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An introduction to the spectrum, symmetries, and dynamics of spin-1/2 Heisenberg chains
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Image of Fig. 1.
Fig. 1.

(Color online) Histograms of the diagonal elements [panels (a) and (b)], eigenvalues [panels (c) and (d)], and IPR averaged over all eigenstates vs. Δ [panel (e)], for the antiferromagnetic XXZ-Hamiltonian with open boundaries for  = 10 and  = 5. The site-basis is used. Panels (a) and (c) have ; panels (b) and (d) have . Panel (c) bin width = 0.2 and panel (d) bin width = 1.0.

Image of Fig. 2.
Fig. 2.

(Color online) Magnetization of each site versus time when the initial state is . The sites are indicated with numbers. Panels (a) and (c) have while panels (b) and (d) have . Top panels have  = 6 and bottom panels have  = 12. All panels are for open chains.

Image of Fig. 3.
Fig. 3.

(Color online) Probability in time to find a specific basis vector for an open chain with  = 6 and . Top panel: initial state (solid line) couples effectively with (circles), (triangles), and (crosses). Bottom panel: initial state (solid line) couples effectively only with (dashed line).


Generic image for table
Table I.

Number of energy bands formed with the diagonal elements of the XXZ-Hamiltonian written in the site-basis. Note: is the integer part of .

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Table II.

The first column numerates the eigenstates of an open XXZ chain with ,  = 6, and  = 3. The second and third columns give, respectively, the eigenvalues Π and of these eigenstates. Columns 4–7 give the probability amplitudes of the initial states [Eqs. (25)–(28) ] written as superpositions of the eigenstates of the Hamiltonian: . The eigenvalues Π and for these initial states are shown in the second and third rows, respectively.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: An introduction to the spectrum, symmetries, and dynamics of spin-1/2 Heisenberg chains