10.15488/2060
Greschner, Sebastian
Kolezhuk, A.K.
Vekua, T.
Fidelity susceptibility and conductivity of the current in one-dimensional lattice models with open or periodic boundary conditions
College Park, MD : American Physical Society
2013
Dewey Decimal Classification::500 | Naturwissenschaften::530 | Physik
Leibniz Universität Hannover
Leibniz Universität Hannover
2017-10-20
2017-10-20
2013
eng
article
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
http://www.repo.uni-hannover.de/handle/123456789/2085
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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.
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