Juha Suorsa

Disentangling entanglement spectra of fractional quantum Hall states on torus geometries.

We analyze the entanglement spectrum of Laughlin states on the torus and show that it is arranged in towers, each of which is generated by modes of two spatially separated chiral edges. This structure is present for all torus circumferences, which allows for a microscopic identification of the prominent features of the spectrum by perturbing around the thin-torus limit.

A general approach to quantum Hall hierarchies

The Abelian hierarchy of quantum Hall states accounts for most of the states in the lowest Landau level, and there is evidence of a similar hierarchy of non-Abelian states emanating from the nu = 5 ...

Quantum Hall wave functions on the torus

We present explicit expressions for a large set of hierarchy wave functions on the torus. Included are the Laughlin states, the states in the positive Jain series, and recently observed states at, ...

Quasihole condensates in quantum Hall liquids

We develop a formalism to describe quasihole condensates in quantum Hall liquids and thereby extend the conformal field theory approach to the full hierarchy of spin-polarized Abelian states and to several classes of non-Abelian hierarchical states. Most previously proposed spin-polarized quantum Hall wave functions appear as special cases. In this paper we explain the physical motivations for the approach, and exemplify it by explicitly constructing the level-two quasihole condensate state at filling fraction 2/3, and the two level-three states at 5/13 and 5/7 which are built from combinations of quasielectron and quasihole condensates.

Condensate-induced transitions and critical spin chains

We show that condensate-induced transitions between two-dimensional topological phases provide a general frameworktorelateone-dimensionalspinmodelsattheircriticalpoints.Wedemonstratethisusingtwoexamples. First, we show that two well-known spin chains, namely, the XY chain and the transverse field Ising chain with only next-nearest-neighbor interactions, differ at their critical points only by a nonlocal boundary term and can be related via an exact mapping. The boundary term constrains the set of possible boundary conditions of the transverse field Ising chain, reducing the number of primary fields in the conformal field theory that describes its critical behavior. We argue that the reduction of the field content is equivalent to the confinement of a set of primary fields, in precise analogy to the confinement of quasiparticles resulting from a condensation of a boson in a topological phase. As the second example we show that when a similar confining boundary term is applied to the XY chain with only next-nearest-neighbor interactions, the resulting system can be mapped to a local spin chain with the u(1)2 × u(1)2 critical behavior predicted by the condensation framework.

Effective spin chains for fractional quantum Hall states

Abstract Fractional quantum Hall (FQH) states are topologically ordered which indicates that their essential properties are insensitive to smooth deformations of the manifold on which they are studied. Their microscopic Hamiltonian description, however, strongly depends on geometrical details. Recent work has shown how this dependence can be exploited to generate effective models that are both interesting in their own right and also provide further insight into the quantum Hall system. We review and expand on recent efforts to understand the FQH system close to the solvable thin-torus limit in terms of effective spin chains. In particular, we clarify how the difference between the bosonic and fermionic FQH states, which is not apparent in the thin-torus limit, can be seen at this level. Additionally, we discuss the relation of the Haldane–Shastry chain to the so-called QH circle limit and comment on its significance to recent entanglement studies.

Link between the hierarchy of fractional quantum Hall states and Haldane's conjecture for quantum spin chains

We study a strong coupling expansion of the � = 1/3 fractional quantum Hall state away from the Tao-Thouless limit and show that the leading quantum fluctuations lead to an effective spin-1 Hamiltonian that lacks parity symmetry. By analyzing the energetics, discrete symmetries of lowlying excitations, and string order parameters, we demonstrate that the � = 1/3 fractional quantum Hall state is adiabatically connected to both Haldane and large-D phases, and is characterized by a string order parameter which is dual to the ordinary one. This result indicates a close relation between (a generalized form of) the Haldane conjecture for spin chains and the fractional quantum Hall effect.