Related papers: Constrained sampling method for analytic continuat…
Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space time by means of a generalized Hamiltonian dynamics in an extra time variable $\tau$ which, at…
Diagrammatic expansions are a central tool for treating correlated electron systems. At thermal equilibrium, they are most naturally defined within the Matsubara formalism. However, extracting any dynamic response function from a Matsubara…
The accurate theoretical description of the dynamic properties of correlated quantum many-body systems such as the dynamic structure factor $S(\mathbf{q},\omega)$ constitutes an important task in many fields. Unfortunately, highly accurate…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
We develop a unified spectral-semigroup framework that connects real-time and imaginary-time quantum dynamics through analytic continuation. Within this formulation, evolution is expressed as an exponential reweighting of spectral…
The numerical simulation of quantum many-body dynamics is typically limited by the linear growth of entanglement with time. Recently numerical studies have shown, however, that for 1D Bethe-integrable models the simulation of local…
Monte Carlo simulations using entropic sampling to estimate the number of configurations of a given energy are a valuable alternative to traditional methods. We introduce {\it tomographic} entropic sampling, a scheme which uses multiple…
Boltzmann sampling based on Metropolis algorithm has been extensively used for simulating a canonical ensemble. An estimate of a mechanical property, like energy, of an equilibrium system, can be made by averaging over a large number…
Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may…
The average spectrum method is a promising approach for the analytic continuation of imaginary time or frequency data to the real axis. It determines the analytic continuation of noisy data from a functional average over all admissible…
Two major challenges of numeric analytic continuation---restoring the spectral density, $s(\omega)$, from the corresponding Matsubara correlator, $g(\tau)$---are (i) producing the most smooth/featureless answer for $s(\omega)$ without…
We present an analytical approach for describing spectrally constrained maximum entropy ensembles of finitely connected regular loopy graphs, valid in the regime of weak loop-loop interactions. We derive an expression for the leading two…
Effects of randomness on the spin-1/2 and 1 antiferromagnetic Heisenberg chains are studied using the quantum Monte Carlo method with the continuous-time loop algorithm. We precisely calculated the uniform susceptibility, string order…
Spectral analysis of the {\em adjoint} propagator in a suitable Hilbert space (and Lie algebra) of quantum observables in Heisenberg picture is discussed as an alternative approach to characterize infinite temperature dynamics of non-linear…
We revisit the problem of determining the real-frequency density response in quantum fluids via analytical continuation of imaginary-time quantum Monte Carlo data. We demonstrate that the average spectrum method (ASM) is capable of…
We analyze the bootstrap approach (a dual optimization method to the variational approach) to one-dimensional spin chains, leveraging semidefinite programming to extract numerical results. We study how correlation functions in the ground…
Our method proposes the efficient generation of samples from an unnormalized Boltzmann density by solving the underlying continuity equation in the low-rank tensor train (TT) format. It is based on the annealing path commonly used in MCMC…
In this paper, we derive corrections to the subleading logarithmic term of the entanglement entropy in systems with spontaneous broken continuous symmetry. Using quantum Monte Carlo simulations, we show that the improved scaling formula…
We present a review of the method we have elaborated to compute the correlation functions of the XXZ spin-1/2 Heisenberg chain. This method is based on the resolution of the quantum inverse scattering problem in the algebraic Bethe Ansatz…
A generic algorithm for the extraction of probabilistic (Bayesian) information about model parameters from data is presented. The algorithm propagates an ensemble of particles in the product space of model parameters and outputs. Each…