Session W28: Quantum Simulation of the Doped 2D Fermi-Hubbard Model

String Patterns in the Doped Hubbard Model

Quantum simulation is rapidly emerging as a powerful technique to understand the physics of strongly correlated materials. Quantum gas microscopy of ultracold fermionic atoms in an optical lattice is perfectly suited to study the Fermi-Hubbard model, a model widely believed to capture the physics of high-temperature superconductivity. We realize a Fermi-Hubbard antiferromagnet and investigate the interplay between hole motion and spin order through doping the antiferromagnet. In addition to using conventional observables such as the spin correlation function and the staggered magnetization, we explore the potential for new pattern-based microscopic observables for quantum simulation of strongly correlated materials.   

Spectroscopic probes for doped quantum magnets -- new directions

Single-particle spectral functions, which are usually measured using photoemission experiments in electron systems, contain direct information about fractionalization and the quasiparticle excitation spectrum. In this talk, I will present recent developments that enable angle-resolved photo-emission spectroscopy (ARPES) of the Fermi-Hubbard model using ultra cold atoms in optical lattices. 

I will discuss numerical results for the one-dimensional t-J model, where a sharp asymmetry in the distribution of spectral weight appears, that can be explained by a slave-fermion mean-field theory of the spin excitations (spinons). While in one dimension the spin (spinon) and charge (chargon) excitations are deconfined, several theories suggest that in two dimensions, dopants can be understood as bound states of these partons. 

Recent progress in the microscopic description of mobile dopants allows us to conjecture a one-to-one relation of the one-dopant spectral function and the properties of the constituting spinons in the undoped parent antiferromagnet (AFM). Using time-dependent matrix product state calculations of the spectral function of a single hole doped into a two-dimensional Heisenberg AFM, we thoroughly test this hypothesis and obtain excellent agreement with our semi-analytical predictions. 

We directly probe the microscopic nature of the spinon-chargon bound states through a new extension of ARPES, which uncovers long-lived rotational resonances. Similar to Regge trajectories in high-energy physics, which reflect the quark structure of mesons, we establish a linear dependence of the rotational energy on the super-exchange coupling. 

Our findings suggest that the rich physics of lightly doped cuprates may originate from an emergent parton structure.   

From Polaronic Metals to Hole Pairing - Exploring Fermi-Hubbard Systems using Quantum Gas Microscopy

More than 30 years ago, Richard Feynman outlined his vision of a quantum simulator for carrying out complex calculations on physical problems. Today, his dream is a reality in laboratories around the world. This has become possible by using complex experimental setups of thousands of optical elements, which allow atoms to be cooled to Nanokelvin temperatures, where they almost come to rest. Recent experiments with quantum gas microscopes allow for an unprecedented view and control of artificial quantum matter in new parameter regimes and with new probes. In our atomic fermionic quantum gas microscope, we can detect both charge and spin degrees of freedom simultaneously, thereby gaining maximum information on the intricate interplay between the two in the Fermi Hubbard model. In my talk, I will show how we can reveal hidden magnetic order, directly image individual magnetic polarons, probe the fractionalisation of spin and charge in dynamical experiments, reveal the crossover from a polaronic metal to a Fermi liquid when continuously increasing the doping in the system. Finally, I wil present latest results on the observation of hole pairing and density wave formation in mixed dimensional Fermi Hubbard ladders. For the first time we thereby have access to directly probe microscopic correlation properties of quantum matter and to explore its real space resolved dynamical features also far from equilibrium.   

Magnetic polarons in- and out-of equilibrium in strongly interacting antiferromagnets

We develop a non-perturbative theoretical framework to describe the microscopic properties of magnetic polarons formed by holes hopping in an anti-ferromagnetic background on a square lattice. Based on the self-consistent Born approximation, we obtain a complete description of the polaron wave function by solving a set of Dyson-like equations that permit to compute relevant spin-hole correlation functions. We apply this new method to analyze the spatial structure of the magnetic polaron, which is shown to have a remarkably high symmetry and a surprising misalignment between its orientation and the crystal momentum. Our theory is then generalised to the out-of-equilibrium case, and we derive an expression for the time-dependent non-perturbative wave-function of the hole after it is initially created at a given lattice site. Using this wave function, we calculate the hole-dynamics and find excellent agreement with recent experimental results both for short and for long times. We end by discussing magnetic polarons in other lattice geometries.