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Inverse participation ratios in the XXZ spin chain

Abstract : We investigate numerically the inverse participation ratios in a spin-1/2 XXZ chain, computed in the “Ising” basis (i.e., eigenstates of σ^z_i). We consider in particular a quantity T, defined by summing the inverse participation ratios of all the eigenstates in the zero-magnetization sector of a finite chain of length N, with open boundary conditions. From a dynamical point of view, T is proportional to the stationary return probability to an initial basis state, averaged over all the basis states (initial conditions). We find that T exhibits an exponential growth, T∼exp(aN), in the gapped phase of the model and a linear scaling, T∼N, in the gapless phase. These two different behaviors are analyzed in terms of the distribution of the participation ratios of individual eigenstates. We also investigate the effect of next-nearest-neighbor interactions, which break the integrability of the model. Although the massive phase of the nonintegrable model also has T∼exp(aN), in the gapless phase T appears to saturate to a constant value.
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https://hal-cea.archives-ouvertes.fr/cea-01377658
Contributor : Grégoire Misguich <>
Submitted on : Friday, October 7, 2016 - 12:44:25 PM
Last modification on : Monday, June 15, 2020 - 2:52:03 PM

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Grégoire Misguich, Vincent Pasquier, Jean-Marc Luck. Inverse participation ratios in the XXZ spin chain. Physical Review B: Condensed Matter and Materials Physics, American Physical Society, 2016, 94, pp.155110. ⟨10.1103/PhysRevB.94.155110⟩. ⟨cea-01377658⟩

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