real space renormalization group approach that enables numerical simulation of large system sizes and systematic extrapolation to the infinite system size limit. For systems smaller than the correlation length, the average entanglement follows a sub-thermal volume law, whose coefficient is a universal scaling function. The full distribution of entanglement follows a universal scaling form, and exhibits a bimodal structure that produces universal subleading power-law corrections to the leading volume-law. For systems larger than the correlation length, the short interval entanglement exhibits a discontinuous jump at the transition from fully thermal volume-law on the thermal side, to pure area-law on the MBL side.Recent experimental advances in synthesizing isolated quantum many-body systems, such as cold-atoms [1][2][3][4], trapped ions [5,6], or impurity spins in solids [7,8], have raised fundamental questions about the nature of statistical mechanics. Even when decoupled from external sources of dissipation, large interacting quantum systems tend to act as their own heat-baths and reach thermal equilibrium. This behavior is formalized in the eigenstate thermalization hypothesis (ETH) [9,10]. Generic excited eigenstates of such thermal systems are highly entangled, with the entanglement of a subregion scaling as the volume of that region ("volume law"). This results in incoherent, classical dynamics at long times. In contrast, strong disorder can dramatically alter this picture by pinning excitations that would otherwise propagate heat and entanglement [11][12][13][14][15][16][17]. In such many-body localized (MBL) systems [18][19][20], generic eigenstates have properties akin to those of ground states. They exhibit short-range entanglement that scales like the perimeter of the subregion [17] ("area law"), and have quantum coherent dynamics up to arbitrarily long time scales [21][22][23][24][25][26][27], even at high energy densities [17,26,[28][29][30][31].A transition between MBL and thermal regimes requires a singular rearrangement of eigenstates from area-law to volume-law entanglement. This many-body (de)localization transition (MBLT) represents an entirely new class of critical phenomena, outside the conventional framework of equilibrium thermal or quantum phase transitions. Developing a systematic theory of this transition promises not only to expand our understanding of possible critical phenomena, but also to yield universal insights into the nature of the proximate MBL and thermal phases.The eigenstate entanglement entropy can be viewed as a non-equilibrium analog of the thermodynamic free energy for a conventional thermal phase transition, and plays a central role in our conceptual understanding of the MBL and ETH phases. Describing the entanglement across the MBLT requires addressing the challenging combination of disorder, interactio...

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confidence: 99%

Scaling Theory of Entanglement at the Many-Body Localization Transition

2017

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“…For example, consider a three-dimensional CFT with the entangling region containing a single opening angle Ω, the corresponding EE is given by [13] 4) where the coefficient of the new logarithmic term a is a function of the opening angle a = a(Ω). Generalisations to higher-dimensional singular surfaces were extensively investigated in [14], where it was observed that more universal terms emerge as spacetime dimension increases. Recently the authors of [15,16] considered the universal corner contributions in 2 + 1-dimensional CFTs in the presence of finite N corrections as new measures of the degrees of freedom and compared those contributions with other physical quantities.…”

Section: Jhep09(2015)133mentioning

confidence: 99%

“…Note that since the metric is conformal to AdS and the boundary is flat, it is still appropriate to parameterise z = ρh(θ) as in [14]. As a result, the equation of motion (3.4) becomes…”

Section: Corner Contributions For D2-branesmentioning

confidence: 99%

“…After some algebra we arrive at the divergent part from I 1 14) as well as the divergent terms from I 2 ,…”

Section: Jhep09(2015)133mentioning

confidence: 99%

“…The second quantity is the universal contribution to the HEE of a sphere with the following induced metric 13) JHEP09 (2015)133 where ρ ∈ [0, H] and ρ(0) = H. The HEE is given by 14) which leads to the following equation of motion…”

Section: Comparison With Other Quantitiesmentioning

confidence: 99%

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Corner contributions to holographic entanglement entropy in non-conformal backgrounds

Pang

2015

J. High Energ. Phys.

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We study corner contributions to holographic entanglement entropy in nonconformal backgrounds: a kink for D2-branes as well as a cone and two different types of crease for D4-branes. Unlike 2 + 1-dimensional CFTs, the corner contribution to the holographic entanglement entropy of D2-branes exhibits a power law behaviour rather than a logarithmic term. However, the logarithmic term emerges in the holographic entanglement entropy of D4-branes. We identify the logarithmic term for a cone in D4-brane background as the universal contribution under appropriate limits and compare it with other physical quantities.

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Universal entanglement of singular surfaces

Bueno

Myers

Witczak-Krempa

2015

Fortschritte der Physik

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In general three-dimensional conformal field theories (CFTs), the entanglement entropy receives a logarithmic contribution whenever the entangling surface contains a sharp corner of opening angle θ . Such contribution is controlled by a regulatorindependent function a(θ ) which vanishes as a(θ ) = σ (θ − π) 2 in the smooth-surface limit (θ → π). We review our recent conjecture that for general three-dimensional CFTs, this corner coefficient σ is determined by C T , the coefficient appearing in the two-point function of the stress tensor through the relation σ/C T = π 2 /24. We also comment on the extension of this conjecture to general Rényi entropies and higherdimensional CFTs.

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Entanglement entropy for singular surfaces

Cited by 74 publications

References 80 publications

Scaling Theory of Entanglement at the Many-Body Localization Transition

Scaling Theory of Entanglement at the Many-Body Localization Transition

Corner contributions to holographic entanglement entropy in non-conformal backgrounds

Universal entanglement of singular surfaces

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