[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Journal of Statistical Mechanics: theory and experiment

We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the ``half-way'' point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.

http://absimage.aps.org/image/MAR08/MWS_MAR08-2007-003180.pdf

Black holes as mirrors: quantum information in random subsystems

The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. This constitutes the topological bulk-boundary correspondence. Here, we establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk-boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principle calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunneling spectroscopy, we probe the unique signatures of the rotational symmetry of the one-dimensional states located at step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator.

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Higher-Order Topology in Bismuth

A review is given on the foundations and applications of non-Hermitian classical and quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra, including Jordan normal form, biorthogonality, exceptional points, pseudo-Hermiticity and parity-time symmetry, are delineated in a pedagogical and mathematically coherent manner. Building on these, we provide an overview of how diverse classical systems, ranging from photonics, mechanics, electrical circuits, acoustics to active matter, can be used to simulate non-Hermitian wave physics. In particular, we discuss rich and unique phenomena found therein, such as unidirectional invisibility, enhanced sensitivity, topological energy transfer, coherent perfect absorption, single-mode lasing, and robust biological transport. We then explain in detail how non-Hermitian operators emerge as an effective description of open quantum systems on the basis of the Feshbach projection approach and the quantum trajectory approach. We discuss their applications to physical systems relevant to a variety of fields, including atomic, molecular and optical physics, mesoscopic physics, and nuclear physics with emphasis on prominent phenomena/subjects in quantum regimes, such as quantum resonances, superradiance, continuous quantum Zeno effect, quantum critical phenomena, Dirac spectra in quantum chromodynamics, and nonunitary conformal field theories. Finally, we introduce the notion of band topology in complex spectra of non-Hermitian systems and present their classifications by providing the proof, firstly given by this review in a complete manner, as well as a number of instructive examples. Other topics related to non-Hermitian physics, including nonreciprocal transport, speed limits, nonunitary quantum walk, are also reviewed.

Non-Hermitian Physics

We calculate logarithmic negativity, a quantum entanglement measure for mixed quantum states, in quantum error-correcting codes and find it to equal the minimal cross sectional area of the entanglement wedge in holographic codes with a quantum correction term equal to the logarithmic negativity between the bulk degrees of freedom on either side of the entanglement wedge cross section. This leads us to conjecture a holographic dual for logarithmic negativity that is related to the area of a cosmic brane with tension in the entanglement wedge plus a quantum correction term. This is closely related to (though distinct from) the holographic proposal for entanglement of purification. We check this relation for various configurations of subregions in ${\mathrm{AdS}}_{3}/{\mathrm{CFT}}_{2}$. These are disjoint intervals at zero temperature, as well as a single interval and adjacent intervals at finite temperature. We also find this prescription to effectively characterize the thermofield double state. We discuss how a deformation of a spherical entangling region complicates calculations and speculate how to generalize to a covariant description.

Entanglement negativity and minimal entanglement wedge cross sections in holographic theories

We study the intrinsic fully gapped odd-parity superconducting order in doped nodal-loop materials with a torus-shaped Fermi surface. We show that the mirror symmetry, which protects the nodal loop in the normal state, also protects the superconducting state as a topological crystalline superconductor. As a result, the surfaces preserving the mirror symmetry host gapless Majorana cones. Moreover, for a Weyl-loop system (twofold degenerate at the nodal loop), the surfaces that break the mirror symmetry (those parallel to the bulk nodal loop) contribute a Chern (winding) number to the quasi-two-dimensional system in a slab geometry, which leads to a quantized thermal Hall effect and a single Majorana zero mode bound at a vortex line penetrating the system. This Chern number can be viewed as a higher-order topological invariant, which supports hinge modes in a cubic sample when mirror symmetry is broken. For a Dirac-loop system (fourfold degenerate at the nodal loop), the fully gapped odd-parity state can be either time-reversal symmetry-breaking or symmetric, similar to the $A$ and $B$ phases of $^{3}\mathrm{He}$. In a slab geometry, the $A$ phase has a Chern number two, while the $B$ phase carries a nontrivial ${\mathbb{Z}}_{2}$ invariant. We discuss the experimental relevance of our results to nodal-loop materials such as CaAgAs.

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Topological crystalline superconductivity and second-order topological superconductivity in nodal-loop materials

We present a derivation of the holographic dual of logarithmic negativity in AdS_{3}/CFT_{2} that was recently conjectured in Phys. Rev. D 99, 106014 (2019PRVDAQ2470-001010.1103/PhysRevD.99.106014). This is given by the area of an extremal cosmic brane that terminates on the boundary of the entanglement wedge. The derivation consists of relating the recently introduced Renyi reflected entropy to the logarithmic negativity in holographic conformal field theories. Furthermore, we clarify previously mysterious aspects of negativity at a large central charge seen in conformal blocks and comment on generalizations to generic dimensions, dynamical settings, and quantum corrections.

Derivation of Holographic Negativity in AdS 3 /CFT 2

We study real-space quantum entanglement included in conformally invariant boundary states in conformal field theories (CFTs) We argue that boundary states essentially have no real-space entanglement, except for constant contributions from long range topological entanglement, by computing the entanglement entropy when the system is bipartition into two spatial regions From the viewpoint of classical gravity duals in holography, this shows that boundary states are dual to trivial spacetimes of zero space-time volume We also point out that a continuous multiscale entanglement renormalization ansatz (cMERA) for any CFTs can be formulated by employing a boundary state as its infrared unentangled state with an appropriate regularization Exploiting this idea, we propose an approximation scheme of cMERA construction for general CFTs

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Boundary states as holographic duals of trivial spacetimes

The Lieb-Schultz-Mattis (LSM) theorem dictates that emergent low-energy states from a lattice model cannot be a trivial symmetric insulator if the filling per unit cell is not integral and if the lattice translation symmetry and particle number conservation are strictly imposed. In this paper, we compare the one-dimensional gapless states enforced by the LSM theorem and the boundaries of one-higher dimensional strong symmetry-protected topological (SPT) phases from the perspective of quantum anomalies. We first note that they can both be described by the same low-energy effective field theory with the same effective symmetry realizations on low-energy modes, wherein non-on-site lattice translation symmetry is encoded as if it were an internal symmetry. In spite of the identical form of the low-energy effective field theories, we show that the quantum anomalies of the theories play different roles in the two systems. In particular, we find that the chiral anomaly is equivalent to the LSM theorem, whereas there is another anomaly that is not related to the LSM theorem but is intrinsic to the SPT states. As an application, we extend the conventional LSM theorem to multiple-charge multiple-species problems and construct several exotic symmetric insulators. We also find that the (3+1)d chiral anomaly provides only the perturbative stability of the gaplessness local in the parameter space.

Shinsei Ryu

Papers

Entanglement negativity and minimal entanglement wedge cross sections in holographic theories

Topological crystalline superconductivity and second-order topological superconductivity in nodal-loop materials

Derivation of Holographic Negativity in AdS 3 /CFT 2

Boundary states as holographic duals of trivial spacetimes

Anomaly manifestation of Lieb-Schultz-Mattis theorem and topological phases