Topological Entanglement Negativity of Conformal Field Theory

In condensed matter physics, conformal field theory (CFT) plays an important role in describing phase transitions and quantum phases of matter. Due to the strong symmetry constraints, a few CFT data are sufficient to determine the correlation functions among local operators. However, it is still an open question what is the complete set of data to determine CFT uniquely. In addition to the scaling dimensions, structure factors, and central charge, a topological invariant has been found to be an important CFT datum to characterize and classify conformal field theories in one spatial dimension. Compared to the gapped topological phases, the topological properties of the conformal field theories are relatively less understood. In this talk, we present how quantum entanglement encodes the topological nature of conformal field theories. We studied a one-dimensional model of noninteracting fermions that realizes two Ising CFTs with different topological invariants. The logarithmic negativity, a computable entanglement measure of the mixed quantum states, can reveal the sharp signature of the quantum phase transitions between the two CFTs having the same central charge but different topological properties. We demonstrate that the quantized values of the negativity reveal which topological sectors the conformal field theories belong to. Furthermore, we examined finite temperature crossovers of the topological entanglement negativity, which can be a foundation for future experimental research.