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The Journal of Physical Chemistry Letters

Probing Hole-Magnon Dynamics in an Antiferromagnet with Beyond-Nearest-Neighbor Couplings

Kaijun Shen, Kewei Sun, Shixu Luo, Maxim F. Gelin, Yang Zhao

Published Oct 27, 2025• 1 citation
Publisher

Abstract

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.

DOI
10.1021/acs.jpclett.5c03005

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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.
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.
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.
I investigate the motion of a single hole in 2D spin lattices with square and triangular geometries. While the spins have nearest neighbor Ising spin couplings J J , the hole is allowed to move only in 1D along a single line in the 2D lattice with nearest neighbor hopping amplitude t t . The non-equilibrium hole dynamics is initialized by suddenly removing a single spin from the thermal Ising spin lattice. I find that for any nonzero spin coupling and temperature, the hole is localized. This is an extension of the thermally induced localization phenomenon [Phys. Rev. Res. 6, 023325 (2024)] to the case, where there is a phase transition to a long-range ordered ferromagnetic phase. The dynamics depends only on the ratio of the temperature to the spin coupling, k_BT / |J| k B T / | J | , and on the ratio of the spin coupling to the hopping J/t J / t . I characterize these dependencies in great detail. In particular, I find universal behavior at high temperatures, common features for the square and triangular lattices across the Curie temperatures for ferromagnetic interactions, and highly distinct behaviors for the two geometries in the presence of antiferromagnetic interactions due geometric frustration in the triangular lattice.
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.
We study the impact of next-nearest-neighbor (NNN) hopping on the low-energy collective excitations of strongly correlated doped antiferromagnetic cuprate spin chains. Specifically, we use exact diagonalization and the density matrix renormalization group method to study the single-particle spectral function, the dynamical spin and charge structure factors, and the Cu LLL-edge resonant inelastic x-ray scattering (RIXS) intensity of the doped $t\text{\ensuremath{-}}t\ensuremath{'}\text{\ensuremath{-}}J$ model for a set of $t\ensuremath{'}$ values. We find evidence that the spin and charge degrees of freedom of the doped holes are not strictly separated anymore as $|t\ensuremath{'}|$ increases and identify the consequences of this in the dynamical response functions. The inclusion of NNN hopping couples the spinon and holon excitations, resulting in the formation of a spin polaron, where a ferromagnetic spin-polarization cloud dresses the doped carrier. The spin polaron manifests itself as additional spectral weight in the dynamical correlation functions, which appear simultaneously in the spin- and charge-sensitive channels. We also demonstrate that RIXS can provide a unique view of the spin polaron, due to its sensitivity to both the spin and charge degrees of freedom.