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

Abstract

We discuss the relationship between fractional quantum Hall (FQH) states at filling factor $\nu =p/(2p+1)$ and quantum spin chains. This series corresponds to the Jain series $\nu =p/(2mp+1)$ with $m=1$ where the composite fermion picture is realized. We show that the FQH states with toroidal boundary conditions beyond the thin-torus 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 the 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.

8 pages and 3figures

References in corpus (7)

• Non-Abelian Anyons and Topological Quantum Computation
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Quantum Hall system in Tao-Thouless limit
• Half-Filled Lowest Landau Level on a Thin Torus
• One-Dimensional Theory of the Quantum Hall System
• Symmetry breaking in Laughlin's state on a cylinder
• Effective spin chains for fractional quantum Hall states

Cited by in corpus (3)

• Composite Fermions on a Torus
• Solvable models for unitary and non-unitary topological phases
• Universal Freezing Transitions of Dipole-Conserving Chains