Quantum Hall correlations in tilted extended Bose-Hubbard chains

Abstract

We demonstrate characteristics of a bosonic fractional quantum Hall (FQH) state in a one-dimensional extended Bose-Hubbard model (eBHM) with a static tilt. In the large tilt limit, quenched kinetic energy leads to emergent dipole moment conservation, enabling mapping to a model generating FQH states. Using exact diagonalization, density matrix renormalization group, and an analytical transfer matrix approach, we analyze energy and entanglement properties to reveal FQH correlations. Our findings set the stage for the use of quenched kinetics in simple time-reversal invariant eBHMs to explore emergent phenomena.

Figures (4)

• Figure 1: (a) Top: Bosons on a 2D periodic surface in a strong magnetic field perpendicular to the surface (not shown). The circumference is $L_y$. LLL single-particle orbitals are drawn as ribbons localized along the $x$-direction. A bipartition separates the system into subsystems A and B used in entanglement calculations. The arrows at the edges of bipartitions depict FQH edge currents. Bottom: A dipole-conserving lattice model where each site (sphere) is mapped from a corresponding FQH orbital in the top. A similar bipartition divides the lattice. (b) Depiction of the dipole-conserving double hop of two bosons to neighboring sites.
• Figure 2: (a) Low-lying energy eigenvalues of $\hat{H}_g$ versus dipole moment eigenvalue, $P$, at $g=0.8$ for $N_s=16$. Here we see the ground state degeneracy between $P$ sectors and the energy gap. The insets depict the density profile for the ground states in $P=0$ and $P=N_s/2$ sectors. (b) The same but for $\hat{H}_{\text{QH}}$ at $L_y = 6.5$.
• Figure 3: Overlap between the ground states of $\hat{H}_g$ and $\hat{H}_{\text{QH}}$ as we vary dipole hopping strength in $\hat{H}_g$ against the torus circumference in the FQH parent model, for $N_s = 16$. The solid line denotes the parameter choice where the lowest-order terms in each model match. The diamond denotes an example parameter $g=0.8$ choice that yields an overlap of $90\%$.
• Figure 4: (a) Entanglement entropy versus $g$, showing both DMRG data (symbols) for the ground state of $\ket{\psi_{g}}$ and analytical result from $\ket{\psi_{g}}_{\text{MPS}}$ (solid line) for $N_s = 64$. The inset depicts the ES, $\xi_n$, versus dipole moment difference for the ground state of $\hat{H}_{\text{QH}}$ (empty squares) and the ground state of $\hat{H}_{g}$ (filled circles) for $g = 0.5$, and adjacent numbers represent $n$. The dashed lines are a guide. (b) The same, but for the bipartite number fluctuations.