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arXiv:1201.0845 · Journal of Physics Conference Series

Relation between high-energy quasiparticles of quasi-one-dimensional antiferromagnets in a magnetic field and a doublon of a Hubbard chain

Masanori Kohno

Published Sep 28, 2011• 2 citations
arXivHTMLPDF

Abstract

In spin-1/2 one-dimensional Heisenberg antiferromagnets and anisotropic triangular Heisenberg antiferromagnets, high-energy states carrying considerable spectral weights have been observed in a magnetic field using inelastic neutron scattering. Such high-energy properties cannot be explained in terms of either Nambu-Goldstone bosons due to spontaneous breaking of continuous symmetries or quasiparticles in a Tomonaga-Luttinger liquid. Here, we show that the mechanism causing the high-energy states is analogous to that of the upper Hubbard band in the one-dimensional Hubbard model, by theoretically tracing the origin of the high-energy states back to string solutions of the Bethe ansatz.

DOI
10.1088/1742-6596/320/1/012021

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In spin-1/2 one-dimensional Heisenberg antiferromagnets and anisotropic triangular Heisenberg antiferromagnets, high-energy states carrying considerable spectral weights have been observed in a magnetic field using inelastic neutron scattering. Such high-energy properties cannot be explained in terms of either Nambu-Goldstone bosons due to spontaneous breaking of continuous symmetries or quasiparticles in a Tomonaga-Luttinger liquid. Here, we show that the mechanism causing the high-energy states is analogous to that of the upper Hubbard band in the one-dimensional Hubbard model, by theoretically tracing the origin of the high-energy states back to string solutions of the Bethe ansatz.
Spectral properties of the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field are investigated by using exact Bethe-ansatz solutions. We argue that not only quasiparticles called psinon and antipsinon but also a quasiparticle representing a 2-string in the Bethe ansatz plays an important role for dynamical properties in a magnetic field. Combined with psinon and antipsinon, the quasiparticle for a 2-string forms a continuum in the high-energy regime for transverse dynamical structure factor S +− ( κ,ω ). In the zero-field limit, the continuum is located on the mode of the lowest excited states in zero field called the des Cloizeaux-Pearson mode. In a magnetic field, the continuum separates from other low-energy continua, and reduces to the mode of bound states of overturned spins from the fully polarized state near the saturation field. We confirm the relevance through comparisons with available experimental results on the quasi-one-dimensional antiferromagnet CuCl 2 ·2N(C 5 D 5 ).
Based on the Bethe ansatz approach and inelastic neutron scattering experiments, we reveal the evolution of confinement of many-body Bethe strings in ordered regions of the quasi-one-dimensional antiferromagnet YbAlO3{\mathrm{YbAlO}}_{3}YbAlO3​. In the antiferromagnetic phase, the spin dynamics is dominated by confined length-1 Bethe strings, whose dominancy in the high-energy branch of the excitation spectrum yields to confined length-2 Bethe strings when the material is tuned to the spin-density-wave phase. In the thermal-induced disordered region, the confinement effect disappears, and the system restores the conventional quantum integrable physics of the one-dimensional Heisenberg model. Our results establish a unified picture based on a Bethe string for the spin dynamics in different magnetic phases of YbAlO3{\mathrm{YbAlO}}_{3}YbAlO3​, and thus provide profound insight into many-body quantum magnetism.
The spin fluctuations parallel to the external magnetic field in the ground state of the one-dimensional (1D) s=12s=\frac{1}{2}s=21​ Heisenberg antiferromagnet are dominated by a two-parameter set of collective excitations. In a cyclic chain of N sites and magnetization 0<Mz<N/2,0<{M}_{z}<N/2,0<Mz​<N/2, the ground state, which contains 2Mz{2M}_{z}2Mz​ spinons, is reconfigured as the physical vacuum for a different species of quasiparticles, identifiable in the framework of the coordinate Bethe ansatz by characteristic configurations of Bethe quantum numbers. The dynamically dominant excitations are found to be scattering states of two such quasiparticles. For $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty},$ these collective excitations form a continuum in $(q,\ensuremath{\omega})$ space with an incommensurate soft mode. Their matrix elements in the dynamic spin structure factor ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ are calculated directly from the Bethe wave functions for finite N. The resulting line- shape predictions for $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ complement the exact results previously derived via algebraic analysis for the exact two-spinon part of ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ in the zero-field limit. They are relevant for neutron-scattering experiments on quasi-1D antiferromagnetic compounds in a strong magnetic field.
Quantum dynamics of strongly correlated systems is a challenging problem. Although the low energy fractional excitations of one-dimensional integrable models are often well understood, exploring quantum dynamics in these systems remains challenging in the gapless regime, especially at intermediate and high energies. Based on the algebraic Bethe ansatz formalism, we study spin dynamics in a representative one-dimensional strongly correlated model, i.e., the antiferromagnetic spin-12\frac{1}{2}21​ XXZ chain with the Ising anisotropy, via the form-factor formulas. Various excitations at different energy scales are identified crucial to the dynamic spin structure factors under the guidance of sum rules. At small magnetic polarizations, gapless excitations dominate the low energy spin dynamics arising from the magnetic-field-induced incommensurability. In contrast, spin dynamics at intermediate and high energies is characterized by the two- and three-string states, which are multiparticle excitations based on the commensurate N\'eel ordered background. Our work is helpful for experimental studies on spin dynamics in both condensed matter and cold atom systems beyond the low energy effective Luttinger liquid theory. Based on an intuitive physical picture, we speculate that the dynamic feature at high energies due to the multiparticle antibound state excitations can be generalized to nonintegrable spin systems.
Using Bethe-ansatz solutions, this Letter uncovers a well-defined continuum in dynamical structure factor S+-(k,omega) of the spin-1/2 antiferromagnetic Heisenberg chain in magnetic fields. It comes from string solutions that continuously connect the mode of the lowest-energy excitations in the zero-field limit and that of bound states of overturned spins from the ferromagnetic state near the saturation field. The relevance to real materials is confirmed through comparisons with experimental results.
This dissertation is devoted to theoretical studies of strongly interacting one-dimensional and quasi one-dimensional electron systems. The properties of one-dimensional electron systems can be studied within the bosonization technique, which presents fermions as collective bosonic density excitations. The power of this approach is the ability to treat electron-electron interaction exactly in the low-energy limit. The approach predicts the failure of Fermi liquid and an absence of long-range order in one-dimensions. The low-energy description of one-dimensional interacting systems is called the Tomonaga-Luttinger liquid theory. For example, the edges of quantum Hall systems are one-dimensional and described by a chiral Tomonaga-Luttinger liquid. Another example is a quantum spin Hall system with helical edge states, which are also described by a Tomonaga-Luttinger liquid. In our first work, a study of magnetized edge states of quantum spin-Hall system is presented. A magnetic field dependent signature of such edges is obtained, which can be verified in a Coulomb drag experiment. The second part of the dissertation is devoted to quasi-one dimensional antiferromagnetic lattices. A spatially anisotropic lattice antiferromagnet can be viewed as an array of one dimensional spin chains coupled in a way to match the lattice symmetry. This allows to use the non-Abelian bosonization technique to describe the low-energy physics of spin chains and study the inter-chain interactions perturbatively. The work presented in the dissertation studies the effect of Dzyaloshinskii-Moriya interaction on the magnetic phase diagram of the spatially anisotropic kagome antiferromagnet. We predict a Dzyaloshinskii-Moriya interaction driven phase transition from Neel to Neel+dimer state. In the third work, a novel model of the fractional quantum Hall effect is given. Wave functions of two-dimensional electrons in strong and quantizing magnetic field are essentially one-dimensional. That invites one to use the one-dimensional phenomenological bosonization to describe the density fluctuations of the two-dimensional interacting electrons in magnetic field. Remarkably, the constructed trial bosonized fermion operator describing the electron states with a fixed Landau gauge momentum is effectively two-dimensional.