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Sampling the stationary points of a complicated potential energy landscape is a challenging problem. Here we introduce a sampling method based on relaxation from stationary points of the highest index of the Hessian matrix. We illustrate…
This paper analyses the GW method for finite electronic systems. In a first step, we provide a mathematical framework for the usual one-body operators that appear naturally in many-body perturbation theory. We then discuss the GW equations…
The optimized effective potential (OEP) method is a promising technique for calculating the ground state properties of a system within the density functional theory. However, it is not widely used as its computational cost is rather high…
Bayesian procedures designed to quantify truncation errors in perturbative calculations of quantum chromodynamics observables are adapted to expansions in effective field theory (EFT). In the Bayesian approach, such truncation errors are…
We evaluate one-interval R\'enyi entropy and entanglement entropy for the excited states of two-dimensional conformal field theory (CFT) on a cylinder, and examine their differences from the ones for the thermal state. We assume the…
The extended quantum Rabi models make a significant contribution to understand the quantum nature of the atom-light interaction. We transform two kinds of extended quantum Rabi model, anisotropic Rabi model and asymmetric Rabi model, into…
We propose concrete protocols to realize quantum criticality due to excited-state quantum phase transitions (ESQPTs) experimentally in presumably the simplest and most resilient system involving a single trapped ion oscillating in a…
We propose an alternative, statistical, derivation of the Thermodynamic Bethe Ansatz based on the tree expansion of the Gaudin determinant. We illustrate the method on the simplest example of a theory with diagonal scattering and no bound…
The most advanced techniques using fault-tolerant quantum computers to estimate the ground-state energy of a chemical Hamiltonian involve compression of the Coulomb operator through tensor factorizations, enabling efficient block-encodings…
We propose a systematic procedure to optimize quantum state tomography protocols for continuous variable systems based on excitation counting preceded by a displacement operation. Compared with conventional tomography based on Husimi or…
For the generalized statistical mechanics based on the Tsallis entropy, a variational perturbation approximation method with the principle of minimal sensitivity is developed by calculating the generalized free energy up to the third order…
Effective operators have been used extensively to understand small deviations from the Standard Model in the search for new physics. So far there has been no general method to fit for small parameters when higher order corrections in these…
We apply a recently developed stochastic method to the Shastry-Sutherland model on 4x4 and 8x8 lattices. This method, which we call the Stochastic State Selection Method here, enables us to evaluate expectation values of powers of the…
An optimized Rayleigh-Schr\"{o}dinger expansion scheme of solving the functional Schr\"odinger equation with an external source is proposed to calculate the effective potential beyond the Gaussian approximation. For a scalar field theory…
A class of fast-slow Hamiltonian systems with potential $U_\varepsilon$ describing the interaction of non-ergodic fast and slow degrees of freedom is studied. The parameter $\varepsilon$ indicates the typical timescale ratio of the fast and…
We prove an analytical expression for the size of the gap between the ground and the first excited state of quantum adiabatic algorithm for the 3-satisfiability, where the initial Hamiltonian is a projector on the subspace complementary to…
We propose a new method of calculating electronically excited states that combines a density functional theory (DFT) based ground state calculation with a linear response treatment that employs approximations used in the time-dependent…
Convergence of three different expansion schemes at finite baryon chemical potentials, including the conventional Taylor expansion, the Pad\'e approximants, and the $T'$ expansion proposed recently in lattice QCD simulations, have been…
In the context of global/goal-oriented error estimation applied to computational mechanics, the need to obtain reliable and guaranteed bounds on the discretization error has motivated the use of residual error estimators. These estimators…
A loop expansion is implemented based on the path integral quantization of the light-cone $\phi^4$ field theory in 1+1 dimensions. The effective potential as a function of the zero-mode field $\omega$ is calculated up to two loop order and…