Coupling a Mobile Hole to an Antiferromagnetic Spin Background: Transient Dynamics of a Magnetic Polaron
Geoffrey Ji, Muqing Xu, Lev Haldar Kendrick, Christie Chiu, Justus C. Brüggenjürgen, Daniel Greif, Annabelle Bohrdt, Fabian Grusdt, Eugene Demler, Martin Lebrat, Markus Greiner
Understanding the interplay between charge and spin and its effects on transport is a ubiquitous challenge in quantum many-body systems. In the Fermi-Hubbard model, this interplay is thought to give rise to magnetic polarons, whose dynamics may explain emergent properties of quantum materials such as high-temperature superconductivity. In this work, we use a cold-atom quantum simulator to directly observe the formation dynamics and subsequent spreading of individual magnetic polarons. Measuring the density- and spin-resolved evolution of a single hole in a 2D Hubbard insulator with short-range antiferromagnetic correlations reveals fast initial delocalization and a dressing of the spin background, indicating polaron formation. At long times, we find that dynamics are slowed down by the spin exchange time, and they are compatible with a polaronic model with strong density and spin coupling. Our work enables the study of out-of-equilibrium emergent phenomena in the Fermi-Hubbard model, one dopant at a time.
Understanding the interplay between charge and spin and its effects on transport is a ubiquitous challenge in quantum many-body systems. In the Fermi-Hubbard model, this interplay is thought to give rise to magnetic polarons, whose dynamics may explain emergent properties of quantum materials such as high-temperature superconductivity. In this work, we use a cold-atom quantum simulator to directly observe the formation dynamics and subsequent spreading of individual magnetic polarons. Measuring the density- and spin-resolved evolution of a single hole in a 2D Hubbard insulator with short-range antiferromagnetic correlations reveals fast initial delocalization and a dressing of the spin background, indicating polaron formation. At long times, we find that dynamics are slowed down by the spin exchange time, and they are compatible with a polaronic model with strong density and spin coupling. Our work enables the study of out-of-equilibrium emergent phenomena in the Fermi-Hubbard model, one dopant at a time.
Understanding the interplay between charge and spin and its effects on transport is a ubiquitous challenge in quantum many-body systems.In the Fermi-Hubbard model, this interplay is thought to give rise to magnetic polarons, whose dynamics may explain emergent properties of quantum materials such as high-temperature superconductivity.In this work, we use a cold-atom quantum simulator to directly observe the formation dynamics and subsequent spreading of individual magnetic polarons.Measuring the density-and spin-resolved evolution of a single hole in a 2D Hubbard insulator with short-range antiferromagnetic correlations reveals fast initial delocalization and a dressing of the spin background, indicating polaron formation.At long times, we find that dynamics are slowed down by the spin exchange time, and they are compatible with a polaronic model with strong density and spin coupling.Our work enables the study of out-of-equilibrium emergent phenomena in the Fermi-Hubbard model, one dopant at a time.
Abstract Tremendous recent progress in the quantum simulation of the Hubbard model paves the way to controllably study doped antiferromagnetic Mott insulators. Motivated by these experimental advancements, we numerically study the real-time dynamics of a single hole created in an antiferromagnet on a square lattice, as described by the t–J model. Initially, the hole spreads ballistically with a velocity proportional to the hopping matrix element. At intermediate to long times, the dimensionality as well as the spin background determine the hole dynamics. A hole created in the ground state of a two dimensional (2D) quantum antiferromagnet propagates again ballistically at long times but with a velocity proportional to the spin exchange coupling, showing the formation of a magnetic polaron. We provide an intuitive explanation of this dynamics in terms of a parton construction, which leads to a good quantitative agreement with the numerical tensor network state simulations. In the limit of infinite temperature and no spin exchange couplings, the dynamics can be approximated by a quantum random walk on a Bethe lattice with coordination number z ̃ = 4 . Adding Ising interactions corresponds to an effective disordered potential, which can dramatically slow down the hole propagation, consistent with subdiffusive dynamics. The study of the hole dynamics paves the way for understanding the microscopic constituents of this strongly correlated quantum state.
The properties of mobile impurities in quantum magnets are fundamental for our understanding of strongly correlated materials and may play a key role in the physics of high-temperature superconductivity. Hereby, the motion of hole-like defects through an antiferromagnet has been of particular importance. It creates magnetic frustrations that lead to the formation of a quasiparticle, whose complex structure continues to pose substantial challenges to theory and numerical simulations. In this article, we develop a nonperturbative theoretical approach to describe the microscopic properties of such magnetic polarons. Based on the self-consistent Born approximation, which is provenly accurate in the strong-coupling regime, 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 magnetic polarons in the strongly interacting regime and find qualitative differences from predictions of previously applied truncation schemes. Our calculations reveal a remarkably high spatial symmetry of the polaronic magnetization cloud and a surprising misalignment between its orientation and the polaron crystal momentum. The developed framework opens up an approach to the microscopic properties of doped quantum magnets and will enable detailed analyses of ongoing experiments based on cold-atom quantum simulations of the Fermi-Hubbard model.
Obtaining a microscopic understanding of the dynamics in strongly correlated electronic systems has remained a challenge for many decades. The interplay between the spin and charge degrees of freedom in these materials at different temperatures and dopant concentrations is not well understood and is still an area of intense scientific research. Recently, quantum simulators based on ultracold atoms in optical lattices have emerged as a promising platform to probe strongly correlated fermionic systems. This thesis reports on the work carried out with a quantum gas microscope of ultracold fermionic Li-6, where Fermi-Hubbard systems are prepared and imaged with single site spin and density resolution. The main results of the thesis explore the microscopic dynamics underlying one-dimensional materials, where individual constituents such as the electron with charge e and spin-1/2 are not relevant to the description of the system anymore and are instead replaced by spin and charge excitations that can propagate independent of one another - a phenomenon called spin-charge separation. In our quantum simulator, we use analogous one-dimensional Fermi-Hubbard chains of Li-6, to perform time- and space-resolved microscopy of the spin and charge excitations following a local quench. By extracting their strikingly different velocities and showing an absence of binding between the excitations, we demonstrate spin-charge separation. Our microscopic technique also allows us to quantitatively extract the excess spin carried by the spin excitiation, connecting our results to the phenomenon of fractionalization. In another set of experiments, Fermi-Hubbard chains are probed at equilibrium and incommensurate spin correlations arising in the presence of both density doping and spin polarization are observed. The wavevector of these incommensurate correlations are found to have a linear dependence on doping and polarization. Finally, the effect of the spin-charge interplay is probed in the crossover from one to two dimensions. The spin correlations across dopants are seen to be dramatically different in two dimensions, and the strong antiferromagnetic correlations across dopants present in one dimension disappear. For a single dopant in a fully two dimensional system, the spin-charge interplay manifests as a distorted spin cloud surrounding the dopant, indicating the formation of a magnetic polaron. The experiments reported here demonstrate the power of a quantum simulator; by probing the physics of strongly correlated systems in real space with unprecedented resolution, we can zoom into emergent phenomena, validate theories and access regimes that are not possible in other experimental settings.
Due to significant progress in quantum gas microscopy in recent years, there is a rapidly growing interest in real-space properties of single mobile dopands created in correlated antiferromagnetic (AFM) Mott insulators. However, a detailed numerical description remains challenging, even for simple toy models. As a consequence, previous numerical simulations for large systems were largely limited to T = 0 . To provide guidance for cold-atom experiments, numerical calculations at finite temperature are required. Here, we numerically study the real-time properties of a single mobile hole in the 2D t − J model at finite temperature and draw a comparison to features observed at T = 0 . We find that a three-stage process of hole motion, which was reported at T = 0 , is valid even at finite temperature. However, already at low temperatures, the average hole velocity at long times is not simply proportional to the spin coupling, contrary to the T = 0 behavior. Comparing our finite-temperature numerical results with the experimental data from quantum gas microscopy we find a qualitative disagreement: in experiment, hole spreading speeds up with increasing J / t , while in our numerics it slows down. The latter is consistent with the numerical findings previously reported at T = 0 .
We study the real-time dynamics of a single hole in a 2D antiferromagnet with long-range couplings. Using an extended t – J model that includes nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping and superexchange, and the multiple Davydov Ansatz as a numerically accurate variational solver, we track hole-magnon dynamics on an 8 × 8 lattice. We show that even moderate frustrating NNN exchange qualitatively changes the magnetic polaron dynamics: frustration initially promotes transient self-localization but at longer times opens additional propagation channels that increase the root-mean-squared displacement. Our results emphasize that modest beyond-NN interactions can substantially modify magnetic polaron formation and transport, with implications for high- T c cuprates and cold-atom quantum simulators.