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In this work, we develop a generalisation of the thermal entropy to complex inverse temperatures, which we call the thermal pseudo-entropy. We show that this quantity represents the pseudo-entropy of the transition matrix between Thermofield Double states at different times. We have studied its properties in various quantum mechanical setups, Schwarzian theory, Random Matrix Theories, and 2D CFTs, including symmetric orbifolds. Our findings indicate a close relationship between the averaged thermal pseudo-entropy and the spectral form factor, which is instrumental in distinguishing chaotic and integrable models. Moreover, we have observed a logarithmic scaling of this quantity in models with a continuous spectrum, with a universal coefficient that is sensitive to the scaling of the density of states near the edge of the spectrum. Lastly, we found the connection between the real and imaginary parts of the thermal pseudo-entropy through the Kramers-Kronig relations., Comment: 43 pages, 23 figures, v2 references added

We present a general theory of potentials that support bound states at positive energies (bound states in the continuum). On the theoretical side, we prove that, for systems described by nonlocal potentials of the form $V(r,r')$, bound states at positive energies are as common as those at negative energies. At the same time, we show that a local potential of the form $V(r)$ rarely supports a positive energy bound state. On the practical side, we show how to construct a (naturally nonlocal) potential which supports an arbitrary normalizable state at an arbitrary positive energy. We demonstrate our theory with numerical examples both in momentum and coordinate spaces with emphasis on the important role played by nonlocal potentials. Finally, we discuss how to observe bound states at positive energies, and where to search for nonlocal potentials which may support them., Comment: 32 pages, 22 figures

Tactile sensation is essential for humans to recognize objects. Various devices have been developed in the past for tactile presentation by electrostatic force, which are easy to configure devices, but there is currently no such device that features stretchability. Considering that the device is worn over the joints of a human body or robot, it is extremely important that the device itself be stretchable. In this study, we propose a stretchable electrostatic tactile surface comprising a stretchable transparent electrode and a stretchable insulating film that can be stretched to a maximum of 50%. This means that when attached to the human body, this surface can respond to the expansion and contraction that occur due to joint movements. This surface can also provide tactile information in response to deformation such as pushing and pulling. As a basic investigation, we measured the lower limit of voltage that can be perceived by changing the configuration of the surface and evaluated the states of stretching and contraction. We also investigated and modeled the relationship between the voltage and the perceived intensity., Comment: 7 pages, 9 figures

In the post-Turing era, evaluating large language models (LLMs) involves assessing generated text based on readers' reactions rather than merely its indistinguishability from human-produced content. This paper explores how LLM-generated text impacts readers' decisions, focusing on both amateur and expert audiences. Our findings indicate that GPT-4 can generate persuasive analyses affecting the decisions of both amateurs and professionals. Furthermore, we evaluate the generated text from the aspects of grammar, convincingness, logical coherence, and usefulness. The results highlight a high correlation between real-world evaluation through audience reactions and the current multi-dimensional evaluators commonly used for generative models. Overall, this paper shows the potential and risk of using generated text to sway human decisions and also points out a new direction for evaluating generated text, i.e., leveraging the reactions and decisions of readers. We release our dataset to assist future research.

Orthorhombic pseudobrookites CoTi$_2$O$_5$ and FeTi$_2$O$_5$ have a low-symmetry crystal structure comprising magnetic Co$^{2+}$/Fe$^{2+}$ ions and nonmagnetic Ti$^{4+}$ ions, where the orbital-nondegenerate Co$^{2+}$/Fe$^{2+}$ ions form one-dimensional chains running along the orthorhombic $a$ axis. These compounds undergo an antiferromagnetic phase transition at $T_N \sim$ 26 K for CoTi$_2$O$_5$ and $T_N \sim$ 40 K for FeTi$_2$O$_5$. We perform ultrasound velocity measurements on single crystals of CoTi$_2$O$_5$ and FeTi$_2$O$_5$. The measurements of these compounds reveal that the symmetry-lowering elastic modes of shear elastic moduli exhibit unusual elastic softness in the paramagnetic phase above $T_N$. This elastic softness indicates the presence of spin-lattice-coupled fluctuations above $T_N$ that should be a precursor to the symmetry-lowering lattice distortion at $T_N$. Furthermore, it is revealed that the magnitude of the unusual elastic softness is larger in CoTi$_2$O$_5$ than in FeTi$_2$O$_5$, which indicates that the spin-lattice coupling is stronger in CoTi$_2$O$_5$ than in FeTi$_2$O$_5$. The present study suggests that CoTi$_2$O$_5$ and FeTi$_2$O$_5$ are unique spin Jahn--Teller systems with low crystal symmetry, where, although the nature of exchange interactions is quasi-one-dimensional, the three-dimensional spin-lattice coupling releases the frustration by further lowering the crystal symmetry., Comment: 9 pages, 7 figures

Stock embedding is a method for vector representation of stocks. There is a growing demand for vector representations of stock, i.e., stock embedding, in wealth management sectors, and the method has been applied to various tasks such as stock price prediction, portfolio optimization, and similar fund identifications. Stock embeddings have the advantage of enabling the quantification of relative relationships between stocks, and they can extract useful information from unstructured data such as text and network data. In this study, we propose stock embedding enhanced with textual and network information (SETN) using a domain-adaptive pre-trained transformer-based model to embed textual information and a graph neural network model to grasp network information. We evaluate the performance of our proposed model on related company information extraction tasks. We also demonstrate that stock embeddings obtained from the proposed model perform better in creating thematic funds than those obtained from baseline methods, providing a promising pathway for various applications in the wealth management industry.

This paper investigates the challenges and resolutions in computing the entanglement entropy for the quantum field theory coupled to de Sitter (dS) gravity along a timelike boundary. The conventional island formula, originally designed to calculate the fine-grained entropy for a non-gravitational system coupled to anti-de Sitter (AdS) gravity, encounters difficulties in de Sitter gravitational spacetime, failing to provide a physically plausible extremal island. To overcome these problems, we introduce a doubly holographic model by embedding a dS$_2$ braneworld in an AdS$_3$ bulk spacetime. This approach facilitates the computation of entanglement entropy through holographic correlation functions, effectively circumventing the constraints of the island formula. We demonstrate that the correct recipe for calculating entanglement entropy with dS gravity involves the non-extremal island, whose boundary is instead defined at the edge of the dS gravitational region. Our findings indicate that, during the island phase, the entanglement wedge of the non-gravitational bath includes the entire dS gravitational space. Using the second variation formula, we further show that the existence of a locally minimal surface anchored on the gravitational brane is intrinsically linked to the extrinsic curvature of the brane., Comment: 64 pages, 20 figures; v2:added an important reference

In this paper we construct CFT states describing a putative holographic dual to local excitations in the three-dimensional de Sitter space (dS), called the bulk local states. We find that the conjugation operation in dS$_3/$CFT$_2$ is notably different from that in AdS$_3/$CFT$_2$. This requires us to combine two bulk local states constructed out of different primary states in a CPT-invariant way. This analysis explains why Green's functions in the dS Euclidean vacuum cannot simply be obtained from the Wick rotation of those in AdS. We also argue that this characteristic feature explains the emergence of a time coordinate from the dual Euclidean CFT. We show that the information metric for the quantum estimation of bulk coordinate values replicates the de Sitter space metric., Comment: 37 pages, typos have been corrected and some clarifications have been added for better readability in version 2

We show that strong subadditivity provides a simple derivation of the $g$-theorem for the boundary renormalization group flow in two-dimensional conformal field theories. We work out its holographic interpretation and also give a derivation of the $g$-theorem for the case of an interface in two-dimensional conformal field theories. We also geometrically confirm strong subadditivity for holographic duals of conformal field theories on manifolds with boundaries., Comment: 7 pages, 6 figures

Causality is fundamental in human cognition and has drawn attention in diverse research fields. With growing volumes of textual data, discerning causalities within text data is crucial, and causal text mining plays a pivotal role in extracting meaningful patterns. This study conducts comprehensive evaluations of ChatGPT's causal text mining capabilities. Firstly, we introduce a benchmark that extends beyond general English datasets, including domain-specific and non-English datasets. We also provide an evaluation framework to ensure fair comparisons between ChatGPT and previous approaches. Finally, our analysis outlines the limitations and future challenges in employing ChatGPT for causal text mining. Specifically, our analysis reveals that ChatGPT serves as a good starting point for various datasets. However, when equipped with a sufficient amount of training data, previous models still surpass ChatGPT's performance. Additionally, ChatGPT suffers from the tendency to falsely recognize non-causal sequences as causal sequences. These issues become even more pronounced with advanced versions of the model, such as GPT-4. In addition, we highlight the constraints of ChatGPT in handling complex causality types, including both intra/inter-sentential and implicit causality. The model also faces challenges with effectively leveraging in-context learning and domain adaptation. We release our code to support further research and development in this field.

For a static time slice of AdS$_3$ we describe a particular class of minimal surfaces which form trivalent networks of geodesics. Through geometric arguments we provide evidence that these surfaces describe a measure of multipartite entanglement. By relating these surfaces to Ryu-Takayanagi surfaces it can be shown that this multipartite contribution is related to the angles of intersection of the bulk geodesics. A proposed boundary dual, the multi-entropy, generalizes replica trick calculations involving twist operators by considering monodromies with finite group symmetry beyond the cyclic group used for the computation of entanglement entropy. We make progress by providing explicit calculations of Renyi multi-entropy in two dimensional CFTs and geometric descriptions of the replica surfaces for several cases with low genus. We also explore aspects of the free fermion and free scalar CFTs. For the free fermion CFT we examine subtleties in the definition of the twist operators used for the calculation of Renyi multi-entropy. In particular the standard bosonization procedure used for the calculation of the usual entanglement entropy fails and a different treatment is required., Comment: 50 pages, 21 figures. v2: Minor correction and typos v3: Added information about general multi-trace measures, minor corrections

In this paper, we present holographic descriptions of entanglement phase transition using AdS/BCFT. First, we analytically calculate the holographic pseudo entropy in the AdS/BCFT model with a brane localized scalar field and show the entanglement phase transition behavior where the time evolution of entropy changes from the linear growth to the trivial one via a critical logarithmic evolution. In this model, the imaginary valued scalar field localized on the brane controls the phase transition, which is analogous to the amount of projections in the measurement induced phase transition. Next, we study the AdS/BCFT model with a brane localized gauge field, where the phase transition looks different in that there is no logarithmically evolving critical point. Finally, we discuss a bulk analog of the above model by considering a double Wick rotation of the Janus solution. We compute the holographic pseudo entropy in this model and show that the entropy grows logarithmically., Comment: 60+21 pages, 36 figures

The Bethe lattice Ising model -- a classical model of statistical mechanics for the phase transition -- provides a novel and intuitive understanding of the prototypical relationship between tensor networks and Anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. After analytically formulating a holographic renormalization group for the Bethe lattice model, we demonstrate the underlying mechanism and the exact scaling dimensions for the power-law decay of boundary spin correlations by introducing the relation between the lattice network and an effective Poincare metric on a unit disk. We compare the Bethe lattice model in the high-temperature region with a scalar field in AdS$_2$, and then discuss its more direct connection to the p-adic AdS/CFT. In addition, we find that the phase transition in the interior induces a crossover behavior of boundary spin correlations, depending on the depth of the corresponding correlation path., Comment: 15 pages, 8 figures

We compute the pseudo entropy in two-dimensional holographic and free Dirac fermion CFTs for excited states under joining local quenches. Our analysis reveals two of its characteristic properties that are missing in the conventional entanglement entropy. One is that, under time evolution, the pseudo entropy exhibits a dip behavior as the excitations propagate from the joined point to the boundaries of the subsystem. The other is that the excess of pseudo entropy over entanglement entropy can be positive in holographic CFTs, whereas it is always non-positive in free Dirac fermion CFTs. We argue that the entropy excess can serve as a measure of multi-partite entanglement. Its positivity implies that the vacuum state in holographic CFTs possesses multi-partite entanglement, in contrast to free Dirac fermion CFTs., Comment: 53 pages, 29 figures

In this paper, we introduce a new quantity called SVD entanglement entropy. This is a generalization of entanglement entropy in that it depends on two different states, as in pre- and post-selection processes. This SVD entanglement entropy takes non-negative real values and is bounded by the logarithm of the Hilbert space dimensions. The SVD entanglement entropy can be interpreted as the average number of Bell pairs distillable from intermediates states. We observe that the SVD entanglement entropy gets enhanced when the two states are in the different quantum phases in an explicit example of the transverse-field Ising model. Moreover, we calculate the R\'enyi SVD entropy in various field theories and examine holographic calculations using the AdS/CFT correspondence., Comment: 42 pages, 23 figures, V2: minor adjustments

A long-standing and intriguing question is: does the holographic principle apply to cosmologies like de Sitter spacetime? In this work, we consider a half dS spacetime wherein a timelike boundary encloses the bulk spacetime, presenting a version of de Sitter holography. By analyzing the holographic entanglement entropy in this space and comparing it with that in AdS/CFT, we argue that gravity on a half dS$_{d+1}$ is dual to a highly non-local field theory residing on dS$_d$ boundary. This non-locality induces a breach in the subadditivity of holographic entanglement entropy. Remarkably, this observation can be linked to another argument that time slices in global de Sitter space overestimate the degrees of freedom by redundantly counting the same Hilbert space multiple times., Comment: 52 pages, Reference added

Robot manipulation tasks by natural language instructions need common understanding of the target object between human and the robot. However, the instructions often have an interpretation ambiguity, because the instruction lacks important information, or does not express the target object correctly to complete the task. To solve this ambiguity problem, we hypothesize that "naming" the target objects in advance will reduce the ambiguity of natural language instructions. We propose a robot system and method that incorporates naming with appearance of the objects in advance, so that in the later manipulation task, instruction can be performed with its unique name to disambiguate the objects easily. To demonstrate the effectiveness of our approach, we build a system that can memorize the target objects, and show that naming the objects facilitates detection of the target objects and improves the success rate of manipulation instructions. With this method, the success rate of object manipulation task increases by 31% in ambiguous instructions., Comment: 8 pages, 7 figures

In this paper, we investigate gluing together two Anti-de Sitter (AdS) geometries along a timelike brane, which corresponds to coupling two brane field theories (BFTs) through gravitational interactions in the dual holographic perspective. By exploring the general conditions for this gluing process, we show that the energy stress tensors of the BFTs backreact on the dynamical metric in a manner reminiscent of the TTbar deformation. In particular, we present explicit solutions for the three-dimensional case with chiral excitations and further construct perturbative solutions with non-chiral excitations., Comment: 35 pages, 9 figures; v2: typos fixed, references added

We define a new complex-valued measure of information called the timelike entanglement entropy (EE) which in the boundary theory can be viewed as a Wick rotation that changes a spacelike boundary subregion to a timelike one. An explicit definition of the timelike EE in 2d field theories is provided followed by numerical computations which agree with the analytic continuation of the replica method for CFTs. We argue that timelike EE should be correctly interpreted as another measure previously considered, the pseudo entropy, which is the von Neumann entropy of a reduced transition matrix. Our results strongly imply that the imaginary part of the pseudo entropy describes an emergent time which generalizes the notion of an emergent space from quantum entanglement. For holographic systems we define the timelike EE as the total complex valued area of a particular stationary combination of both space and timelike extremal surfaces which are homologous to the boundary region. For the examples considered we find explicit matching of our optimization procedure and the careful implementation of the Wick rotation in the boundary CFT. We also make progress on higher dimensional generalizations and relations to holographic pseudo entropy in de Sitter space., Comment: 61 pages, 25 figures