Disordered impenetrable two-component fermions in one dimension

We study the one-dimensional Hubbard model for two-component fermions with infinitely strong on-site repulsion (t - 0 model) in the presence of disorder. Our analytical treatment demonstrates that the type of disorder drastically changes the nature of the emerging phases. The case of spin-independent disorder can be treated as a single-particle problem with Anderson localization. On the contrary, recent numerical findings show that spin-dependent disorder, which can be realized as a random magnetic field, leads to the many-body localization-delocalization transition. We find an explicit analytic expression for the matrix elements of the random magnetic field between the eigenstates of the t - 0 model with potential disorder on a finite lattice. Analysis of the matrix elements supports the existence of the many-body localization-delocalization transition in this system and provides an extended physical picture of the random magnetic field.</p

Driven-Dissipative Time Crystalline Phases in a Two-Mode Bosonic System with Kerr Nonlinearity

For the driven-dissipative system of two coupled bosonic modes in a nonlinear cavity resonator, we demonstrate a sequence of phase transitions from a trivial steady state to two distinct dissipative time crystalline phases. These effects are already anticipated at the level of the semiclassical analysis of the Lindblad equation using the theory of bifurcations and are further supported by the full quantum treatment. The system is predicted to exhibit different dynamical phases characterized by an oscillating nonequilibrium steady state with nontrivial periodicity, which is a hallmark of time crystals. We expect that these phases can be directly probed in various cavity QED experiments

Driven-Dissipative Time Crystalline Phases in a Two-Mode Bosonic System with Kerr Nonlinearity

For the driven-dissipative system of two coupled bosonic modes in a nonlinear cavity resonator, we demonstrate a sequence of phase transitions from a trivial steady state to two distinct dissipative time crystalline phases. These effects are already anticipated at the level of the semiclassical analysis of the Lindblad equation using the theory of bifurcations and are further supported by the full quantum treatment. The system is predicted to exhibit different dynamical phases characterized by an oscillating nonequilibrium steady state with nontrivial periodicity, which is a hallmark of time crystals. We expect that these phases can be directly probed in various cavity QED experiments