Exact Momentum Distribution of a Fermi Gas in One Dimension

I consider general interacting systems of quantum particles in one spatial dimension. These consist of bosons or fermions, which can have any number of components, arbitrary spin or a combination thereof, featuring low-energy two- and multiparticle interactions. The single-particle dispersion can be Galilean (non-relativistic), relativistic, or have any other form that may be relevant for the continuum limit of lattice theories. Using an algebra of generalized functions, stat...

We consider a system of one-dimensional non-interacting fermions in external harmonic confinement. Using an efficient Green's function method we evaluate the exact profiles and the pair correlation function, showing a direct signature of the Fermi statistics and of the single quantum-level occupancy. We also study the dynamical properties of the gas, obtaining the spectrum both in the collisionless and in the collisional regime. Our results apply as well to describe a one-dim...

We present an exact mapping of models of interacting fermions onto boson models. The bosons correspond to collective excitations in the initial fermionic models. This bosonization is applicable in any dimension and for any interaction between fermions. We show schematically how the mapping can be used for Monte Carlo calculations and argue that it should be free from the sign problem. Introducing superfields we derive a field theory that may serve as a new way of analytical s...

Various sophisticated approximation methods exist for the description of quantum many-body systems. It was realized early on that the theoretical description can simplify considerably in one-dimensional systems and various exact solutions exist. The focus in this introductory paper is on fermionic systems and the emergence of the Luttinger liquid concept.

Due to the vast growth of the many-body level density with excitation energy, its smoothed form is of central relevance for spectral and thermodynamic properties of interacting quantum systems. We compute the cumulative of this level density for confined one-dimensional continuous systems with repulsive short-range interactions. We show that the crossover from an ideal Bose gas to the strongly correlated, fermionized gas, i.e., partial fermionization, exhibits universal behav...

Usually, we study the statistical behaviours of noninteracting Fermions in finite (mainly two and three) dimensions. For a fixed number of fermions, the average energy per fermion is calculated in two and in three dimensions and it becomes equal to 50 and 60 per cent of the fermi energy respectively. However, in the higher dimensions this percentage increases as the dimensionality increases and in infinite dimensions it becomes 100 per cent. This is an intersting result, at l...

We present a Green's function method for the evaluation of the particle density profile and of the higher moments of the one-body density matrix in a mesoscopic system of N Fermi particles moving independently in a linear potential. The usefulness of the method is illustrated by applications to a Fermi gas confined in a harmonic potential well, for which we evaluate the momentum flux and kinetic energy densities as well as their quantal mean-square fluctuations. We also study...

In a series of ten papers, of which this is the first, we prove that the temperature zero renormalized perturbation expansions of a class of interacting many-fermion models in two space dimensions have nonzero radius of convergence. The models have "asymmetric" Fermi surfaces and short range interactions. One consequence of the convergence of the perturbation expansions is the existence of a discontinuity in the particle number density at the Fermi surface. Here, we present a...

We consider translation invariant quantum systems in thermodynamic limit. We argue that their energy-momentum spectra should have shapes consistent with effective models involving quasiparticles. Our main example is second quantized homogeneous interacting Fermi gas in a large cubic box with periodic boundary conditions, at zero temperature. We expect that its energy-momentum spectrum has a positive energy gap and a positive critical velocity.

We propose a new method for the evaluation of the particle density and kinetic pressure profiles in inhomogeneous one-dimensional systems of non-interacting fermions, and apply it to harmonically confined systems of up to N=1000 fermions. The method invokes a Green's function operator in coordinate space, which is handled by techniques originally developed for the calculation of the density of single-particle states from Green's functions in the energy domain. In contrast to ...