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The particle-particle random phase approximation (pp-RPA) has been shown to be capable of describing double, Rydberg, and charge transfer excitations, for which the conventional time-dependent density functional theory (TDDFT) might not be…
Tensor network contraction is a powerful computational tool in quantum many-body physics, quantum information and quantum chemistry. The complexity of contracting a tensor network is thought to mainly depend on its entanglement properties,…
In this chapter, we introduce the relaxed inertial proximal splitting algorithm (RIPSA) for hierarchical equilibrium problems. Using Opial-Passty's lemma, we first establish weak ergodic and weak convergence of the sequence generated by the…
The ground-state correlation energy calculated in the random-phase approximation (RPA) is known to be identical to that calculated using a subset of terms appearing in coupled-cluster theory with double excitations. In particular, this…
We calculate the energy spectrum of closed strings in SU(N) gauge theories with N=2,3,4,6,8 in 2+1 dimensions to a high accuracy. We attempt to control all systematic errors, and this allows us to perform a precise comparison with different…
We present a new formulation of the tensionless string ($T= 0$) where the space-time conformal symmetry is manifest. Using a Hamiltonian BRST scheme we quantize this {\em Conformal String} and find that it has critical dimension $D=2$. This…
The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still…
Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…
We present a detailed study of the time-dependent Gutzwiller approximation for the Hubbard model. The formalism, labelled GA+RPA, allows us to compute random-phase approximation-like (RPA) fluctuations on top of the Gutzwiller approximation…
In this Ph.D. thesis, we study tachyon condensation in string field theories. In chapter 2, we review Witten's bosonic string field theory and calculate the tachyon potential. In chapter 3, we calculate the tachyon potential in Berkovits'…
In this thesis are shown developments in the random phase approximation (RPA) in the context of range-separated theories. We present advances in the formalism of the RPA in general, and particularly in the "dielectric matrix" formulation of…
We study the low-energy collective excitations and dynamical response functions of weakly coupled random antiferromagnetic spin-1/2 chains. The interchain coupling leads to Neel order at low temperatures. We use the real-space…
The accurate computation of non-linear optical properties (NLOPs) in large polymers requires accounting for electronic correlation effects with a reasonable computational cost. The Random Phase Approximation (RPA) used in the adiabatic…
The random-phase-approximation (RPA) method with separable residual forces (SRPA) is proposed for the description of multipole electric oscillations of valence electrons in deformed alkali metal clusters. Both the deformed mean field and…
We study the collective excitation spectrum of a d=3 site-disordered Anderson-Hubbard model at half-filling, via a random-phase approximation (RPA) about broken-symmetry, inhomogeneous unrestricted Hartree-Fock (UHF) ground states. We focus…
We present a new approach to bootstrapping string-like theories by exploiting a local crossing symmetric dispersion relation and field redefinition ambiguities. This approach enables us to use mass-level truncation and to go beyond the dual…
We compute leading order quantum corrections to the Regge trajectory of a rotating string with massive endpoints using semiclassical methods. We expand the bosonic string action around a classical rotating solution to quadratic order in the…
We explore several random phase approximation (RPA) correlation energy variants within the adiabatic-connection fluctuation-dissipation theorem approach. These variants differ in the way the exchange interactions are treated. One of these…
The complete expression of the heavy quark-antiquark potential up to order $1/m^2$ is known from QCD in terms of Wilson loop expectation values. We use that expression and a mapping, assumed to be valid at large distances, between Wilson…
Phase-rectified signal averaging (PRSA) is a widely used algorithm to analyze nonstationary biomedical time series. The method operates by identifying hinge points in the time series according to prescribed rules, extracting segments…