It is commonly recognized that the primordial scalar spectral index $n_s$ is approximately $0.96-0.975$, depending on the dataset. However, this view is being completely altered by the early dark energy (EDE) resolutions of the Hubble tension, known as the most prominent tension the standard $\Lambda$CDM model is suffering from. In corresponding models with pre-recombination EDE, resolving the Hubble tension (i.e., achieving $H_0\sim 73$km/s/Mpc) must be accompanied by a shift of $n_s$ towards unity to maintain consistency with the cosmological data, which thus implies a scale invariant Harrison-Zel'dovich spectrum with $n_s=1$ $(|n_s-1|\simeq {\cal O}(0.001))$. In this work, we strengthen and reconfirm this result with the latest ground-based CMB data from ACT DR6 and SPT-3G D1, the precise measurements at high multipoles beyond the Planck angular resolution and sensitivity. Our work again highlights the importance of re-examining our understanding on the very early Universe within the broader context of cosmological tensions.

With the help of a given distance matrix of size $n$, we construct an infinite family of distances $d_p$ (where $p \geq 2$) on the the complex projective space $\mathbb{P}(\mathbb{C}^n)$, modelling the space of pure states of an $n$-dimensional quantum system. The construction can be seen as providing a natural way to isometrically embed any given finite metric space into the space of pure quantum states 'spanned' upon it. In order to show that the maps $d_p$ are indeed distance functions -- in particular, that they satisfy the triangle inequality -- we employ methods of analysis, multilinear algebra and convex geometry, obtaining a non-trivial convexity result in the process. The paper significantly extends earlier work, resolving an important question about the geometry of quantum state space imposed by the quantum Wasserstein distances and solidifying the foundation for applications of distances $d_p$ in quantum information science.

We investigate black hole superradiance evolution of the interacting multiple fields. We consider a model of two scalar fields interacting with a cubic coupling, and study the superradiant evolution of the cloud. We demonstrate that superradiance is typically suppressed when the superradiant field couples to another field, even with a very weak coupling strength. This implies that the constraints on dark particles derived from single-field analyses can be revised in the presence of interactions. Moreover, we find that the multi-field superradiant evolution and its corresponding observational signatures can be different across parameter spaces, which makes black hole superradiance an even more powerful probe of the dark sector in particle physics.

It has been noted that with the pre-recombination early dark energy (EDE) resolution of Hubble tension, the preference of recent datasets for the evolving dark energy (DE) can be suppressed significantly. In this work, we clarify and reconfirm this result with DESI DR2 and the latest ACT DR6 and SPT-3G D1, the tightest small-scale CMB constraints up to date. In the $w_0w_a$CDM model with EDE, a quintessence-like component ($w_0+w_a\geq-1$) can be 1$\sigma$ consistent with Planck+ACT+SPT+DESI+Pantheon+SH0ES datasets, and $\Delta\chi^2\lesssim -14$ compared with $w_0w_a$CDM model without EDE. This reveals the possibility that when the potential resolutions of Hubble tension are considered, current accelerated expansion can attribute to a canonical evolving scalar field or cosmological constant, and again highlights the importance of re-examining the nature of DE within the broader context of cosmological tensions.

We study the dual CFT description of the $d+1$-dimensional Reissner-Nordström-Anti de Sitter (RN-AdS$_{d+1}$) black hole in the large dimension (large $d$) limit, both for the extremal and nonextremal cases. The central charge of the dual CFT$_2$ (or chiral CFT$_1$) is calculated for the near horizon near extremal geometry which possess an AdS$_2$ structure. Besides, the $Q$-picture hidden conformal symmetry in the nonextremal background can be naturally obtained by a probe charged scalar field in the large $d$ limit, without the need to input the usual limits to probe the hidden conformal symmetry. Furthermore, an new dual CFT description of the nonextremal RN-AdS$_{d+1}$ black hole is found in the large $d$ limit and the duality is analyzed by comparing the entropies, the absorption cross sections and the retarded Green's functions obtained both from the gravity and the dual CFT sides.

Quantum field theory (QFT) for interacting many-electron systems is fundamental to condensed matter physics, yet achieving accurate solutions confronts computational challenges in managing the combinatorial complexity of Feynman diagrams, implementing systematic renormalization, and evaluating high-dimensional integrals. We present a unifying framework that integrates QFT computational workflows with an AI-powered technology stack. A cornerstone of this framework is representing Feynman diagrams as computational graphs, which structures the inherent mathematical complexity and facilitates the application of optimized algorithms developed for machine learning and high-performance computing. Consequently, automatic differentiation, native to these graph representations, delivers efficient, fully automated, high-order field-theoretic renormalization procedures. This graph-centric approach also enables sophisticated numerical integration; our neural-network-enhanced Monte Carlo method, accelerated via massively parallel GPU implementation, efficiently evaluates challenging high-dimensional diagrammatic integrals. Applying this framework to the uniform electron gas, we determine the quasiparticle effective mass to a precision significantly surpassing current state-of-the-art simulations. Our work demonstrates the transformative potential of integrating AI-driven computational advances with QFT, opening systematic pathways for solving complex quantum many-body problems across disciplines.

This thesis contains of two parts: The first part is a pedagogical introduction into the field of bosonic SFT. After discussing some general properties we expect, Witten's open SFT and Zwiebach's closed SFT are presented in detail. This means we set up the action, explain the algebraical and geometrical structure and mention physical applications. In the open case we review the most important analytic solutions including the necessary operator technology whileas in the closed case we focus on quantization and the more elaborate construction of the vertices. The second part contains of reprints of papers completed within the PhD: 2301.13182, 2402.00308, 2410.16228 and 2411.15123.

The mass transfer process is prevalent during the inspiral phase of compact binary systems. Detection of gravitational waves from the inspiral phase of binaries with white dwarfs will allow us to measure the mass transfer rate. Mass transfer effects provide additional contributions to the phase of gravitational waves, which can break the degeneracy between binary masses and redshift. Based on the analytic mass transfer rate to the first order post-Newtonian evolution of orbital angular frequency, we use the Fisher matrix to forecast the ability of DECIGO to measure the redshift of compact binaries with mass transfer. We conclude that for compact binary systems containing white dwarfs, the redshift can be determined to an accuracy of $10\%$ for $z=0.01$ with a $SNR\thicksim 30$.

The holographic entanglement entropy of an infinite strip subsystem on the asymptotic AdS boundary is used as a probe to study the thermodynamic instabilities of planar R-charged black holes (or their dual field theories). We focus on the single-charge AdS black holes in $D=5$, which correspond to spinning D3-branes with one non-vanishing angular momentum. Our results show that the holographic entanglement entropy indeed exhibits the thermodynamic instability associated with the divergence of the specific heat. When the width of the strip is large enough, the finite part of the holographic entanglement entropy as a function of the temperature resembles the thermal entropy, as is expected. As the width becomes smaller, however, the two entropies behave differently. In particular, there exists a critical value for the width of the strip, below which the finite part of the holographic entanglement entropy as a function of the temperature develops a self-intersection. We also find similar behavior in the single-charge black holes in $D=4$ and $7$.

Gravitational waves undergo redshift as they propagate through the expanding universe, and the redshift may exhibit time-dependent drift. Consequently, for any isolated gravitational wave sources, the mass parameter $\mathcal{M}$ and the redshift $z$ exhibit an observational degeneracy, typically manifesting in the waveform as the redshifted mass $\mathcal{M}(1+z)$. Matching together the wave propagation and the wave generation solutions, we show that dimensionless source parameters depending on mass $\mathcal{M}$ can break this degeneracy. Notably, the postmerger signal from binary neutron stars contains several dimensionless parameters that satisfy this condition, including the quality factors of different frequency components and their frequency ratios. Considering the observations of solely the postmerger signal by the Neutron star Extreme Matter Observatory or the Einstein Telescope, based on the Fisher analysis, we find that the redshift can be measured with fractional uncertainties of $\sim30\%$ for sources at $0.01

It was found by Hung, Myers and Smolkin that there is entropy discrepancy for the CFTs in 6-dimensional space-time, between the field theoretical and the holographic analysis. Recently, two different resolutions to this puzzle have been proposed. One of them suggests to utilize the anomaly-like entropy and the generalized Wald entropy to resolve the HMS puzzle, while the other one initiates to use the entanglement entropy which arises from total derivative terms in the Weyl anomaly to explain the HMS mismatch. We investigate these two proposals carefully in this note. By studying the CFTs dual to Einstein gravity, we find that the second proposal can not solve the HMS puzzle. Moreover, the Wald entropy formula is not well-defined on horizon with extrinsic curvatures, in the sense that, in general, it gives different results for equivalent actions.

We study the thermoelectric transport under shear strain in two spatial dimensional quantum matter using the holographic duality. General analytic formulae for the DC thermoelectric conductivities subjected to finite shear strain are obtained in terms of the black hole horizon data. Off-diagonal terms in the conductivity matrix appear also at zero magnetic field, resembling an emergent electronic nematicity which cannot nevertheless be identified with the presence of an anomalous Hall effect. For an explicit model study, we numerically construct a family of strained black holes and obtain the corresponding nonlinear stress-strain curves. We then compute all electric, thermoelectric, and thermal conductivities and discuss the effects of strain. While the shear elastic deformation does not affect the temperature dependence of thermoelectric and thermal conductivities quantitatively, it can strongly change the behavior of the electric conductivity. For both shear hardening and softening cases, we find a clear metal-insulator transition driven by the shear deformation. Moreover, the violation of the previously conjectured thermal conductivity bound is observed for large shear deformation.

The quasinormal modes (QNMs) of a rotating quantum corrected black hole (RQCBH) are studied by employing the hyperboloidal framework for the scalar perturbation. This framework is used to cast the QNMs spectra problem into the two-dimensional eigenvalues problem, then the spectra are calculated by imposing two-dimensional pseudo-spectral method. Based on the resulting spectra, a parameter estimation pipeline for this RQCBH model with gravitational wave data is constructed by using \texttt{pyRing} in the ringdown phase. We find that, even when the RQCBH spectra exhibits a small deviation from the Kerr spectra, the strong correlation between the extra parameter coming from the quantum gravity theory and the intrinsic parameter of black hole may significantly affect the posterior distributions of the mass $M$ and the dimensionless spin $\bar{a}$.

We study the extended Bose-Hubbard model on a two-dimensional honeycomb lattice by using large scale quantum Monte Carlo simulations. We present the ground state phase diagrams for both the hard-core case and the soft-core case. For the hard-core case, the transition between $\rho=1/2$ solid and the superfluid is first order and the supersolid state is unstable towards phase separation. For the soft-core case, due to the presence of the multiple occupation, a stable particle induced supersolid (SS-p) phase emerges when 1/2<\rho<1. The transition from the solid at $\rho=1/2$ to the SS-p is second order with the superfluid density scaling as $\rho_{s} \sim \rho-1/2$. The SS-p has the same diagonal order as the solid at $\rho=1/2$. As the chemical potential increasing further, the SS-p will turn into a solid where two bosons occupying each site of a sublattice through a first order transition. We also calculate the critical exponents of the transition between $\rho=1/2$ solid and superfluid at the Heisenberg point for the hard core case. We find the dynamical critical exponent $z=0.15$, which is smaller than results obtained on smaller lattices. This indicates that $z$ approaches zero in the thermodynamic limit, so the transition is also first order even at the Heisenberg point.

In this paper, we investigate the potential of dark sirens by the space-borne atom interferometric gravitational-wave detectors to probe the Hubble constant. In the mid-frequency band, the sources live a long time. The motion of a detector around the Sun as well as in Earth orbit would induce large Doppler and reorientation effects, providing a precise angular resolution. Such precise localization for the GW sources makes it possible to observe the dark sirens with only one potential host galaxy, which are dubbed "golden dark sirens". We construct the catalogs of golden dark sirens and estimate that there are around 79 and 35 golden dark sirens of binary neutron stars (BNS) and binary black holes (BBH) that would be pass the detection threshold of AEDGE in 5 years. Our results show that with 5, 10, and all 79 golden dark BNS tracked by AEDGE one can constrain $H_0$ at 5.5\%, 4.1\%, and 1.8\% precision levels. With 5, 10, and all 35 golden dark BBH one can constrain $H_0$ at 2.2\%, 1.8\%, and 1.5\% precision levels, respectively. It suggests that only 5-10 golden dark BBH by AEDGE are sufficient to arbitrate the current tension between local and high-$z$ measurements of $H_0$.

We investigate the consequences of heavy quark spin symmetry (HQSS) on hidden-charm pentaquark $P_c$ states. As has been proposed before, assuming the $P_c(4440)$ and the $P_c(4457)$ as $S$-wave $\bar{D}^*\Sigma_c$ molecules, seven hadronic molecular states composed of $\bar{D}\Sigma_c$, $\bar{D}\Sigma_c^*$, $\bar{D}^*\Sigma_c$, and $\bar{D}^*\Sigma_c^*$ can be obtained, with the $\bar{D}\Sigma_c$ molecule corresponding to the $P_c(4312)$. These seven states can decay into $J/\psi N$ and $\eta_c N$, and we use HQSS to predict ratios of partial widths of the $S$-wave decays. For the decays into $J/\psi N$, it is found that among all six $P_c$ molecules with spin $1/2$ or $3/2$, at least four states decay much more easily into the $J/\psi N$ than the $P_c(4312)$, and two of them couple dominantly to the $\bar D^*\Sigma_c^*$. While no significant peak around the $\bar{D}^*\Sigma_c^*$ threshold is found in the $J/\psi p$ distribution, these higher $P_c$ states either are produced with lower rates or some special production mechanism for the observed $P_c$ states might play an important role, such as an intricate interplay between the production of pentaquarks and triangle singularities.

Using the density matrix renormalization group (DMRG) method we study a two-channel Kondo lattice model on a half filled ladder. Our model involves an on-site s-wave and a nearest neighbor d-wave coupling between the local moments and the conduction electrons on the ladder. By changing the relative strength of the two Kondo interactions we examine the evolution of the system from a conventional Kondo insulator with a singlet at each site to a new kind of semimetallic state formed by overlapping of Zhang-Rice-like singlets. The DMRG is used to study how the spin and charge correlation functions evolve between these two regimes.

We consider two fully frustrated Ising models: the antiferromagnetic triangular model in a field of strength, $h=H T k_B$, as well as the Villain model on the square lattice. After a quench from a disordered initial state to T=0 we study the nonequilibrium dynamics of both models by Monte Carlo simulations. In a finite system of linear size, $L$, we define and measure sample dependent "first passage time", $t_r$, which is the number of Monte Carlo steps until the energy is relaxed to the ground-state value. The distribution of $t_r$, in particular its mean value, < t_r(L) >, is shown to obey the scaling relation, < t_r(L) > \sim L^2 \ln(L/L_0), for both models. Scaling of the autocorrelation function of the antiferromagnetic triangular model is shown to involve logarithmic corrections, both at H=0 and at the field-induced Kosterlitz-Thouless transition, however the autocorrelation exponent is found to be $H$ dependent.

Matrix Product States (MPS), also known as Tensor Train (TT) decomposition in mathematics, has been proposed originally for describing an (especially one-dimensional) quantum system, and recently has found applications in various applications such as compressing high-dimensional data, supervised kernel linear classifier, and unsupervised generative modeling. However, when applied to systems which are not defined on one-dimensional lattices, a serious drawback of the MPS is the exponential decay of the correlations, which limits its power in capturing long-range dependences among variables in the system. To alleviate this problem, we propose to introduce long-range interactions, which act as shortcuts, to MPS, resulting in a new model \textit{ Shortcut Matrix Product States} (SMPS). When chosen properly, the shortcuts can decrease significantly the correlation length of the MPS, while preserving the computational efficiency. We develop efficient training methods of SMPS for various tasks, establish some of their mathematical properties, and show how to find a good location to add shortcuts. Finally, using extensive numerical experiments we evaluate its performance in a variety of applications, including function fitting, partition function calculation of $2-$d Ising model, and unsupervised generative modeling of handwritten digits, to illustrate its advantages over vanilla matrix product states.

Ultralight dark matter (ULDM) is an attractive candidate for cold dark matter, one of the main mysterious components of the Universe. Recent studies suggest that gravitational-wave (GW) laser interferometers can also detect bosonic ULDM fields, which would produce monochromatic signals resembling those from gravitational waves (GWs). Distinguishing between these potential origins therefore would be essential. In this work, we develop a method to address this challenge for space-based GW interferometers (such as LISA and Taiji) by utilizing the null-response channel (NRC) in interferometric combinations, a channel constructed to have zero response to a specific type of source from a given direction. We find that while the GW NRC remains blind to GWs from a specific direction, it still responds to ULDM, particularly at frequencies above the interferometer's critical frequency. The ULDM NRC exhibits similar behavior. Based on these observations, we outline a test procedure to discriminate between signal origins. Our method provides a new diagnostic tool for analyzing monochromatic signals in space-based GW interferometers, potentially expanding the scientific scope of future missions.