Spin chains in a field: Crossover from quantum to classical behavior

Parkinson, John; Bonner, Jill C.

doi:10.1103/physrevb.32.4703

Cited by 212 publications

(105 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As for the region 0 k/π 1/2, the spin-triplet spectrum is believed to be embedded in a continuum spectrum of a pair of magnons with the total spin-z component to be 0 [20]. The exact diagonalization for N = 14 indeed tells us that the lowest excitation at k = 0 is spin singlet, presumably a (−π, π) pair of spin-triplet magnons from k = ±π [5,13]. We believe that the spin-triplet magnon spectrum for spin-1 for the entire Brillouin zone has been determined for the first time by EPT.…”

mentioning

confidence: 99%

“…In particular, Haldane conjectured in 1983 that the half-odd integer and integer spins might behave essentially differently [3], which together with a field theoretic prediction of Affleck [4] for a logarithmic correction to the power-law behavior in the spin-spin correlation function in the spin-1 2 case, triggered an intensive study of HA ranging from the exact diagonalization [5,6] and Monte Carlo [7,8] to DMRG (density matrix renormalization group) [9][10][11]. These studies along with the Bethe ansatz solution for the spin-1 2 case [12] lead to a confirmation of the both claims.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Entanglement perturbation theory for the elementary excitation in one dimension

Chung¹,

Wang²

2009

Physics Letters A

View full text Add to dashboard Cite

The entanglement perturbation theory is developed to calculate the excitation spectrum in one dimension. Applied to the spin-1 2 antiferromagnetic Heisenberg model, it reproduces the des CloiseauxPearson Bethe ansatz result. As for spin-1, the spin-triplet magnon spectrum has been determined for the first time for the entire Brillouin zone, including the Haldane gap at k = π.PACS numbers: 71.10. Li, 02.90.+p, 71.10.Fd, 75.10.Jm The importance of elementary excitations in condensed matter systems may be best understood in the superfluid 4 He. The Tisza two-fluid model with the experimentally found phonon-roton spectrum explains fundamental properties of the superfluid 4 He [1]. Feynman's effort then to explain the roton spectrum is well known [2]. From the theorem of Bloch-Floquet, the elementary excitation with momentum k for a translationally invariant Hamiltonian H is written aswhere |g is the ground state and the summation over l extends over the entire lattice sites. The O l is a local cluster operator to be determined for a given Hamiltonian.In spite of a simplicity and validity of the expression (1), not much progress has been made along this line since the days of Feynman. The Heisenberg antiferromagnet (HA) described by the Hamiltonianis probably the best studied system concerning the excitation spectrum. In particular, Haldane conjectured in 1983 that the half-odd integer and integer spins might behave essentially differently [3], which together with a field theoretic prediction of Affleck [4] for a logarithmic correction to the power-law behavior in the spin-spin correlation function in the spin-1 2 case, triggered an intensive study of HA ranging from the exact diagonalization [5,6] and Monte Carlo [7,8] to DMRG (density matrix renormalization group) [9][10][11]. These studies along with the Bethe ansatz solution for the spin-1 2 case [12] lead to a confirmation of the both claims. Concerning the elementary excitation for the entire Brillouin zone, however, Takahashi's two attempts following the Feynman variational method for 4 He and a projector-Monte Carlo method were the only studies [13,14]. And none of the previous studies gave a serious consideration to the expression (1).In this Letter, we analyze (1) exactly for the HA (2) with periodic boundary conditions by the recently developed entanglement perturbation theory (EPT). EPT is a novel many-body method which takes into account correlations systematically. Its mathematical implementation is singular value decomposition (SVD), intuitively divide and conquer. EPT has addressed so far classical statistical mechanics [15], 1D quantum ground states [16] and 2D quantum ground states [17]. We here address the elementary excitation in one dimension. By EPT, we are not only free from a negative sign problem which is inherent to MC for quantum spins and fermions, but can also handle an order of magnitude larger systems than MC and DMRG. The key of the success lies in our ability of calculating the ground state |g precisely and most importantly in an u...

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

Entanglement perturbation theory for the elementary excitation in one dimension

Chung¹,

Wang²

2009

Physics Letters A

View full text Add to dashboard Cite

show abstract

“…For n ≥ 0.4N s the value of c n (N, 1) has already fallen below 5 for N ≤ 20, whereas for s = 1/2 this value is not reached until n > 0.75N s. In this sense, increasing s from 1/2 to 1 is a significant step on our way toward the classical limit, stated in item II of the previous section. Systems of larger intrinsic spins have also been studied in recent years, 17,18,38,39,40 but with less frequency than s = 1/2 and s = 1 systems. Since a knowledge of the spectral coefficients for s = 3/2, 2 and 5/2 is important for a number of molecular rings, these data are presented in .…”

Section: 34mentioning

confidence: 99%

Low-temperature magnetization and the excitation spectrum of antiferromagnetic Heisenberg spin rings

Engelhardt

Luban

2006

Phys. Rev. B

View full text Add to dashboard Cite

Accurate results are obtained for the low temperature magnetization versus magnetic field of Heisenberg spin rings consisting of an even number N of intrinsic spins s = 1/2, 1, 3/2, 2, 5/2, 3, 7/2 with nearest-neighbor antiferromagnetic (AF) exchange by employing a numerically exact quantum Monte Carlo method. A straightforward analysis of this data, in particular the values of the levelcrossing fields, provides accurate results for the lowest energy eigenvalue EN (S, s) for each value of the total spin quantum number S. In particular, the results are substantially more accurate than those provided by the rotational band approximation. For s ≤ 5/2, data are presented for all even N ≤ 20, which are particularly relevant for experiments on finite magnetic rings. Furthermore, we find that for s ≥ 3/2 the dependence of EN (S, s) on s can be described by a scaling relation, and this relation is shown to hold well for ring sizes up to N = 80 for all intrinsic spins in the range 3/2 ≤ s ≤ 7/2. Considering ring sizes in the interval 8 ≤ N ≤ 50, we find that the energy gap between the ground state and the first excited state approaches zero proportional to 1/N α , where α ≈ 0.76 for s = 3/2 and α ≈ 0.84 for s = 5/2. Finally, we demonstrate the usefulness of our present results for EN (S, s) by examining the Fe12 ring-type magnetic molecule, leading to a new, more accurate estimate of the exchange constant for this system than has been obtained heretofore.

show abstract

“…χ is the uniform spin susceptibility, and h c = 2J is the magnetic field above which the magnetization saturates [14,15]. Diagonalizing Equation (6) yields the following energy eigenvalues:…”

Section: The Magnetic Current In the Bond-mean Field Theorymentioning

confidence: 99%

Magnetic Transport in Spin Antiferromagnets for Spintronics Applications

Azzouz

2017

Symmetry

View full text Add to dashboard Cite

Abstract:Had magnetic monopoles been ubiquitous as electrons are, we would probably have had a different form of matter, and power plants based on currents of these magnetic charges would have been a familiar scene of modern technology. Magnetic dipoles do exist, however, and in principle one could wonder if we can use them to generate magnetic currents. In the present work, we address the issue of generating magnetic currents and magnetic thermal currents in electrically-insulating low-dimensional Heisenberg antiferromagnets by invoking the (broken) electricity-magnetism duality symmetry. The ground state of these materials is a spin-liquid state that can be described well via the Jordan-Wigner fermions, which permit an easy definition of the magnetic particle and thermal currents. The magnetic and magnetic thermal conductivities are calculated in the present work using the bond-mean field theory. The spin-liquid states in these antiferromagnets are either gapless or gapped liquids of spinless fermions whose flow defines a current just as the one defined for electrons in a Fermi liquid. The driving force for the magnetic current is a magnetic field with a gradient along the magnetic conductor. We predict the generation of a magneto-motive force and realization of magnetic circuits using low-dimensional Heisenberg antiferromagnets. The present work is also about claiming that what the experiments in spintronics attempt to do is trying to treat the magnetic degrees of freedoms on the same footing as the electronic ones.

show abstract

Spin chains in a field: Crossover from quantum to classical behavior

Abstract: . Spin chains in a field: Crossover from quantum to classical behavior. Phys. Rev. B 32, 4703 (1985). It appears that calculations on significantly longer chains are required to observe with confidence the large-N asymptotic limiting behavior.

Cited by 212 publications

References 50 publications

Entanglement perturbation theory for the elementary excitation in one dimension

Entanglement perturbation theory for the elementary excitation in one dimension

Low-temperature magnetization and the excitation spectrum of antiferromagnetic Heisenberg spin rings

Magnetic Transport in Spin Antiferromagnets for Spintronics Applications

Contact Info

Product

Resources

About