Spin-chain description of fractional quantum Hall states in the Jain series

• DOI: 10.1103/physrevb.86.155104
• Publication Date: 2012-10-03T17:09:27Z
• Authors: Zheng-Yuan Wang; Shintaro Takayoshi; Masaaki Nakamura
• Keywords: Composite fermion; Quantum number

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