Theoretical and experimental studies on one-dimensional magnetic systems

Steiner, Michael; Villain, Jacques; Windsor, C. G.

doi:10.1080/00018737600101372

Cited by 722 publications

(239 citation statements)

References 189 publications

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“…We expect these results to be universally valid at large x and t, ignoring a possible Drude weight term, since the Fourier transform is dominated by the small ω and q region, at large t and x. G int has the classic diffusion form. Note that diffusion occurs in a more limited domain than originally proposed for high-T ferromagnets [41][42][43] however. We have shown it to occur at low T , where γ T , ignoring a possible non-zero Drude weight term in the self-energy, but only inside the light cone at |x|/v 1/γ |t| and only for the uniform part of the spin correlation function.…”

Section: F Spin Diffusionmentioning

confidence: 84%

“…For all 0 < ∆ ≤ 1, at finite temperatures and sufficiently long times the autocorrelation function becomes dominated by a low-energy term with the universal power-law decay t −1/2 expected for diffusion in one dimension. [41][42][43] Note that the more limited diffusive behavior we have found is related to the Lorentz invariance of the underlying low energy effective Lagrangian. The b and c terms break Lorentz invariance but only produce an unimportant T -dependent shift of the velocity.…”

Section: F Spin Diffusionmentioning

confidence: 98%

“…14 The debate about the role of integrability in transport properties of integrable models is connected with the question of diffusion in S = 1/2 spin chains. The term spin diffusion first appeared in the context of the phenomenological theory, [41][42][43] where it refers to a characteristic form of long-time decay of the spin correlation function. In the phenomenological theory, the case where the total magnetization in the direction of quantization, S z = j S z j , is conserved is considered.…”

Section: (12)mentioning

confidence: 99%

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Conservation laws, integrability, and transport in one-dimensional quantum systems

2011

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In integrable one-dimensional quantum systems an infinite set of local conserved quantities exists which can prevent a current from decaying completely. For cases like the spin current in the XXZ model at zero magnetic field or the charge current in the attractive Hubbard model at half filling, however, the current operator does not have overlap with any of the local conserved quantities. We show that in these situations transport at finite temperatures is dominated by a diffusive contribution with the Drude weight being either small or even zero. For the XXZ model we discuss in detail the relation between our results, the phenomenological theory of spin diffusion, and measurements of the spin-lattice relaxation rate in spin chain compounds. Furthermore, we study the Haldane-Shastry model where the current operator is also orthogonal to the set of conserved quantities associated with integrability but becomes itself conserved in the thermodynamic limit.

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Section: F Spin Diffusionmentioning

confidence: 84%

Section: F Spin Diffusionmentioning

confidence: 98%

Section: (12)mentioning

confidence: 99%

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Conservation laws, integrability, and transport in one-dimensional quantum systems

2011

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“…For instance, spin chains in solid state physics represent a vast reservoir of possible quantum channels, characterized by the most diverse Hamiltonians, though with fixed parameters [6,7]. On the other hand, initializing a spin chain embedded on a solid-state matrix might be a hard task.…”

Section: Introductionmentioning

confidence: 99%

Initializing an unmodulated spin chain to operate as a high-quality quantum data bus

et al. 2011

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We study the quality of state and entanglement transmission through quantum channels described by spin chains varying both the system parameters and the initial state of the channel. We consider a vast class of one-dimensional many-body models which contains some of the most relevant experimental realizations of quantum data-buses. In particular, we consider spin-1/2 XY and XXZ model with open boundary conditions. Our results show a significant difference between free-fermionic (non-interacting) systems (XY) and interacting ones (XXZ), where in the former case initialization can be exploited for improving the entanglement distribution, while in the latter case it also determines the quality of state transmission. In fact, we find that in non interacting systems the exchange with fermions in the initial state of the chain always has a destructive effect, and we prove that it can be completely removed in the isotropic XX model by initializing the chain in a ferromagnetic state. On the other hand, in interacting systems constructive effects can arise by scattering between hopping fermions and a proper initialization procedure. Remarkably our results are the first example in which state and entanglement transmission show maxima at different points as the interactions and initializations of spin chain channels are varied.

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“…One-dimensional (1D) correlated lattice systems with L sites show exotic spin transport properties at finite temperature T > 0 whose nature has been a problem of long-standing both theoretical [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and experimental [21][22][23][24][25][26][27] interest. Often integrable quantum systems show dissipationless ballistic transport behavior.…”

Section: Introductionmentioning

confidence: 99%

Vanishing spin stiffness in the spin-12Heisenberg chain for any nonzero temperature

2015

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Whether at zero spin density m = 0 and finite temperatures T > 0 the spin stiffness of the spin-1/2 XXX chain is finite or vanishes remains an unsolved and controversial issue, as different approaches yield contradictory results. Here we provide an exact upper bound on the stiffness within a canonical ensemble at any fixed value of spin density m and show that it is proportional to m 2 L in the thermodynamic limit of chain length L → ∞, for any finite, nonzero temperature. Moreover, we explicitly compute the stiffness at m = 0 and confirm that it vanishes. This allows us to exactly exclude the possibility of ballistic transport within the canonical ensemble for T > 0.

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Theoretical and experimental studies on one-dimensional magnetic systems

Cited by 722 publications

References 189 publications

Conservation laws, integrability, and transport in one-dimensional quantum systems

Conservation laws, integrability, and transport in one-dimensional quantum systems

Initializing an unmodulated spin chain to operate as a high-quality quantum data bus

Vanishing spin stiffness in the spin-12Heisenberg chain for any nonzero temperature

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