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arXiv:2410.00904 · Physical review. B./Physical review. B

Kinetic magnetism and stripe order in the antiferromagnetic bosonic t − J model

Timothy J. Harris, Ulrich Schollwöck, Annabelle Bohrdt, Fabian Grusdt

Published Jun 1, 2026• 0 citations
arXivHTMLPDF

Abstract

Unraveling the microscopic mechanisms governing the physics of doped quantum magnets is key to advancing our understanding of strongly correlated quantum matter. Quantum simulation platforms, e.g., ultracold atoms in optical lattices or tweezer arrays, provide a powerful tool to investigate the interplay between spin and charge motion in microscopic detail. Here, in a twist, we disentangle the role of particle statistics from the physics of strong correlations by exploring the strong coupling limit of doped bosonic quantum magnets, specifically the antiferromagnetic (AFM) bosonic t − J model. Using large-scale density matrix renormalization group calculations, we map out the phase diagram on the two-dimensional square lattice at finite doping. In the low-doping regime, bosonic holes form partially filled stripes, akin to those observed in high- T c cuprates. As doping increases, a transition occurs to a partially polarized ferromagnetic (FM) phase, driven by the motion of mobile bosonic charge carriers forming Nagaoka polarons. At high doping or large t / J , the system evolves into a fully polarized FM. These findings shed light on the role of particle statistics in strongly correlated many-body systems, revealing connections to stripe formation and the physics of kinetic (Nagaoka-type) ferromagnetism. Our results may be realized in state-of-the-art quantum simulation platforms, including bosonic quantum gas microscopes, Rydberg atom tweezer arrays, and ultracold polar molecules, paving the way for future experimental studies of doped bosonic quantum magnets.

DOI
10.1103/djyg-5jtq

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Unraveling the microscopic mechanisms governing the physics of doped quantum magnets is key to advancing our understanding of strongly correlated quantum matter. Quantum simulation platforms, e.g., ultracold atoms in optical lattices or tweezer arrays, provide a powerful tool to investigate the interplay between spin and charge motion in microscopic detail. Here, in a twist, we disentangle the role of particle statistics from the physics of strong correlations by exploring the strong coupling limit of doped bosonic quantum magnets, specifically the antiferromagnetic (AFM) bosonic t − J model. Using large-scale density matrix renormalization group calculations, we map out the phase diagram on the two-dimensional square lattice at finite doping. In the low-doping regime, bosonic holes form partially filled stripes, akin to those observed in high- T c cuprates. As doping increases, a transition occurs to a partially polarized ferromagnetic (FM) phase, driven by the motion of mobile bosonic charge carriers forming Nagaoka polarons. At high doping or large t / J , the system evolves into a fully polarized FM. These findings shed light on the role of particle statistics in strongly correlated many-body systems, revealing connections to stripe formation and the physics of kinetic (Nagaoka-type) ferromagnetism. Our results may be realized in state-of-the-art quantum simulation platforms, including bosonic quantum gas microscopes, Rydberg atom tweezer arrays, and ultracold polar molecules, paving the way for future experimental studies of doped bosonic quantum magnets.
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Microscopically understanding competing orders in strongly correlated systems is a key challenge in modern quantum many-body physics. For example, the study of magnetic polarons and their relation to pairing in the Fermi-Hubbard model in different geometries remains one of the central questions, and may help to understand the mechanism underlying unconventional superconductivity in cuprates or transition metal dichalcogenides. With recent advances in analog quantum simulation of the Fermi-Hubbard model on nonbipartite lattices, frustrated physics can now be explored experimentally in systems lacking particle-hole symmetry. Here, we study the singly doped $t\ensuremath{-}J$ model on the triangular lattice, focusing on the competition between kinetic and magnetic frustration as a function of temperature. In doublon doped systems, we uncover a crossover between Nagaoka-type ferromagnetic (FM) correlations at high temperature and exchange mediated antiferromagnetic (AFM) order around the doublon at low temperature. For hole-doped systems, kinetic Haerter-Shastry-type AFM at high temperature as well as exchange interactions at low temperature favor ${120}^{\ensuremath{\circ}}$ order, strengthening magnetic correlations compared to the undoped system. In the ground state, the presence of AFM correlations throughout a wide range of interactions indicates confinement of both types of dopants. In this regime we firmly establish the presence of linear confining potentials via energy scaling arguments, supporting the picture of geometric strings in the frustrated triangular $t\ensuremath{-}J$ model.
We study kinetic magnetism for the Fermi-Hubbard models in triangular type lattices, including a zigzag ladder, four- and six-legged triangular cylinders and a full two-dimensional triangular lattice. We focus on the regime of strong interactions, U≫tU\gg tU≫t and filling factors around one electron per site. For temperatures well above the hopping strength, the Curie-Weiss form of the magnetic susceptibility suggests effective antiferromagnetic correlations for systems that are hole doped with respect to ν=1ν=1ν=1, and ferromagnetic correlations for systems with electron dopings. We show that these correlations arise from magnetic polaron dressing of charge carrier propagating in a spin incoherent Mott insulator. Effective interactions corresponding to these correlations can strongly exceed the magnetic super-exchange energy. In the case of hole doping, antiferromagnetic polarons originate from kinetic frustration of individual holes in a triangular lattice. In the case of electron doping, Nagaoka type ferromagnetic correlations are induced by propagating doublons. These results provide a theoretical explanation of recent experimental results in moire TMDC materials. To understand many-body states arising from antiferromagentic polarons at low temperatures, we study hole doped systems in finite magnetic fields. At low dopings and intermediate magnetic fields we find a magnetic polaron phase, separated from the fully polarized state by a metamagnetic transition. With decreasing magnetic field the system shows a tendency to phase separate, with hole rich regions forming antiferromagnetic spinbags. We demonstrate that direct observations of magnetic polarons in triangular lattices can be achieved in experiments with ultracold atoms, which allow measurements of three point hole-spin-spin correlations.
Kinetic-to-magnetic frustration crossover and linear confinement in the doped triangular t−Jt-Jt−J model
Microscopically understanding competing orders in strongly correlated systems is a key challenge in modern quantum many-body physics. For example, the study of magnetic polarons and their relation to pairing in the Fermi-Hubbard model in different geometries remains one of the central questions, and may help to understand the mechanism underlying unconventional superconductivity in cuprates or transition metal dichalcogenides. With recent advances in analog quantum simulation of the Fermi-Hubbard model on non-bipartite lattices, frustrated physics can now be explored experimentally in systems lacking particle-hole symmetry. Here, we study the singly doped t−Jt-Jt−J model on the triangular lattice, focusing on the competition between kinetic and magnetic frustration as a function of temperature. In doublon doped systems, we uncover a crossover between Nagaoka-type ferromagnetic (FM) correlations at high temperature and exchange mediated antiferromagnetic (AFM) order around the doublon at low temperature. For hole doped systems, kinetic Haerter-Shastry-type AFM at high temperature as well as exchange interactions at low temperature favor 120∘120^{\circ}120∘ order, strengthening magnetic correlations compared to the undoped system. In the ground state, the presence of AFM correlations throughout a wide range of interactions indicates confinement of both types of dopants. In this regime we firmly establish the presence of linear confining potentials via energy scaling arguments, supporting the picture of geometric strings in the frustrated triangular t−Jt-Jt−J model.
The interplay of spin and charge degrees of freedom is believed to underlie various unresolved phenomena in strongly correlated systems. Quantum simulators based on neutral atoms provide an excellent testbed for investigating such phenomena and resolving their microscopic origins. Up to now, the majority of experimental and theoretical studies has focused on systems with fermionic exchange statistics. Here we expand the existing cold atom toolbox through the use of negative temperature states, enabling us to realize an antiferromagnetic, bosonic t−Jt-Jt−J model in two spatial dimensions, subject to a strong staggered magnetic field in a quantum gas microscope. Through comparison of the spreading dynamics of a single hole in a Néel versus a spin-polarized initial state, we establish the relevance of memory effects resulting from the buildup of strong spin-charge correlations in the dynamics of charge carriers in antiferromagnets. We further numerically predict rich dynamics of pairs of doped holes, which we demonstrate to be bound by a similar memory effect, while their center-of-mass can expand freely. Our work paves the way for the systematic exploration of the effect of antiferromagnetic spin ordering on the properties of individual charge carriers as well as finite doping phases: Our study demonstrates that the staggered field can be used to single out the effect of antiferromagnetism and holds the prospect to prepare low-temperature states in the near future.