Related papers: A variational approach to the partition function o…
Two improvements with respect to previous formulations are presented for the calculation of the partition function $\mathcal{Z}$ of small, isolated and interacting many body systems. By including anharmonicities and employing a variational…
The Lipkin-Meshkov-Glick is a simple, but not trivial, model of a quantum many-body system which allows us to solve the many-body Schr\"odinger equation without making any approximation. The model, which in its unperturbed case is composed…
{Many-body quantum states at thermal equilibrium are ubiquitous in nature. Investigating their dynamical properties is a formidable task due to the complexity of the Hilbert space they live in. Quantum computers may have the potential to…
The Lipkin-Meshkov-Glick (LMG) model was devised to test the validity of different approximate formalisms to treat many-particle systems. The model was constructed to be exactly solvable and yet non-trivial, in order to capture some of the…
Based on the path integral representation of the partition function of a many body system with separable two body interaction we propose a systematic extension of the perturbed static path approximation (PSPA) to lower temperatures.…
The Lipkin-Meshkov-Glick model is used to examine the validity of some approximate methods in a many-body theory at finite temperatures. Namely, the thermal random phase approximation (TRPA) and the thermal renormalized random phase…
Variational representations of quantum states abound and have successfully been used to guess ground-state properties of quantum many-body systems. Some are based on partial physical insight (Jastrow, Gutzwiller projected, and fractional…
Using the new variational approach proposed recently for a systematic improvement of the locally harmonic Feynman-Kleinert approximation to path integrals we calculate the partition function of the anharmonic oscillator for all temperatures…
We introduce a non-linear differential flow equation for density matrices that provides a monotonic decrease of the free energy and reaches a fixed point at the Gibbs thermal state. We use this equation to build a variational approach for…
In this work, we present a compact analytical approximation for the quantum partition function of systems composed of quantum oscillators. The proposed formula is general and applicable to an arbitrary number of oscillators described by a…
Variational quantum algorithms have emerged as a powerful tool for harnessing the potential of near-term quantum devices to address complex challenges across quantum science and technology. Yet, the robust and scalable quantification of…
A variational Perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls' inequality, a perturbative expansion scheme for the…
Interacting quantum systems illustrate complex phenomena including phase transitions to novel ordered phases. The universal nature of critical phenomena reduces their description to determining only the transition temperature and the…
We develop a variational approach at finite temperature that incorporates many-body correlation self-consistently. The grand potential is constructed in terms of Green's function expressed by the variational parameters. We apply this…
Precise variational solutions are given for problems involving diverse fermionic and bosonic $N=2-7$-body systems. The trial wave functions are chosen to be combinations of correlated Gaussians, which are constructed from products of the…
The key problem of statistical physics standing over one hundred years is how to exactly calculate the partition function (or free energy) of many-body interaction systems, which severely hinders application of the theory for realistic…
A precise variational solution to $N$=2--6-body problems is reported. The trial wave functions are chosen to be combinations of correlated Gaussians, which facilitate a fully analytical calculation of the matrix elements. The nonlinear…
Current methods to describe the thermodynamic behavior of many-particle systems are often based on perturbation theory with an unperturbed system consisting of free particles. Therefore, only a few methods are able to describe both strongly…
We present a novel generic framework to approximate the non-equilibrium steady states of dissipative quantum many-body systems. It is based on the variational minimization of a suitable norm of the quantum master equation describing the…
The possibility to simulate the properties of many-body open quantum systems with a large number of degrees of freedom is the premise to the solution of several outstanding problems in quantum science and quantum information. The challenge…