Related papers: Finite Temperature Phase Transitions in the SU$(N)…
We perform large scale projector determinant quantum Monte-Carlo simulations to study the insulating states of the half-filled SU(6) Hubbard model on the square lattice. The transition from the antiferromagnetic state to the valence bond…
A quantum phase transition is typically induced by tuning an external parameter that appears as a coupling constant in the Hamiltonian. Another route is to vary the global symmetry of the system, generalizing, e.g., SU(2) to SU(N). In that…
We study low temperature properties of the Hubbard model for the bismuth nickelate, where degenerate orbitals in the nickel ions and a single orbital in the bismuth ions are taken into account, combining dynamical mean-field theory with the…
The finite-temperature phase diagram of the attractive Hubbard model is studied by means of the Dynamical Mean Field Theory. We first consider the normal phase of the model by explicitly frustrating the superconducting ordering. In this…
We study the finite temperature phase diagram of the Heisenberg-Kitaev model on a three dimensional hyperhoneycomb lattice. Using semiclassical analysis and classical Monte-Carlo simulations, we investigate quantum and thermal…
Various topics at the interface between condensed matter physics and the physics of ultra-cold fermionic atoms in optical lattices are discussed. The lectures start with basic considerations on energy scales, and on the regimes in which a…
We study the dissipative Fermi-Hubbard model in the limit of weak tunneling and strong repulsive interactions, where each lattice site is tunnel-coupled to a Markovian fermionic bath. For cold baths at intermediate chemical potentials, the…
Motivated by the possibility to load multi-color fermionic atoms in optical lattices, we study the entropy dependence of the properties of the one-dimensional antiferromagnetic SU(N) Heisenberg model, the effective model of the SU(N)…
We study phenomenologically on the basis of two bilinearly coupled Heisen- berg models the phase diagram of some ferrimagnetic substances. Calculations are performed with the help of Landau energy obtained through applying the…
Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultra-cold fermions confined in an optical lattice with a harmonic trapping…
We present rigorous results for the SU($n$) Fermi-Hubbard model on the railroad-trestle lattice. We first study the model with a flat band at the bottom of the single-particle spectrum and prove that the ground states exhibit SU($n$)…
Orbital degrees of freedom play an important role for understanding the emergence of unconventional quantum phases. Ultracold atomic gases in optical lattices provide a wonderful platform to simulate orbital physics. In this work, we…
The Hubbard model is reformulated in terms of different ``colored'' fermion species for the electrons or holes at different lattice sites. Antiferromagnetic ordering or d-wave superconductivity can then be described in terms of…
Temperature vs. chemical-potential phase diagrams of an SO(5) model for high-(T_c) cuprates are calculated by Monte Carlo simulation. There is a bicritical point where the second-order antiferromagnetism (AF) and superconductivity…
We investigate the zero-temperature phase diagram of two-orbital SU(N) fermionic models at incommensurate filling which are directly relevant to strontium and ytterbium ultracold atoms loading into a one-dimensional optical lattice. Using a…
Localized defects, unavoidable in real solids, may be simulated in (generically defect-free) cold-atom systems, e.g., via modifications of the optical lattice. We study the Hubbard model on a square lattice with single impurities, pairs of…
While the exact phase diagram of the Fermi-Hubbard model remains poorly understood despite decades of progress, nearly 60 years ago, Nagaoka proved that a single dopant in an otherwise half-filled Hubbard system can bring about…
When atoms are loaded into an optical lattice, the process of gradually turning on the lattice is almost adiabatic. In this paper we investigate how the temperature changes when going from the gapless superfluid phase to the gapped Mott…
We use determinant Quantum Monte Carlo (DQMC), in combination with the principal component analysis (PCA) approach to unsupervised learning, to extract information about phase transitions in several of the most fundamental Hamiltonians…
In this thesis, we study quantum phase transitions and topological phases in low dimensional fermionic systems. In the first part, we study quantum phase transitions and the nature of currents in one-dimensional systems, using field…