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Mott Transition Mott Physics Frustrated Magnet Spin Chain Metallic Ferromagnetism Magnetic Transition Theoretical Approaches

 Quantum spin chains

In one-dimensional (1D) systems, we can investigate anomalous features originating from strong quantum fluctuations in great detail owing to very accurate and reliable numerical and analytical techniques available for 1D systems. In addition, qunatum fluctuatioins in 1D generally tend to become more significant than those in higher dimensions. Thus, we can sometimes extract general features for strongly correlated systems through investigation of 1D systems and sometimes observe interesting features characteristic to 1D systems. Here, I introduce two topics for 1D quantum spin systesms: high-energy states in spin-1/2 quantum spin chains in a magnetic field [1] and quantum criticality of a spin-1 quantum spin chain with bond alternation [2]. The former will be a universal feature of quantum spin systems in a magnetic field, and the latter will be charactereristic to 1D chains.

 High-energy excitations of a spin-1/2 Heisenberg chain in a magnetic field [1]
@It is known that the excitaions of a spin-1/2 Heisenberg chain in zero magnetic field are explained in terms of spinons carrying a fractional qunatum number S = 1/2. In a magnetic field, it is also known that the low-energy excitations can be well explained in terms of a spinon-like quasiparticle in a magnetic field (psinon) and its anti-particle (anti-psinon). However, I found that spectral weights calculated using exact solutions with psinons and anti-psinons are insufficient to satisfy the sum rule, which implies that excitations other than combinations of psinons and antipsinons carry considerable spectral weights. By calculating the spectral weights of string solutions which had been considered to be not so important for dynamical properties, solutions with a 2-string (which can be regarded as a pair of anti-psinons) turned out to carry considerable spectral weights in the dynamical structure factor S+-(k, ω). The excitations of the 2-string solutions separate from the 2-spinon continuum in a magnetic field and form a continuum in the high-energy regime. As the magnetic field increases, the continuum shifts to higher energies with the spectral weight gradually lost. Eventually, just below the saturation field, it reduces to the 2-magnon bound states known in a ferromagnetic Heisenberg chain [1]. This high-energy continuum has quantitatively explained the high-energy states observed in neutron inelastic scattering experiments [1]. Note that the mechanism of the high-energy states is similar to that of the upper Hubbard band of a Hubbard chain [3], which can be intuitively understood by mapping the spin chain to the hard-core boson model with nearest neighbor repulsions [4].

 Quantum criticality and comparisons with experiments for a spin-1 chain with bond alternation [2]
Usually, antiferromagnets in high dimensions have antiferromagnetic long-range order. The excitation from the ordered ground state is well explained by spin-wave theory. Namely, the excitation can be understood as quantum fluctuations around the classical (S → ∞) spin configuration. On the other hand, antiferromangetic Heisenberg chains have no magnetic long-range order, and the low-energy behavior depends on the length of spin S. Specifically, spin chains with half-odd integer spin (S = 1/2, 3/2, 5/2, …) show gapless excitations from a quasi-long-range order with spin correlations decaying in a power-law with logarithmic corrections, whereas spin chains with integer spins (S = 1, 2, 3, …) show gapped excitaions (Haldane gap). This gap has been predicted to be tunable by the strength of bond alternation and to close at some ratio of the bond alternation. Because the compound [{Ni(333-tet)(μ-N3)}n](ClO4)n, which can be regarded as a spin-1 antiferromgantic chain, shows gapless behavior, I have performed quantum Monte Carlo simulations to confirm quantiatively whether it is a realization of the theoretically predicted gapless point [2]. The numerical results have well explained the finite temperature properties of the compound as those at the gapless point of the spin-1 Heinseberg chain with bond-alternation except a tiny deviation in the very low-temperature regime. In addition, quantum critical behavior has been clarified in detail through accurate determination of the ratio of the bond alternation at the gapless point and estimation of logarithmic corrections [2].


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© 2011 Masanori Kohno