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arXiv:1901.01113 · Physical review. B./Physical review. B

Microscopic spinon-chargon theory of magnetic polarons in the t−J model

Fabian Grusdt, Annabelle Bohrdt, Eugene Demler

Published Jun 17, 2019• 61 citations
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Abstract

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-${T}_{c}$ 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.

DOI
10.1103/physrevb.99.224422

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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.
Sub-dimensional magnetic polarons in the one-hole doped SU(3) ttt-JJJ model
The physics of doped Mott insulators is at the heart of strongly correlated materials and is believed to constitute an essential ingredient for high-temperature superconductivity. In systems with higher SU(N) spin symmetries, even richer magnetic ground states appear at a filling of one particle per site compared to the case of SU(2) spins, but their fate upon doping remains largely unexplored. Here we address this question by studying a single hole in the SU(3) ttt-JJJ model, whose undoped ground state features long-range, diagonal spin stripes. By analyzing both ground state and dynamical properties utilizing the density matrix renormalization group, we establish the appearence of magnetic polarons consisting of chargons and flavor defects, whose dynamics is constrained to a single effective dimension along the ordered diagonal. We semi-analytically describe the system using geometric string theory, where paths of hole motion are the fundamental degrees of freedom. With recent advances in the realization and control of SU(N) Fermi-Hubbard models with ultracold atoms in optical lattices, our results can directly be observed in quantum gas microscopes with single-site resolution. Our work suggests the appearance of intricate ground states at finite doping constituted by emergent, coupled Luttinger liquids along diagonals, and is a first step towards exploring a wealth of physics in doped SU(N) Fermi-Hubbard models on various geometries.
The physics of doped Mott insulators is at the heart of strongly correlated materials and is believed to constitute an essential ingredient for high-temperature superconductivity. In systems with higher SU(N)\mathrm{SU}(N)SU(N) spin symmetries, even richer magnetic ground states appear at a filling of one particle per site compared to the case of SU(2)\mathrm{SU}(2)SU(2) spins, but their fate upon doping remains largely unexplored. Here we address this question by studying a single hole in the SU(3) $t\text{\ensuremath{-}}J$ model whose undoped ground state features long-range, diagonal spin stripes. By analyzing both ground-state and dynamical properties utilizing the density matrix renormalization group, we establish the appearence of magnetic polarons consisting of chargons and flavor defects whose dynamics is constrained to a single effective dimension along the ordered diagonal. We semi-analytically describe the system using geometric string theory, where paths of hole motion are the fundamental degrees of freedom. With recent advances in the realization and control of SU(N)\mathrm{SU}(N)SU(N) Fermi-Hubbard models with ultracold atoms in optical lattices, our results can directly be observed in quantum gas microscopes with single-site resolution. Our work suggests the appearance of intricate ground states at finite doping constituted by emergent, coupled Luttinger liquids along diagonals, and is a first step towards exploring a wealth of physics in doped SU(N)\mathrm{SU}(N)SU(N) Fermi-Hubbard models on various geometries.
When a mobile hole is moving in an anti-ferromagnet it distorts the surrounding Neel order and forms a magnetic polaron. Such interplay between hole motion and anti-ferromagnetism is believed to be at the heart of high-Tc superconductivity in cuprates. We study a single hole described by the t-Jz model with Ising interactions between the spins in 2D. This situation can be experimentally realized in quantum gas microscopes. When the hole hopping is much larger than couplings between the spins, we find strong evidence that magnetic polarons can be understood as bound states of two partons, a spinon and a holon carrying spin and charge quantum numbers respectively. We introduce a microscopic parton description which is benchmarked by comparison with results from advanced numerical simulations. Using this parton theory, we predict a series of excited states that are invisible in the spectral function and correspond to rotational excitations of the spinon-holon pair. This is reminiscent of mesonic resonances observed in high-energy physics, which can be understood as rotating quark antiquark pairs. We also apply the strong coupling parton theory to study far-from equilibrium dynamics of magnetic polarons observable in current experiments with ultracold atoms. Our work supports earlier ideas that partons in a confining phase of matter represent a useful paradigm in condensed-matter physics and in the context of high-Tc superconductivity. While direct observations of spinons and holons in real space are impossible in traditional solid-state experiments, quantum gas microscopes provide a new experimental toolbox. We show that, using this platform, direct observations of partons in and out-of equilibrium are possible. Extensions of our approach to the t-J model are also discussed. Our predictions in this case are relevant to current experiments with quantum gas microscopes for ultracold atoms.
It is a widely accepted view that the interplay of spin and charge degrees of freedom in doped antiferromagnets (AFMs) gives rise to the rich physics of high-temperature superconductors. Nevertheless, it remains unclear how effective low-energy degrees of freedom and the corresponding field theories emerge from microscopic models, including $t\ensuremath{-}J$ and Hubbard Hamiltonians. A promising view comprises that the charge carriers have a rich internal parton structure on intermediate scales, but the interplay of the emergent partons with collective magnon excitations of the surrounding AFM remains unexplored. Here we study a doped one-dimensional spin chain in a staggered magnetic field and demonstrate that it supports a zoo of various long-lived excitations. These include magnons, mesonic pairs of spinons and chargons along with their rovibrational excitations, and tetra-parton bound states of mesons and magnons. We identify these types of quasiparticles in various spectra using density-matrix renormalization group simulations. Moreover, we introduce a strong-coupling theory describing the polaronic dressing and molecular binding of mesons to collective magnon excitations. The effective theory can be solved by standard tools developed for polaronic problems and can be extended to study similar physics in two-dimensional doped AFMs in the future. Experimentally, the doped spin-chain in a staggered field can be directly realized in quantum gas microscopes.
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.
In strongly correlated quantum materials, the behavior of charge carriers is dominated by strong electron-electron interactions. These can lead to insulating states with spin order, and upon doping to competing ordered states including unconventional superconductivity. The underlying pairing mechanism remains poorly understood however, even in strongly simplified theoretical models. Recent advances in quantum simulation allow to study pairing in paradigmatic settings, e.g. in the t-J t − J and t-J_z t − J z Hamiltonians. Even there, the most basic properties of paired states of only two dopants, such as their dispersion relation and excitation spectra, remain poorly studied in many cases. Here we provide new analytical insights into a possible string-based pairing mechanism of mobile holes in an antiferromagnet. We analyze an effective model of partons connected by a confining string and calculate the spectral properties of bound states. Our model is equally relevant for understanding Hubbard-Mott excitons consisting of a bound doublon-hole pair or confined states of dynamical matter in lattice gauge theories, which motivates our study of different parton statistics. Although an accurate semi-analytic estimation of binding energies is challenging, our theory provides a detailed understanding of the internal structure of pairs. For example, in a range of settings we predict heavy states of immobile pairs with flat-band dispersions - including for the lowest-energy d d -wave pair of fermions. Our findings shed new light on the long-standing question about the origin of pairing and competing orders in high-temperature superconductors.