Related papers: Machine Learning Universal Bosonic Functionals
We investigate local and global properties of the one-dimensional Bose-Hubbard model with an external confining potential, describing an atomic condensate in an optical lattice. Using quantum Monte Carlo techniques we demonstrate that a…
Bosonic statistics give rise to remarkable phenomena, from the Hong-Ou-Mandel effect to Bose-Einstein condensation, with applications spanning fundamental science to quantum technologies. Modeling bosonic systems relies heavily on effective…
Expanding upon previous work, using the path-integral formalism we derive expressions for the one-particle reduced density matrix and the two-point correlation function for a quadratic system of bosons that interact through a general class…
We derive the self-energy functional theory for bosonic lattice systems with broken $U(1)$ symmetry by parametrizing the bosonic Baym-Kadanoff effective action in terms of one- and two-point self-energies. The formalism goes beyond other…
In this work, we propose a machine learning-based approach to address a specific aspect of the Quantum Marginal Problem: reconstructing a global density matrix compatible with a given set of quantum marginals. Our method integrates a…
The variational determination of the two-boson reduced density matrix is described for a one-dimensional system of $N$ (where $N$ ranges from $2$ to $10^4$) harmonically trapped bosons interacting via contact interaction. The ground-state…
A quantum theory of feedback of bosonic many-atom systems is formulated. The feedback-induced many-atom correlations are treated by use of a parameterized correlation function, for which closed equations of motion are derived. Therefrom the…
We revisit the machine-learning (ML) approach to the universal density functional $F[\mathbf{n}]$ of the one-dimensional Hubbard model with a site-dependent random potential $\mathbf{v}=\{v_{i}\}$. We generate exact ground-state data via…
While recent advances have established efficient quantum algorithms for preparing Gibbs states of finite-dimensional systems, comparable complexity results for bosonic and other infinite-dimensional models remain unexplored. We introduce…
We establish one-body reduced density-matrix functional theory for the canonical ensemble in a finite basis set at an elevated temperature. Including temperature guarantees differentiability of the universal functional by occupying all…
Quantum mechanical few-body systems in reduced dimensionalities can exhibit many interesting properties such as scale-invariance and universality. Analytical descriptions are often available for integer dimensionality, however, numerical…
We use density-matrix renormalization group, applied to a one-dimensional model of continuum Hamiltonians, to accurately solve chains of hydrogen atoms of various separations and numbers of atoms. We train and test a machine-learned…
One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory.…
A detailed analysis of density-functional theory for quantum-electrodynamical model systems is provided. In particular, the quantum Rabi model, the Dicke model, and a generalization of the latter to multiple modes are considered. We prove a…
These notes deal with the mean-field approximation for equilibrium states of N-body systems in classical and quantum statistical mechanics. A general strategy for the justification of effective models based on statistical independence…
We present a new, simple renormalization group method of investigating groundstate properties of interacting bosonic systems. Our method reduces the number of particles in a system, which makes numerical calculations possible for large…
We present an \textit{ab initio} theory for superconductors, based on a unique mapping between the statistical density operator at equilibrium, on the one hand, and the corresponding one-body reduced density matrix $\gamma$ and the…
Bosonic Gaussian unitaries are fundamental building blocks of central continuous-variable quantum technologies such as quantum-optic interferometry and bosonic error-correction schemes. In this work, we present the first time-efficient…
The ground-state correlation properties of a one-dimensional Bose system described by the Lieb-Liniger Hamiltonian are investigated by using exact quantum Monte Carlo techniques. The pair distribution function, static structure factor,…
The solution of complex many-body lattice models can often be found by defining an energy functional of the relevant density of the problem. For instance, in the case of the Hubbard model the spin-resolved site occupation is enough to…