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arXiv:cond-mat/0608467 · Physics Letters A

Possible observation of “string excitations” of a hole in a quantum antiferromagnet

Efstratios Manousakis

Published Dec 2, 2006• 14 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2006.11.066

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String excitations of a hole in a quantum antiferromagnet and photoelectron spectroscopy

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The aim of the present paper is twofold. The first goal is to show that high resolution angle-resolved photoelectron spectra from cuprates indicate the presence of string-like excitations of the quasihole excitation in a quantum antiferromagnet. In order to compare with the experimental intensity plots, we calculate the spectral function of the $t\ensuremath{-}J$ and the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}\ensuremath{-}J$ models within the self-consistent Born approximation for widely accepted values of the parameters of these models. The main features of the high resolution photoelectron spectra are in general agreement with the results based on the above models and can be understood by considering not only the lowest-energy quasiparticle peak but, also, the higher-energy string-like excitations of the hole. These features are (a) the energy-momentum dispersion of the string-like excitations, (b) the momentum dependence of the spectral weight of the quasiparticle peak, and (c) the way in which the spectral weight of the lowest-energy quasiparticle peak is transferred to higher-energy string excitations, including the fact that it vanishes near the $\ensuremath{\Gamma}$ point. The second goal of the present paper is to make the case that a proper analysis of both the numerical results obtained from these models and of the experimental results, suggests a theoretical picture for the internal structure of the hole-quasiparticle and a string-exchange pairing mechanism due to strong antiferromagnetic correlations among the background spins. We find that, using a simple model in which the Hilbert space is restricted to states of only unbroken strings attached to the holes and in which the holes are connected with unbroken strings, we can provide a good quantitative description of the most accurate numerical results. We find that the holes experience an effective interaction due to a string-exchange mechanism which is characterized by a rather large string tension and this can provide pairing energy scales much larger than those suggested by spin-fluctuation-mediated pairing models. In addition, it is argued that such string-exchange interaction tends to bind holes in a bound state with the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry.

arXiv:cond-mat/0702288•Physical Review B•Jan 8, 2007•79 citations
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.
We investigate a rare instance of an exactly solvable nonequilibrium many-body problem. In particular, we derive an exact solution for the nonequilibrium dynamics of an initially localized single hole in a fully anisotropic antiferromagnetic Bethe lattice, described by the $t\ensuremath{-}{J}_{z}$ model. The solvability of the model relies on the fractal self-similarity of Bethe lattices, making it possible to compute the full motion of the hole as it moves through the lattice, as well as exactly characterizing the resulting effect on spin-spin correlation functions. We find that the hole remains bound to its initial position with large aperiodic oscillations in the hole density distribution. We track this back to the irregular pattern of the eigenenergies of the magnetic polaron ground state and string excitations, which we also determine exactly.
The aim of the present paper is twofold. The first goal is to show that high resolution angle-resolved photoelectron spectra from cuprates indicate the presence of string-like excitations of the quasihole excitation in a quantum antiferromagnet. In order to compare with the experimental intensity plots, we calculate the spectral function of the $t\ensuremath{-}J$ and the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}\ensuremath{-}J$ models within the self-consistent Born approximation for widely accepted values of the parameters of these models. The main features of the high resolution photoelectron spectra are in general agreement with the results based on the above models and can be understood by considering not only the lowest-energy quasiparticle peak but, also, the higher-energy string-like excitations of the hole. These features are (a) the energy-momentum dispersion of the string-like excitations, (b) the momentum dependence of the spectral weight of the quasiparticle peak, and (c) the way in which the spectral weight of the lowest-energy quasiparticle peak is transferred to higher-energy string excitations, including the fact that it vanishes near the $\ensuremath{\Gamma}$ point. The second goal of the present paper is to make the case that a proper analysis of both the numerical results obtained from these models and of the experimental results, suggests a theoretical picture for the internal structure of the hole-quasiparticle and a string-exchange pairing mechanism due to strong antiferromagnetic correlations among the background spins. We find that, using a simple model in which the Hilbert space is restricted to states of only unbroken strings attached to the holes and in which the holes are connected with unbroken strings, we can provide a good quantitative description of the most accurate numerical results. We find that the holes experience an effective interaction due to a string-exchange mechanism which is characterized by a rather large string tension and this can provide pairing energy scales much larger than those suggested by spin-fluctuation-mediated pairing models. In addition, it is argued that such string-exchange interaction tends to bind holes in a bound state with the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry.