4 0 0.5 1 50 100 150 200 t=1/ S (a) 0 0.5 1 50 100 t=1/ C E (t) (b) FIG. 3: (Color online) (a) Renyi entropy S α , and (b) capacity of entanglement C E defined by Eq. (8), of non-Abelian (red solid line) and Abelian (blue dashed line) states. The black dotted line is a linear fitting. The parameters are the same as those in Fig. 2. glement spectra. If we define ρ = e $^{−H}$, the quantity S$_{α}$ (1 − 1 /α ) = − 1 α log Tr e − α H is the same as the free en- ergy of a thermal system with Hamiltonian H and tem- perature t = 1 /α . The behavior of the low energy spec- trum of H can be obtained from the following quantity: C$_{E}$ ( t ) = − t ∂ 2 ∂t 2 [ (1 − t ) S$_{1}$$_{/t}$ ] , (8) which is termed as “ capacity of entanglement ” and is the analog of heat capacity C$_{v}$ in a thermal system. The explicit expression of S$_{α}$ and C$_{E}$ ( t ) is given in the Sup- plementary material, which leads to the numerical results shown in Fig. 3. As expected, in the limit of t → 0, C$_{E}$ ( t ) vanishes exponentially for Abelian phase but linearly for non-Abelian phase, since the latter has a gapless entan- glement spectrum with constant density of state. More generically, if the entanglement Hamiltonian H describes a (1 + 1) dimensional conformal field theory (CFT) in long wavelength limit [7, 17] , the capacity of entangle- ment is given by C$_{E}$ ( t ) = ( πcL/ 3 v ) t for t → 0, with L the length of the boundary, and c and v the central charge and velocity of the CFT, respectively [40]. Moreover, if H describes a critical theory with dynamical exponent z , from dimensional analysis one can obtain the asymptotic behavior C$_{E}$ ( t ) ∝ Lt 1 /z for t → 0. Thus we see that the capacity of entanglement characterizes some impor- tant qualitative behavior of the entanglement spectrum in generic systems. We sincerely thank S.-B. Chung, J. Cui, E. Fradkin, T. L. Hughes, Y. Ran, S. Ryu, Z. Wang, and X.-G. 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