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

Мова статті: 
Автор(и) статті: 
S. Greschner, A. K. Kolezhuk, and T. Vekua
Вихідні данні статті: 
Phys. Rev. B vol. 88, Issue 19, Article No. 195101 (2013) [11 pages]
Назва журналу: 
Physical Review B
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Ключові слова: 
fidelity, conductivity, one-dimensional systems
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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, χJLγ, 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.
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Кафедра математики, теоретичної фізики і комп-рних технологій
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Дизайн: Інститут високих технологій
Ivan Ivanov