## Spin-chain description of fractional quantum Hall states in Jain's series    [PDF]

Zheng-Yuan Wang, Shintaro Takayoshi, Masaaki Nakamura
We discuss relationship between fractional quantum Hall (FQH) states at filling factor $\nu= p/(2p+1)$ and quantum spin chains. This series corresponds to the Jain's states $\nu= p/(2p+1)$ with $m = 1$ where the composite fermion picture is realized. We show that the FQH states with toroidal boundary conditions beyond the thin-torus (TT) limit, can be mapped to effective quantum spin $S = 1$ chains with $p$ spins in each unit cell. We calculate energy gaps and the correlation functions for both the FQH systems and the corresponding effective spin chains, using exact diagonalization and infinite time-evolving block decimation (iTEBD) algorithm. We confirm that the mass gaps of these effective spin chains are decreased as $p$ is increased which is similar to $S = p$ integer Heisenberg chains. These results shed new light on a link between the hierarchy of FQH states and the Haldane conjecture for quantum spin chains.
View original: http://arxiv.org/abs/1205.4850