Abstract
We introduce a family of strongly-correlated spin wave functions on arbitrary spin- and spin-1 lattices in one and two dimensions. These states are lattice analogues of Moore–Read states of particles at filling fraction , which are non-Abelian fractional quantum Hall states in 2D. One parameter enables us to perform an interpolation between the continuum limit, where the states become continuum Moore–Read states of bosons (odd q) and fermions (even q), and the lattice limit. We show numerical evidence that the topological entanglement entropy stays the same along the interpolation for some of the states we introduce in 2D, which suggests that the topological properties of the lattice states are the same as in the continuum, while the 1D states are critical states. We then derive exact parent Hamiltonians for these states on lattices of arbitrary size. By deforming these parent Hamiltonians, we construct local Hamiltonians that stabilize some of the states we introduce in 1D and in 2D.
Highlights
The fractional quantum Hall (FQH) effect is one of the most fascinating phenomena in strongly correlated electronic systems, in which the electrons of a two-dimensional electron gas subject to a strong magnetic field form an incompressible quantum liquid supporting fractionally charged quasiparticle excitations
Since its discovery in 1987 [2], one FQH state has attracted a lot of attention: Unlike the states at filling factors with odd denominators, the ν = 5 2 FQH state with electrons occupying the second Landau level cannot be explained by a hierarchical construction based on the Laughlins states [3]
Parent Hamiltonians of the states in the lattice limit were derived using analytical tools from conformal field theory (CFT) and in some cases it was shown that these states could be stabilized by local Hamiltonians in one and two dimensions
Summary
The fractional quantum Hall (FQH) effect is one of the most fascinating phenomena in strongly correlated electronic systems, in which the electrons of a two-dimensional electron gas subject to a strong magnetic field form an incompressible quantum liquid supporting fractionally charged quasiparticle excitations. For the Laughlin states, this construction of wave functions written as CFT correlators provides states that are close to, but not exactly the same as the Kalmeyer–Laughlin states on a lattice of finite size, but that become the same in the thermodynamic limit [28] This modification of the lattice construction has made it possible to construct exact parent Hamiltonians for strongly interacting lattice spin systems of arbitrary sizes [28, 39,40,41,42], including topological FQH states such as Laughlin states of hardcore bosons and fermions [30]. In this paper we fill this gap by extending the construction of lattice wave functions from CFT correlators to non-Abelian FQH states Using this approach we construct a family of lattice versions of the Moore–Read state at filling fraction 1 q.
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