Quantum simulations with ultracold atoms, aided by advanced numerical techniques, provide an unprecedented microscopic perspective on strongly correlated quantum matter. In this seminar I will present experimental and theoretical results for 2D Hubbard and t-J models supporting a microscopic picture of spinons and chargons forming bound states at low doping. I will show that we have reached a detailed theoretical understanding of their internal structure, which is captured by a simple effective theory inspired by atomic and molecular physics. At strong coupling, the chargon properties feature several universal aspects. In the seminar I will discuss ARPES spectra and generalizations thereof, non-equilibrium quench dynamics and several equilibrium properties of doped charge carriers.
We introduce topological phases of matter distinguished by ground state spin expectation value textures in the Brillouin zone with non-trivial topological charge, corresponding to momentum-space skyrmions detectable using spin-ARPES, which we call topological skyrmion phases of matter. Such topological phases are protected by a generalized particle-hole symmetry present in all centrosymmetric superconductors, and occur in effectively non-interacting systems. When spin-orbit coupling is non-negligible, the magnitude of the ground state spin expectation value may change as a function of momentum yet still correspond to momentum-space skyrmions with well-defined, quantized topological charge so long as the magnitude is finite everywhere in the Brillouin zone (since the skyrmion number is computed with the normalized spin vectors). Across some lines in phase space, however, the magnitude can pass through zero at certain points in the Brillouin zone through smooth changes in the ground state spin texture possible without closing of direct gaps in the dispersion, thereby changing the skyrmion number from one integer-quantized value to another. Thus, in addition to a more conventional topological phase transition which occurs with closing of the superconducting gap, we observe a second type of topological phase transition which occurs without closing of any direct gaps in the dispersion. This is the first counterexample to the flat band limit assumption used in construction, for instance, of Wilson loops, the entanglement spectrum, and the ten-fold way classification scheme of topological phases of matter. We show each kind of topological phase transition occurs in the phase space of an established tight-binding model for Sr2RuO4 with spin-triplet superconductivity. In remaining time, we will discuss more recent work.