Abstract
We introduce a two-parameter family of strongly-correlated wave functions for bosons and fermions in lattices. One parameter, q, is connected to the filling fraction. The other one, η, allows us to interpolate between the lattice limit () and the continuum limit () of families of states appearing in the context of the fractional quantum Hall effect or the Calogero–Sutherland model. We give evidence that the main physical properties along the interpolation remain the same. Finally, in the lattice limit, we derive parent Hamiltonians for those wave functions and in 1D, we determine part of the low-energy spectrum.
Highlights
The fractional quantum Hall (FQH) effect has attracted a longstanding interest in physics. 2D electrons displaying such an effect form incompressible quantum liquids with a bulk gap, gapless edge states, and quasiparticle excitations with fractional charge and fractional statistics
In 1D, we show that the states are critical and describe Tomonaga–Luttinger liquids (TLLs) with Luttinger parameter K = 1/q, and in 2D we find that the states have topological entanglement entropy (TEE) [26, 27] −ln (q)/2
We demonstrate that important properties of the states (4) stay the same as a function of the interpolation parameter, which indicates that the states remain within the same phase when interpolated between the lattice limit and the continuum limit
Summary
The fractional quantum Hall (FQH) effect has attracted a longstanding interest in physics. 2D electrons displaying such an effect form incompressible quantum liquids with a bulk gap, gapless edge states, and quasiparticle excitations with fractional charge and fractional statistics. Kalmeyer and Laughlin (KL) proposed a state [5,6,7] that is a lattice version of the bosonic Laughlin state with q = 2 This state has been shown to share some of the most defining properties of its continuum counterpart, like the fractional statistics of quasiparticle excitations [8] and the presence of chiral edge states [9]. We provide an explicit connection between the continuum Laughlin/CS states on the one side and a set of lattice Laughlin/CS states on the other for all filling factors 1/q We do this by introducing a family of lattice wave functions for hardcore bosons and fermions, which is defined on arbitrary lattices in 1D and 2D and allows us to continuously interpolate between the two limits. Hamiltonians are closely related to Haldanes inverse-square model [14], and we find that part of the spectrum is given by integer eigenvalues described by a simple formula
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