Fractionalized Order parameters
Y. Komijani, A. Toth, P. Chandra, P. Coleman, , Order Fractionalization, ArXiv:1811.11115.
- Usual order parameters are characterized by off-diagonal long range order (ODLRO) and they can be characterized by the electronic self-energy which is local and instantaneous (left figure, top).
- Here, we extend the concept of ODLRO into the time domain, proposing that in a
broken symmetry state, quantum operators can fractionalize into half-integer order
- This means that the electronic self-energy becomes a product of two spinorial order parameters and an intermediate fermionic resonance (figure left bottom).
- Using numerical renormalization group (NRG) studies we show how such fractionalized order can be induced in quantum impurity models. This is shown in the right figure, where a small channel aysmmetry leads to appearance of the fermionic resonance in one channel but not the other.
We then conjecture
that such order develops spontaneously in lattice quantum systems, due to positive
feedback, leading to a new family of phases, manifested by a coincidence of broken
symmetry and fractionalized excitations that can be detected by experiment.