Capacity of entanglement and distribution of density matrix eigenvalues in gapless systems

Understand

We propose that the properties of the capacity of entanglement (COE) in gapless systems can efficiently be investigated through the use of the distribution of eigenvalues of the reduced density matrix (RDM).

• The COE is defined as the fictitious heat capacity calculated from the entanglement spectrum.
• Its dependence on the fictitious temperature can reflect the low-temperature behavior of the physical heat capacity, and thus provide a useful probe of gapless bulk or edge excitations of the system.
• Assuming a power-law scaling of the COE with an exponent $\alpha$ at low fictitious temperatures, we derive an analytical formula for the distribution function of the RDM eigenvalues.