Related papers: Fermionic mean-field dynamics for spin systems bey…
In this work, we derive the time-dependent Hartree(-Fock) equations as an effective dynamics for fermionic many-particle systems. Our main results are the first for a quantum mechanical mean-field dynamics for fermions; in previous works,…
We introduce a new method for deriving the time-dependent Hartree or Hartree-Fock equations as an effective mean-field dynamics from the microscopic Schroedinger equation for fermionic many-particle systems in quantum mechanics. The method…
The time-dependent Hartree-Fock (TDHF) method is an approach to simulate the mean field dynamics of electrons within the assumption that the electrons move independently in their self-consistent average field and within the space of single…
Recent work has highlighted that the strong correlation inherent in spin Hamiltonians can be effectively reduced by mapping spins to fermions via the Jordan-Wigner transformation (JW). The Hartree-Fock method is straightforward in the…
The Jordan--Wigner transformation permits one to convert spin $1/2$ operators into spinless fermion ones, or vice versa. In some cases, it transforms an interacting spin Hamiltonian into a noninteracting fermionic one which is exactly…
We report on an implementation of the multiconfigurational time-dependent Hartree method (MCTDH) for spin-polarized fermions (MCTDHF). Our approach is based on a mapping for opera- tors in Fock space that allows a compact and efficient…
We formulate a time-dependent Fluctuating Local Field (TD-FLF) method for correlated fermion dynamics, extending the stationary FLF approach. The wavefunction is approximated as an ensemble of non-interacting states subject to a classical…
We introduce equations of motion for a parity-violating fermionic mean-field theory (PV-FMFT): a numerically efficient fermionic mean-field theory based on parity-violating fermionic Gaussian states (PV-FGS). This work provides explicit…
We consider quantum spin chains with a hidden free fermionic structure, distinct from the Jordan-Wigner transformation and its generalizations. We express selected local operators with the hidden fermions. This way we can exactly solve the…
The $\lambda \phi^4$ model in a finite volume is studied within a non-gaussian Hartree-Fock approximation (tdHF) both at equilibrium and out of equilibrium, with particular attention to the structure of the ground state and of certain…
A set of weakly interacting spin-1/2 Fermions, confined by a harmonic oscillator potential, and interacting with each other via a contact potential, is a model system which closely represents the physics of a dilute gas of two-component…
This article examines the time-dependent Hartree-Fock (TDHF) approximation of single-particle dynamics in systems of interacting fermions. We find the TDHF approximation to be accurate when there are sufficiently many particles and the…
The time-dependent Hartree and Hartree-Fock equations provide effective mean-field descriptions for the dynamics of large fermionic systems and play a fundamental role in many areas of physics. In this work, we rigorously derive the…
We revisit the derivation of the time-dependent Hartree-Fock equation for interacting fermions in a regime coupling a mean-field and a semiclassical scaling, contributing two comments to the result obtained in 2014 by Benedikter, Porta, and…
Microscopic methods and tools to describe nuclear dynamics have considerably been improved in the past few years. They are based on the time-dependent Hartree-Fock (TDHF) theory and its extensions to include pairing correlations and quantum…
We study the quantum dynamics of a large number of interacting fermionic particles in a constant magnetic field. In a coupled mean-field and semiclassical scaling limit, we show that solutions of the many-body Schr\"odinger equation…
Mapping spins to fermions via the Jordan-Wigner (JW) transformation can render mean-field (Hartree-Fock, HF) descriptions effective for strongly correlated spin systems. As established in recent work, the application of such approaches is…
The Jordan-Wigner transformation is applied to study magnetic properties of the quantum spin-1/2 $XX$ model on the diamond chain. Generally, the Hamiltonian of this quantum spin system can be represented in terms of spinless fermions in the…
We investigate a reformulation of the dynamics of interacting fermion systems in terms of a stochastic extension of Time Dependent Hartree-Fock equations. The noise is found from a path-integral representation of the evolution operator and…
We review recent results concerning the evolution of fermionic systems. We are interested in the mean field regime, where particles experience many weak collisions. For fermions, the mean field regime is naturally linked with a…