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  • 1
    Electronic Resource
    Electronic Resource
    Correlation functions of the XY model (abstract) (1990)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 67 (1990), S. 5457-5457 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Recently an elegant and quite powerful finite-system approach to determine the exponents ηx and ηz from simple spectral properties has been proposed. For critical systems, the two exponents can be expressed in terms of finite-size spectral gaps as follows: η(N)x=2ΔE01(N)/ΔE(N), η(N)z=2ΔE00(N)/ΔE(N). Here ΔE(N) is the finite-size gap between the ground state (SzT=0,k=0) and the lowest excitation at k=2π/N; ΔE01(N) is the gap to the lowest ||SzT||=1 excitations (at k=π), and ΔE00(N) is the gap to the next lowest SzT=0 excited state. The η(N) sequence is then extrapolated to N→∞. For XY models, differences between s=1/2 and s≥1 appear. For s=1/2, the excitations which determine ΔE00(N) and ΔE(N) are degenerate, which implies that ηz=1/2, in agreement with the exact analytic result. For spin-1, however, the next lowest SzT=0 state is located at k=2π/N instead of k=π, and is therefore identical to the state which determines the gap ΔE.The resulting equality ΔE=ΔE00 implies ηz=2, as in the spin-1/2 case. In fact, our result corresponds to power-law decay for all s, and hence we differ from Schulz and Ziman, who claim the out-of-plane correlation function decays exponentially for s〉1/2. For the in-plane correlation function, the spectral gap method again agrees with the exact result ηx=0.5 for s=1/2. The consensus of this and other numerical methods for s=1 gives a value ηx(approximately-equal-to)0.20, considerably different from the case of s=1/2. Hence it is tempting to conjecture that ηx is s dependent, implying that XY models belong to different universality classes for different s. However, a finite-size study of the conformal anomaly produces the result that c=1, independent of s. This situation is further discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.345843
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  • 2
    Electronic Resource
    Electronic Resource
    Excitation spectra of generalized antiferromagnetic Heisenberg spin chains (abstract) (1988)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 63 (1988), S. 4160-4160 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We compare the excitation spectra in the presence of a magnetic field of a number of integrable (exactly solvable) and nonintegrable quantum spin chains of various spin value s. The archetypal Bethe-ansatz integrable model is the s= 1/2 Heisenberg antiferromagnet (HB AFM). The excitation spectra are characterized by a soft mode which tracks across the Brillouin zone as the field increases to its saturation value. A class of Bethe-ansatz integrable models with SU(2) symmetry and the general spin s display excitation spectra qualitatively similar to the spin- 1/2 model above, for all s. A second class of Bethe-ansatz integrable models has SU(n) symmetry, where n=2s+1. Like the SU(2) integrable chains, these models have gapless excitation spectra, but the basic Brillouin zone changes from k=±2π/(2s+1)a. Studies show that periodicity of the SU(3) member of the class changes (increases) as the field increases to saturation. For both classes of integrable models, there is a single type of excitation pattern which is generically similar for all s. In the case of the other models, on the other hand, numerical studies show that the excitations divide into at least two distinct classes. In the case of the s=1 HB AFM, at high fields (corresponding to SzT=N,N−1, . . .,N/2) the excitations map approximately onto the complete set of excitations for s= 1/2 , whereas at low fields (SzT=N/2,N/2−1,. . .,0) the excitations have notable classical character. In the case of the s=1 model with pure biquadratic exchange, one set of excitations, corresponding to SzT even (SzT=N,N−2,. . .,2,0), again shows an approximate mapping to the complete excitation set for s= 1/2 . The second class of excitations, corresponding to SzT odd, are very different. They are symmetric about k=±π/2a for all SzT, i.e., correspond to a basic Brillouin zone of ±π/2a.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.340526
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  • 3
    Electronic Resource
    Electronic Resource
    Scaling behavior in the S=1 antiferromagnetic XXZ chain (abstract) (1988)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 63 (1988), S. 3560-3560 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A recent remarkable prediction by Haldane is the 1D integer spin antiferromagnets of XXZ type should show strikingly different T=0 phase behavior from their counterparts with half-integer spin. The consensus of a wide variety of numerical evidence is in support of the Haldane prediction. However, one aspect which has been particularly difficult to confirm has been the behavior in the vicinity of the critical point Δ=Δ2. The point Δ2 is predicted to be a second-order transition in the universality class of the transverse Ising model at its critical field. It has been numerically established that at Δ=Δ2∼1.18–1.20, the Haldane gap disappears and an excited SzT=0 state becomes degenerate with the SzT=0 ground state for Δ≥Δ2. The mapping to the transverse Ising model implies the existence in the limit N→∞ of an infinite continuum of scaling states quasi-degenerate with the ground state(s) at Δ=Δ2. Numerical calculations to determine the presence of these scaling states have been performed up to N=12 spins for the spin-1 XXZ model. The development of this scaling continuum is only apparent for large N, when a class of k=0, SzT=0 high-lying spectral excitations develop a minimum in the vicinity of Δ∼1.18 which intensifies with increasing N. These excitations extrapolate well below the lower edge of the triplet continuum, and we conclude these are the Haldane scaling states. This conclusion is reinforced by a detailed study of the corresponding excitations for the spin-1/2 transverse Ising model. However, we also find a class of k=0, ||SzT||=1 excitations which show similar scaling behavior in the vicinity of Δ2. These states were not included in the Haldane prediction. The implications for the behavior of the correlation functions at Δ2 are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.340716
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  • 4
    Electronic Resource
    Electronic Resource
    Nonintegrability and quantum spin chains (1987)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 61 (1987), S. 3950-3952 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: This study concerns the concept of nonintegrability in quantum many-body systems, which is related to the important and unresolved problem of quantum chaos. Our findings strongly indicate that nonintegrability affects the reliability of many approximation techniques which have proved to be successful in the study of integrable models. This report is based on finite-size studies of the low-lying spectral excitations of both integrable and nonintegrable 1D quantum spin models. In integrable cases, the characteristic excitation pattern of the infinite system is apparent even in relatively short chains. This is generally not the case in nonintegrable systems where we observe several classes of excitations with qualitatively different character. In some situations, the nature of the lowest-lying excitations actually changes with increasing system size, which makes finite-size studies very vulnerable to misleading conclusions if care is not taken.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.338594
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  • 5
    Electronic Resource
    Electronic Resource
    Unusual critical behavior in a bilinear-biquadratic exchange Hamiltonian (1987)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 61 (1987), S. 4432-4434 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We have performed a variety of numerical studies on the general bilinear-biquadratic spin-1 Hamiltonian H/J=∑Ni=1[Si⋅Si+1 −β(Si⋅Si+1)2], over the range 0≤β≤∞. The model is Bethe Ansatz integrable at the special point β=1, where the spectrum is gapless, but is otherwise believed to be nonintegrable. Affleck has predicted that an excitation gap opens up linearly in the vicinity of β=1. Our studies involving spectral excitations (dispersion spectra), scaled-gap, and finite-size scaling calculations are not consistent with the Affleck prediction. The situation appears complex, with novel crossover effects occurring in both regimes, β〈1 and β〉1, complicating the analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.338400
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  • 6
    Electronic Resource
    Electronic Resource
    Heisenberg spin chains: Quantum-classical crossover and the Haldane conjecture (1985)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 57 (1985), S. 3319-3321 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A comprehensive investigation has been made of the spectral excitations and static properties of Heisenberg antiferromagnetic chains of spin 1/2, 1, 3/2, and 2, using Lanczös, Bethe Ansatz, and Monte Carlo techniques. An unusual and unanticipated crossover mechanism for spin chains with 1/2≤S≤∞ has been discovered. The validity of the Haldane conjecture concerning the presence of a spectral excitation gap for integer-spin chains has been investigated by exact finite chains calculations of (a) the primary singlet-triplet excitation gap, (b) higher excitation gaps, and (c) the Fourier transform of the ground state correlation functions. A new Monte Carlo method has extended the spin-1 gap calculations to N=32.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.335134
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  • 7
    Electronic Resource
    Electronic Resource
    Efficient lateral minority carrier transport in proton-implanted p-type silicon (1995)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 67 (1995), S. 88-90 
    Details
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A highly efficient lateral transport mechanism has been observed in stable defect layers (SDL) in p-type silicon. The SDLs were produced by proton implantation followed by rapid thermal anneal. Photogenerated carriers have been collected at a Schottky junction several millimeters away from the generation site. This transport distance is more than 30 times the diffusion length in comparable bulk material. A model is proposed in which bending of the energy bands near the SDL expels majority carriers, leaving no substantial recombination mechanism for minority carriers trapped in the layer. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.115517
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  • 8
    Electronic Resource
    Electronic Resource
    A coupled-cluster study of the ground-state energy and properties of an anisotropic quantum spin lattice model exhibiting antiferromagnetism in various phases (1991)
    Springer
    Theoretical chemistry accounts 80 (1991), S. 181-205 
    Details
    ISSN: 1432-2234
    Keywords: Coupled cluster method ; Quantum spin lattice models ; XXZ-model Hamiltonian ; Low-dimensional anisotropic quantum antiferromagnets ; Phase transitions ; Calculation of staggered magnetization and correlation functions ; Ground states and excited states
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary We extend the domain of applicability of the coupled-cluster method (CCM) to include quantum-mechanical spin-1/2 systems on discrete lattices. We study the specific case of anisotropic antiferromagnetic interactions described by the nearest-neighbour XXZ-model Hamiltonian. The isotropic version of this model on a two-dimensional (2-d) square lattice is of great current interest as a possible description of the interactions between the electrons in the singly-occupied $$d_{x^2 - y^2 } $$ orbitals on the copper atoms in the ceramic copper oxide materials displaying high-temperature superconductivity. Although very few exact results are known for the 2-d XXZ-model, its 1-d counterpart has been exactly solved by Bethe-ansatz techniques, and we therefore use it here as a benchmark for our new CCM techniques. Even starting with the classical Néel state as the model reference state, we find that the CCM is capable at relatively low levels of truncation of giving accurate values for the ground-state energies. In this regard, we discuss several new CCM truncation hierarchies which have not previously been applied to either atoms and molecules or continuous extended systems. Furthermore, the method gives a good qualitative description of most of the known or anticipated behaviour of the correlation functions, order parameters, and elementary excitations over an entire (zero-temperature) phase, right up to the transition point, as the anisotropy is varied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01119619
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  • 9
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    Sign rules for anisotropic quantum spin systems (2000)
    American Physical Society
    Details
    Publication Date: 2000-03-01
    Print ISSN: 0163-1829
    Electronic ISSN: 1095-3795
    Topics: Physics
    Published by American Physical Society
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  • 10
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    Magnon-Magnon and Exciton-Magnon Interaction Effects on Antiferromagnetic Spectra (1968)
    American Physical Society
    Details
    Publication Date: 1968-07-15
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
    Published by American Physical Society
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