M. F. M. Meiklejohn

Finite Size Effects in Topological Quantum Phase Transitions

“…This follows from dimensional analysis and a finite size scaling assumption. It is a natural generalization of the classical result for the quantum case [24] and for topological transitions [15]. In Eq.…”

“…Quantum topological transitions as conventional phase transitions also exhibit finite size scaling properties [15]. For a finite system close to quantum criticality, the characteristic length ξ and the finite size L are the relevant length scales.…”

“…Here, it is defined by the form of the the dispersion relation of the excitations at the QCP, g = 0, i.e., ω(g = 0) ∝ k z . In general for isotropic systems close to the topological transition, the spectrum of excitations can be written as, ω = |g| 2νz + k 2z [15]. The wavevector k is that for which the gap ∆ = |g| νz closes at the transition.…”

“…The wavevector k is that for which the gap ∆ = |g| νz closes at the transition. In the cases of interest here the dynamic exponent z takes the Lorentz invariant value z = 1, as a consequence of the Dirac-like nature of the dispersion relation at the transition [15].…”

“…For a finite system close to quantum criticality, the characteristic length ξ and the finite size L are the relevant length scales. The singular part of its free energy δ F C (g, L) is expected to have a finite size contribution that can be written as [15],…”