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arXiv:2106.14510 · Physical review. B./Physical review. B

Spatial structure of magnetic polarons in strongly interacting antiferromagnets

K. Knakkergaard Nielsen, M. A. Bastarrachea-Magnani, Thomas Pohl, Georg M. Bruun

Published Oct 21, 2021• 25 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.104.155136

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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.
Adding a dopant to an antiferromagnetic spin background disturbs the magnetic order and leads to the formation of a quasiparticle coined the magnetic polaron, which plays a central role in understanding strongly correlated materials. Recently, remarkably detailed insights into the spatial properties of such polarons have been obtained using atoms in optical lattices. Motivated by this we develop a nonperturbative scheme for calculating the wave function of the magnetic polaron in a bilayer antiferromagnet using the self-consistent Born approximation. The scheme includes an infinite number of spin waves, which is crucial for an accurate description of the most interesting regime of strong correlations. Utilizing the developed wave function, we explore the spatial structure of the polaron dressing cloud consisting of magnetically frustrated spins surrounding the hole. Mimicking the nonmonotonic behavior of the antiferromagnetic order, we find that the dressing cloud first decreases and then increases in size with increasing interlayer hopping. The increase reflects the decrease in the magnetic order as a quantum phase transition to a disordered state is approached for large interlayer hopping. We, furthermore, find that the symmetry of the ground state dressing cloud changes as the interlayer coupling increases. Our results should be experimentally accessible using quantum simulation with optical lattices.
The physics of strongly correlated fermions described by Hubbard or t − J models in the underdoped regime—relevant for high-temperature superconductivity in cuprate compounds—remains a subject of ongoing debate. In particular, the nature of charge carriers in this regime is poorly understood, in part due to the unusual properties of their spectral function. In this Letter, we present unbiased numerical results for the one-hole spectral function in a t − J model at finite temperatures. Our study provides valuable insights into the underlying physics of magnetic (or spin-) polaron formation in a doped antiferromagnet (AFM). For example, we find how the suppression of spectral weight outside the magnetic Brillouin zone—a precursor of Fermi arc formation–disappears with increasing temperature, revealing nearly-deconfined spinon excitations of the undoped AFM. The pristine setting we consider can be directly explored using quantum simulators. Our calculations demonstrate that coherent quasiparticle peaks associated with magnetic polarons can be observed up to temperatures T > J above the spin-exchange J , routinely obtained in such experiments. This paves the way for future studies of the fate of magnetic polarons in the pseudogap phase.
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.
We develop a nonperturbative theory for hole dynamics in antiferromagnetic spin lattices, as described by the t-J model. This is achieved by generalizing the self-consistent Born approximation to nonequilibrium systems, making it possible to calculate the full time-dependent many-body wave function. Our approach reveals three distinct dynamical regimes, ultimately leading to the formation of magnetic polarons. Following the initial ballistic stage of the hole dynamics, coherent formation of string excitations gives rise to characteristic oscillations in the hole density. Their damping eventually leaves behind magnetic polarons that undergo ballistic motion with a greatly reduced velocity. The developed theory provides a rigorous framework for understanding nonequilibrium physics of defects in quantum magnets and quantitatively explains recent observations from cold-atom quantum simulations in the strong coupling regime.
The interplay of spin and charge degrees of freedom, introduced by doping mobile holes into a Mott insulator with strong antiferromagnetic (AFM) correlations, is at the heart of strongly correlated matter such as high-Tc{T}_{c}Tc​ cuprate superconductors. Here, we capture this interplay in the strong coupling regime and propose a trial wave function of mobile holes in an AFM. Our method provides a microscopic justification for a class of theories which describe doped holes moving in an AFM environment as mesonlike bound states of spinons and chargons. We discuss a model of such bound states from the perspective of geometric strings, which describe a fluctuating lattice geometry introduced by the fast motion of the chargon, relative to the spinon. This is demonstrated to give rise to short-range hidden string order, signatures of which have recently been revealed by ultracold atom experiments at elevated temperatures. We present evidence for such short-range hidden string correlations also at zero temperature by performing numerical density-matrix renormalization-group simulations. To test our microscopic approach, we calculate the ground-state energy and dispersion relation of a hole in an AFM, as well as the magnetic polaron radius, and obtain good quantitative agreement with advanced numerical simulations at strong coupling. We discuss extensions of our analysis to systems without long-range AFM order to systems with short-range magnetic correlations.