The effective partition function of a fractional quantum Hall system, which is described by the Laughlin quasiparticle wave function, is obtained in the path-integral representation. It shows that the quasiparticles cannot be treated as ordinary anyons in view of the freeze of the kinetic energy and the ``bosonic aspect'' of the Hilbert space. By using the constrained anyon systems, we find that one type of filling fractions is more stable than other fractions predicted by the standard hierarchy theory. This work also sheds considerable light on the possible equivalence between the hierarchy theory and the composite-fermion approach proposed by Jain recently.The effective partition function of a fractional quantum Hall system, which is described by the Laughlin quasiparticle wave function, is obtained in the path-integral representation. It shows that the quasiparticles cannot be treated as ordinary anyons in view of the freeze of the kinetic energy and the ``bosonic aspect'' of the Hilbert space. By using the constrained anyon systems, we find that one type of filling fractions is more stable than other fractions predicted by the standard hierarchy theory. This work also sheds considerable light on the possible equivalence between the hierarchy theory and the composite-fermion approach proposed by Jain recently.

Physical Review LettersApr 13, 19927 citations

Emergence and mechanism in the fractional quantum Hall effect

Jonathan Bain

Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern PhysicsNov 1, 201613 citations

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

Zheng-Yuan Wang, Shintaro Takayoshi, Masaaki Nakamura

We discuss the relationship between fractional quantum Hall (FQH) states at filling factor $\ensuremath{\nu}=p/(2p+1)$ and quantum spin chains. This series corresponds to the Jain series $\ensuremath{\nu}=p/(2mp+1)$ 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.We discuss the relationship between fractional quantum Hall (FQH) states at filling factor $\ensuremath{\nu}=p/(2p+1)$ and quantum spin chains. This series corresponds to the Jain series $\ensuremath{\nu}=p/(2mp+1)$ 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.

arXiv:1205.4850Physical Review BOct 2, 201215 citations

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.