Related papers: Gaussian phase-space representations for fermions
We present numerical methods to solve the Generalized Hartree-Fock theory for fermionic systems in lattices, both in thermal equilibrium and out of equilibrium. Specifically, we show how to determine the covariance matrix corresponding to…
The phase structure of Nambu-Jona-Lasinio model with N-component fermions in curved space-time is studied in the leading order of the 1/N expansion. The effective potential for composite operator $\bar{\psi}\psi$ is calculated by using the…
Quantization of the system comprising gravitational, fermionic and electromagnetic fields is developed in the loop representation. As a result we obtain a natural unified quantum theory. Gravitational field is treated in the framework of…
A general framework for analyzing the recently discovered phase transitions in the steady state of dissipation-driven open quantum systems is still missing. In order to fill this gap we extend the so-called fidelity approach to quantum…
We propose a general extended coherent state approach to the qubit (or fermion) and multi-mode boson coupling systems. The application to the spin-boson model with the discretization of a bosonic bath with arbitrary continuous spectral…
We introduce a new method for representing the low energy subspace of a bosonic field theory on the qubit space of digital quantum computers. This discretization leads to an exponentially precise description of the subspace of the…
In this lecture we present a brief outline of boson Fock space stochastic calculus based on the creation, conservation and annihilation operators of free field theory, as given in the 1984 paper of Hudson and Parthasarathy. We show how a…
Quantum computers are the ideal platform for quantum simulations. Given enough coherent operations and qubits, such machines can be leveraged to simulate strongly correlated materials, where intricate quantum effects give rise to…
Bosonic qubits are a promising route to building fault-tolerant quantum computers on a variety of physical platforms. Studying the performance of bosonic qubits under realistic gates and measurements is challenging with existing analytical…
A unified approach to the analysis of quantum phase transitions in some different Curie-Weiss models is proposed such that they are treated and analyzed under the same general scheme. This approach takes three steps: balancing the quantum…
Generalised Dyson boson-fermion mappings are considered. These are techniques used in the analysis of the quantum many-body problem, and are instances of so-called boson expansion methods. A generalised Dyson boson-fermion mapping is a…
We consider the entropy and decoherence in fermionic quantum systems. By making a Gaussian Ansatz for the density operator of a collection of fermions we study statistical 2-point correlators and express the entropy of a system fermion in…
As large-scale multimode Gaussian states begin to become accessible in the laboratory, their representation and analysis become a useful topic of research in their own right. The graphical calculus for Gaussian pure states provides powerful…
Hydrodynamic theories offer successful approaches that are capable of simulating the otherwise difficult-to-compute dynamics of quantum many-body systems. In this work we derive, within the positive-P phase-space formalism, a new stochastic…
We present efficient circuits that can be used for the phase space tomography of quantum states. The circuits evaluate individual values or selected averages of the Wigner, Kirkwood and Husimi distributions. These quantum gate arrays can be…
Based on the Bogoliubov non-ideal gas model, we discuss the energy spectrum and phase transition of the superfluid Fermi gas of atoms with a weak attractive interaction on the canonical noncommutative space. Because the interaction of a…
Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many body systems. As with all numerical integration of differential equations, the initial conditions of the system being…
Simulating time evolution is one of the most natural applications of quantum computers and is thus one of the most promising prospects for achieving practical quantum advantage. Here, we develop quantum algorithms to extract thermodynamic…
P representation techniques, which have been very successful in quantum optics and in other fields, are also useful for general bosonic quantum dynamical many-body calculations such as Bose-Einstein condensation. We introduce a…
This is an introductory lecture to the theory of degenerate Fermi gases, in the context of present experiments on atomic Fermi gases. In part one, some properties of the ideal Fermi gas are presented, including a discussion of the…