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Sep 21, 2013
09/13

by
Zheng-Yuan Wang; Masaaki Nakamura

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Recently, it was discussed that the $\nu=1/3$ fractional quantum Hall state can be expressed by a one-dimensional lattice model with an exact matrix-prduct ground state, when toroidal boundary conditions are assumed for a narrow strip [Phys. Rev. Lett. {\bf 109} (2012) 016401]. In this article, we discuss how the excitation spectra of this system are calculated analytically based on the matrix-product formalism. We introduce variational wave functions for various momenta and optimize them. The...

Source: http://arxiv.org/abs/1301.7549v1

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Sep 20, 2013
09/13

by
Zheng-Yuan Wang; Shintaro Takayoshi; Masaaki Nakamura

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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...

Source: http://arxiv.org/abs/1205.4850v4

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117

Sep 23, 2013
09/13

by
Masaaki Nakamura; Zheng-Yuan Wang; Emil J. Bergholtz

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We discuss the relationship between the fractional quantum Hall effect in the vicinity of the thin-torus, a.k.a. Tao-Thouless (TT), limit and quantum spin chains. We argue that the energetics of fractional quantum Hall states in Jain sequence at filling fraction $\nu=p/(2p+1)$ (and $\nu=1-p/(2p+1)$) in the lowest Landau level is captured by S=1 spin chains with $p$ spins in the unit cell. These spin chains naturally arise at sub-leading order in $\e^{-2\pi^2/L_1^2}$ which serves as an expansion...

Source: http://arxiv.org/abs/1105.2105v1

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Sep 23, 2013
09/13

by
Masaaki Nakamura; Zheng-Yuan Wang; Emil J. Bergholtz

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We introduce an exactly solvable fermion chain that describes a $\nu=1/3$ fractional quantum Hall (FQH) state beyond the thin-torus limit. The ground state of our model is shown to be unique for each center of mass sector, and it has a matrix product representation that enables us to exactly calculate order parameters, correlation functions, and entanglement spectra. The ground state of our model shows striking similarities with the BCS wave functions and quantum spin-1 chains. Using the...

Source: http://arxiv.org/abs/1110.5033v3