Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT

We investigate a weak version of subsystem eigenstate thermalization hypothesis (ETH) for a two-dimensional large central charge conformal field theory by comparing the local equivalence of high energy state and thermal state of canonical ensemble. We evaluate the single-interval R\'enyi entropy and entanglement entropy for a heavy primary state in short interval expansion. We verify the results of R\'enyi entropy by two different replica methods. We find nontrivial results at the eighth order of short interval expansion, which include an infinite number of higher order terms in the large central charge expansion. We then evaluate the relative entropy of the reduced density matrices to measure the difference between the heavy primary state and thermal state of canonical ensemble, and find that the aforementioned nontrivial eighth order results make the relative entropy unsuppressed in the large central charge limit. By using Pinsker's and Fannes-Audenaert inequalities, we can exploit the results of relative entropy to yield the lower and upper bounds on trace distance of the excited-state and thermal-state reduced density matrices. Our results are consistent with subsystem weak ETH, which requires the above trace distance is of power-law suppression by the large central charge. However, we are unable to pin down the exponent of power-law suppression. As a byproduct we also calculate the relative entropy to measure the difference between the reduced density matrices of two different heavy primary states.Comment: 28 pages, 4 figures;v2 change author list;v3 related subtleties about weak ETH clarified; v4 minor correction to match JHEP versio

Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis

We calculate various quantities that characterize the dissimilarity of reduced density matrices for a short interval of length $\ell$ in a two-dimensional (2D) large central charge conformal field theory (CFT). These quantities include the R\'enyi entropy, entanglement entropy, relative entropy, Jensen-Shannon divergence, as well as the Schatten 2-norm and 4-norm. We adopt the method of operator product expansion of twist operators, and calculate the short interval expansion of these quantities up to order of $\ell^9$ for the contributions from the vacuum conformal family. The formal forms of these dissimilarity measures and the derived Fisher information metric from contributions of general operators are also given. As an application of the results, we use these dissimilarity measures to compare the excited and thermal states, and examine the eigenstate thermalization hypothesis (ETH) by showing how they behave in high temperature limit. This would help to understand how ETH in 2D CFT can be defined more precisely. We discuss the possibility that all the dissimilarity measures considered here vanish when comparing the reduced density matrices of an excited state and a generalized Gibbs ensemble thermal state. We also discuss ETH for a microcanonical ensemble thermal state in a 2D large central charge CFT, and find that it is approximately satisfied for a small subsystem and violated for a large subsystem.Comment: V1, 34 pages, 5 figures, see collection of complete results in the attached Mathematica notebook; V2, 38 pages, 5 figures, published versio

Holographic R\'enyi entropy in AdS3_3/LCFT2_2 correspondence

The recent study in AdS$_3$/CFT$_2$ correspondence shows that the tree level contribution and 1-loop correction of holographic R\'enyi entanglement entropy (HRE) exactly match the direct CFT computation in the large central charge limit. This allows the R\'enyi entanglement entropy to be a new window to study the AdS/CFT correspondence. In this paper we generalize the study of R\'enyi entanglement entropy in pure AdS$_3$ gravity to the massive gravity theories at the critical points. For the cosmological topological massive gravity (CTMG), the dual conformal field theory (CFT) could be a chiral conformal field theory or a logarithmic conformal field theory (LCFT), depending on the asymptotic boundary conditions imposed. In both cases, by studying the short interval expansion of the R\'enyi entanglement entropy of two disjoint intervals with small cross ratio $x$, we find that the classical and 1-loop HRE are in exact match with the CFT results, up to order $x^6$. To this order, the difference between the massless graviton and logarithmic mode can be seen clearly. Moreover, for the cosmological new massive gravity (CNMG) at critical point, which could be dual to a logarithmic CFT as well, we find the similar agreement in the CNMG/LCFT correspondence. Furthermore we read the 2-loop correction of graviton and logarithmic mode to HRE from CFT computation. It has distinct feature from the one in pure AdS$_3$ gravity.Comment: 28 pages. Typos corrected, published versio

Boundary-induced singularity in strongly-correlated quantum systems at finite temperature

Exploring the bulk-boundary correspondences and the boundary-induced phenomena in the strongly-correlated quantum systems belongs to the most fundamental topics of condensed matter physics. In this work, we show that the entanglement-bath Hamiltonian (EBH) can induce exotic thermodynamic properties in the bulk of a quantum spin chain from the boundaries, analogous to heat bath. The EBH is defined as the local Hamiltonian located on the boundary of a finite-size system, which approximately generates the bulk entanglement Hamiltonian of the translational-invariant system in the thermodynamic limit (i.e., the infinite boundary condition). The ``boundary quench point'' (BQP) is identified by the discontinuity in the coefficients of the EBH and in the bulk entropy versus the effective boundary temperature. The physical implication of BQP is to distinguish the point, below which the thermal effects become insignificant and the bulk properties are dominated by the ground state. It singularity differs from those in the conventional thermodynamic phase transition points that normally fall into the Landau-Ginzburg paradigm. The relations between the symmetry of Hamiltonian and BQP, and the impacts from the entanglement-bath dimension are also explored. Our work shows the opportunities on exploring the exotic phenomena induced by the competition between the bulk and boundaries.Comment: 10 pages, 8 figure

1,3-Bis(4-meth­oxy­benz­yl)-6-methyl­pyrimidine-2,4(1H,3H)-dione

The title compound, C21H22N2O4, was prepared by reaction of 6-methyl­pyrimidine-2,4(1H,3H)-dione and 1-chloro­methyl-4-meth­oxy­benzene. In the title mol­ecule, the central pyrimidine ring forms dihedral angles of 62.16 (4) and 69.77 (3)° with the two benzene rings. In the crystal, weak inter­molecular C—H⋯O hydrogen bonds link the mol­ecules into chains

Robust Dancer: Long-term 3D Dance Synthesis Using Unpaired Data

How to automatically synthesize natural-looking dance movements based on a piece of music is an incrementally popular yet challenging task. Most existing data-driven approaches require hard-to-get paired training data and fail to generate long sequences of motion due to error accumulation of autoregressive structure. We present a novel 3D dance synthesis system that only needs unpaired data for training and could generate realistic long-term motions at the same time. For the unpaired data training, we explore the disentanglement of beat and style, and propose a Transformer-based model free of reliance upon paired data. For the synthesis of long-term motions, we devise a new long-history attention strategy. It first queries the long-history embedding through an attention computation and then explicitly fuses this embedding into the generation pipeline via multimodal adaptation gate (MAG). Objective and subjective evaluations show that our results are comparable to strong baseline methods, despite not requiring paired training data, and are robust when inferring long-term music. To our best knowledge, we are the first to achieve unpaired data training - an ability that enables to alleviate data limitations effectively. Our code is released on https://github.com/BFeng14/RobustDancerComment: Preliminary video demo: https://youtu.be/gJbxG9QlcU

Human herpesvirus 6A induces apoptosis of primary human fetal astrocytes via both caspase-dependent and -independent pathways

<p>Abstract</p> <p>Background</p> <p>Human herpesvirus 6 (HHV-6) is a T-lymphtropic and neurotropic virus that can infect various types of cells. Sequential studies reported that apoptosis of glia and neurons induced by HHV-6 might act a potential trigger for some central nervous system (CNS) diseases. HHV-6 is involved in the pathogenesis of encephalitis, multiple sclerosis (MS) and fatigue syndrome. However, the mechanisms responsible for the apoptosis of infected CNS cells induced by HHV-6 are poorly understood. In this study, we investigated the cell death processes of primary human fetal astrocytes (PHFAs) during productive HHV-6A infection and the underlying mechanisms.</p> <p>Results</p> <p>HHV-6A can cause productive infection in primary human fetal astrocytes. Annexin V-PI staining and electron microscopic analysis indicated that HHV-6A was an inducer of apoptosis. The cell death was associated with activation of caspase-3 and cleavage of poly (ADP-ribose) polymerase (PARP), which is known to be an important substrate for activated caspase-3. Caspase-8 and -9 were also significantly activated in HHV-6A-infected cells. Moreover, HHV-6A infection led to Bax up-regulation and Bcl-2 down-regulation. HHV-6A infection increased the release of Smac/Diablo, AIF and cytochrome c from mitochondria to cytosol, which induced apoptosis via the caspase-dependent and -independent pathways. In addition, we also found that anti-apoptotic factors such as IAPs and NF-κB decreased in HHV-6A infected PHFAs.</p> <p>Conclusion</p> <p>This is the first demonstration of caspase-dependent and -independent apoptosis in HHV-6A-infected glial cells. These findings would be helpful in understanding the mechanisms of CNS diseases caused by HHV-6.</p