Related papers: Exact solution for infinitely strongly interacting…
We derive exact results for a model of strongly-interacting spinless fermions hopping on a two-dimensional lattice. By exploiting supersymmetry, we find the number and type of ground states exactly. Exploring various lattices and limits, we…
We study the topological properties of superconductors with paired $j=\frac{3}{2}$ quasiparticles. Higher spin Fermi surfaces can arise, for instance, in strongly spin-orbit coupled band-inverted semimetals. Examples include the Bi-based…
An interacting spin-fermion model is exactly solved on an open chain. In a certain representation, it is the nearest-neighbor Hubbard model in the limit of infinite $U$ (local interaction). Exact solution of its complete energy…
We establish several properties of the solutions to the linear integral equations describing the infinite volume properties of the XXZ spin-1/2 chain in the disordered regime. In particular, we obtain lower and upper bounds for the dressed…
We investigate the two-body properties of a spin-1/2 Fermi gas subject to a spin-orbit coupling induced by laser fields. When an attractive s-wave interaction between unlike spins is present, the system may form a dimer bound state.…
We consider the many-body ground state of polarized fermions interacting via zero-range $\mathfrak{p}$-wave forces in a one-dimensional geometry. We rigorously prove that in the limit of infinite attractions spectral properties of any-order…
Exact two-dimensional analytic wave functions for an arbitrary number $N$ of contact-interacting lowest-Landau-level (LLL) spinful fermions are derived with the use of combined numerical and symbolic computational approaches via analysis of…
In the present work, we start from a minimal Hamiltonian for Fermi systems where the s-wave scattering is the only low energy constant at play. Many-Body Perturbative approach that is usually valid at rather low density is first discussed.…
For a fermion gas with equally spaced energy levels, the density and the pair correlation function are obtained. The derivation is based on the path integral approach for identical particles and the inversion of the generating functions for…
We consider a one-dimensional gas of spin-1/2 fermions interacting through $\delta$-function repulsive potential of an arbitrary strength. For the case of all fermions but one having spin up, we calculate time-dependent two-point…
We provide an analytically tractable toy model of an infinitely heavy impurity interacting with the spin-polarized gas of bath fermions via a contact potential in 1D and placed in a harmonic trap. The solution to this problem requires…
Highly polarized mixtures of atomic Fermi gases constitute a novel Fermi liquid. We demonstrate how information on thermodynamic properties may be used to calculate quasiparticle scattering amplitudes even when the interaction is resonant…
We study relativistic fermionic systems in $3+1$ spacetime dimensions at finite chemical potential and zero temperature, from a path-integral point of view. We show how to properly account for the $i\varepsilon$ term that projects on the…
A generalized Fermi-Bose mapping method is used to determine the exact ground states of several models of mixtures of strongly interacting ultracold gases in tight waveguides, which are generalizations of the Tonks-Girardeau (TG) gas (1D…
We carry out a detailed examination of the ground state property of few-boson system in a one-dimensional hard wall potential with a $\delta -$ split in the center. In the Tonks-Girardeau limit with infinite repulsion between particles, we…
We show that self-localized ground states can be created in the spin-balanced gas of fermions with repulsion between the spin components, whose strength grows from the center to periphery, in combination with the harmonic-oscillator (HO)…
A method is proposed for constructing an exact ground-state wave function of a two-dimensional model with spin 1/2. The basis of the method is to represent the wave function by a product of fourth-rank spinors associated with the sites of a…
A gas of ultracold $^6$Li atoms (effective spin 1/2) confined to an elongated trap with one-dimensional properties is a candidate to display three different phases: (i) fermions bound in Cooper-pair-like states, (ii) unbound spin-polarized…
We investigate the ground-state properties of ultracold two-component Fermi gases in the presence of a transverse harmonic potential, focusing on the strongly interacting regime in which pairs of fermions form tightly bound molecules. Using…
This thesis considers out-of-equilibrium dynamics of strongly interacting non-relativistic Fermi gases in several two and three dimensional geometries. The tools of second-order hydrodynamics and gauge-gravity duality will be utilized to…