S=1/2 magnetic chains as domain wall systems

Mikeska, H. J.; Miyashita, Seiji; Ristow, Gerald H.

doi:10.1088/0953-8984/3/17/015

Cited by 13 publications

(10 citation statements)

References 26 publications

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“…Therefore the time evolution of the high-energy state |ini for J z > 1 is identical to that for J ′ z = −J z < −1, where |ini is a low-energy state. At the quantum phase transition from the ferromagnetic state to the critical phase at J ′ z = −1 the ground state, a kink state for J ′ z < −1 (if we impose the boundary condition spin up on the left boundary and spin down on the right boundary) 13 , changes drastically to a state with no kink and power-law correlations for J ′ z > −1. Therefore, our initial state is very close to an eigenstate -the ground state -for J ′ z < −1, but not for J ′ z > −1.…”

Section: Long-time Properties Of the Time-evolutionmentioning

confidence: 99%

Real-time dynamics in spin-12chains with adaptive time-dependent density matrix renormalization group

et al. 2005

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We investigate the influence of different interaction strengths and dimerizations on the magnetization transport in antiferromagnetic spin 1/2 XXZ-chains. We focus on the real-time evolution of the inhomogeneous initial state | ↑ . . . ↑↓ . . . ↓ in using the adaptive time-dependent densitymatrix renormalization group (adaptive t-DMRG). Time-scales accessible to us are of the order of 100 units of time measured in /J for almost negligible error in the observables. We find ballistic magnetization transport for small S z S z -interaction and arbitrary dimerization, but almost no transport for stronger S z S z -interaction, with a sharp crossover at J z = 1. Additionally, we perform a detailed analysis of the error made by the adaptive time-dependent DMRG using the fact that the evolution in the XX-model is known exactly. We find that the error at small times is dominated by the error made by the Trotter decomposition whereas for longer times the DMRG truncation error becomes the most important, with a very sharp crossover at some "runaway" time. Overall, errors are extremely small before the "runaway" time.

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Section: Long-time Properties Of the Time-evolutionmentioning

confidence: 99%

Real-time dynamics in spin-12chains with adaptive time-dependent density matrix renormalization group

et al. 2005

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“…and therefore decays as n −n , provided the argument α remains fixed at some finite value. If N ≫ 1, and assuming α is indeed fixed, then the correction terms in (13) can be neglected so long as the center of the eigenstate wavepacket is not near the boundaries of the chain.…”

Section: Quantum Solution (Exact)mentioning

confidence: 99%

Bloch oscillations of magnetic solitons in anisotropic spin-12chains

Kyriakidis

Loss

1998

Phys. Rev. B

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We study the quantum dynamics of soliton-like domain walls in anisotropic spin-1/2 chains in the presence of magnetic fields. In the absence of fields, domain walls form a Bloch band of delocalized quantum states while a static field applied along the easy axis localizes them into Wannier wave packets and causes them to execute Bloch oscillations, i.e. the domain walls oscillate along the chain with a finite Bloch frequency and amplitude. In the presence of the field, the Bloch band, with a continuum of extended states, breaks up into the Wannier-Zeeman ladder-a discrete set of equally spaced energy levels. We calculate the dynamical structure factor S zz (q, ω) in the one-soliton sector at finite frequency, wave vector, and temperature, and find sharp peaks at frequencies which are integer multiples of the Bloch frequency. We further calculate the uniform magnetic susceptibility and find that it too exhibits peaks at the Bloch frequency. We identify several candidate materials where these Bloch oscillations should be observable, for example, via neutron scattering measurements. For the particular compound CoCl 2 ·2H 2 O we estimate the Bloch amplitude to be on the order of a few lattice constants, and the Bloch frequency on the order of 100 GHz for magnetic fields in the Tesla range and at temperatures of about 18 Kelvin. 75.60.Ch, 75.40.Gb, 75.90.+w, 76.60.Es, 71.70.Ej

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“…In the absence of an external field and at low temperatures real ferromagnets usually exhibit domain wall structures. But it is commonly believed that pinning effects due to impurities and defects are crucial to stabilize domain walls against quantum fluctuations [3,4,5,6,7]. In other words, in models of quantum ferromagnetism that do not incorporate impurities or defects, one should not expect to find stable domain walls because they are destroyed by quantum fluctuations.…”

Section: Introductionmentioning

confidence: 99%

The complete set of ground states of the ferromagnetic XXZ chains

Koma¹,

Nachtergaele²

1998

Advances in Theoretical and Mathematical Physics

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We show that the well-known translation invariant ground states and the recently discovered kink and antikink ground states are the complete set of pure infinite-volume ground states (in the sense of local stability) of the spin-S ferromagnetic XXZ chains withx+1 ], for all ∆ > 1, and all S ∈ 1 2 N. For the isotropic model (∆ = 1) we show that all ground states are translation invariant.For the proof of these statements we propose a strategy for demonstrating completeness of the list of the pure infinite-volume ground states of a quantum many-body system, of which the present results for the XXX and XXZ chains can be seen as an example. The result for ∆ > 1 can also be proved by an easy extension to general S of the method used in [T. Matsui, Lett. Math. Phys. 37 (1996) 397] for the spin-1/2 ferromagnetic XXZ chain with ∆ > 1. However, our proof is different and does not rely on the existence of a spectral gap. In particular, it also works to prove absence of non-translationally invariant ground states for the isotropic chains (∆ = 1), which have a gapless excitation spectrum.Our results show that, while any small amount of the anisotropy is enough to stabilize the domain walls against the quantum fluctuations, no boundary condition exists that would stabilize a domain wall in the isotropic model (∆ = 1).

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S=1/2 magnetic chains as domain wall systems

Cited by 13 publications

References 26 publications

Real-time dynamics in spin-12chains with adaptive time-dependent density matrix renormalization group

Real-time dynamics in spin-12chains with adaptive time-dependent density matrix renormalization group

Bloch oscillations of magnetic solitons in anisotropic spin-12chains

The complete set of ground states of the ferromagnetic XXZ chains

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