Fidelity susceptibility and conductivity of the current in one-dimensional lattice models with open or periodic boundary conditions

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Greschner, S.; Kolezhuk, A.K.; Vekua, T.: Fidelity susceptibility and conductivity of the current in one-dimensional lattice models with open or periodic boundary conditions. In: Physical Review B - Condensed Matter and Materials Physics 88 (2013), Nr. 19, No. 195101. DOI: https://doi.org/10.1103/PhysRevB.88.195101

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Abstract: 
We study, both numerically and analytically, the finite-size scaling of the fidelity susceptibility χJ with respect to the charge or spin current in one-dimensional lattice models and relate it to the low-frequency behavior of the corresponding conductivity. It is shown that in gapless systems with open boundary conditions the leading dependence on the system size L stems from the singular part of the conductivity and is quadratic, with a universal form χJ=[7ζ(3)/2π4]KL2, where K is the Luttinger liquid parameter and ζ(x) is the Riemann ζ function. In contrast to that for periodic boundary conditions the leading system size dependence is directly connected to the regular part of the conductivity and is subquadratic, χJ∝Lγ, where the K-dependent exponent γ is equal to 1 in most situations (as a side effect, this relation provides an alternative way to study the low-frequency behavior of the regular part of the conductivity). For open boundary conditions, we also study another current-related quantity, the fidelity susceptibility to the lattice tilt χP, and show that it scales as the quartic power of the system size, χP=[31ζ(5)/8π6](KL4/u2), where u is the sound velocity. Thus, the ratio L2χJ/χP directly measures the sound velocity in open chains. The behavior of the current fidelity susceptibility in gapped phases is discussed, particularly in the topologically ordered Haldane state. © 2013 American Physical Society.
License of this version: Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Document Type: article
Publishing status: publishedVersion
Issue Date: 2013
Appears in Collections:Fakultät für Mathematik und Physik

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1 image of flag of Germany Germany 45 60.00%
2 image of flag of Netherlands Netherlands 10 13.33%
3 image of flag of United States United States 7 9.33%
4 image of flag of China China 5 6.67%
5 image of flag of Hong Kong Hong Kong 3 4.00%
6 image of flag of No geo information available No geo information available 1 1.33%
7 image of flag of Ukraine Ukraine 1 1.33%
8 image of flag of New Zealand New Zealand 1 1.33%
9 image of flag of Japan Japan 1 1.33%
10 image of flag of Spain Spain 1 1.33%

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