Employing large-scale quantum Monte Carlo simulations, we reveal the full phase diagram of the extended Hubbard model of hard-core bosons on the pyrochlore lattice with partial fillings. When the intersite repulsion is dominant, the system is in a cluster Mott insulator phase with an integer number of bosons localized inside the tetrahedral units of the pyrochlore lattice. We show that the full phase diagram contains three cluster Mott insulator phases with 1/4, 1/2, and 3/4 boson fillings, respectively. We further demonstrate that all three cluster Mott insulators are Coulomb liquid phases and its low-energy property is described by the emergent compact U(1) quantum electrodynamics. In addition to measuring the specific heat and entropy of the cluster Mott insulators, we investigate the correlation function of the emergent electric field and verify it is consistent with the compact U(1) quantum electrodynamics description. Our result sheds light on the magnetic properties of various pyrochlore systems, as well as the charge physics of the cluster magnets.
We study the Mott transition from a metal to cluster Mott insulators in the 1/4- and 1/8-filled pyrochlore lattice systems [corrected]. It is shown that such Mott transitions can arise due to charge localization in clusters or in tetrahedron units, driven by the nearest-neighbor repulsive interaction. The resulting cluster Mott insulator is a quantum spin liquid with a spinon Fermi surface, but at the same time a novel fractionalized charge liquid with charge excitations carrying half the electron charge. There exist two emergent U(1) gauge fields or "photons" that mediate interactions between spinons and charge excitations, and between fractionalized charge excitations themselves, respectively. In particular, it is suggested that the emergent photons associated with the fractionalized charge excitations can be measured in x-ray scattering experiments. Various other experimental signatures of the exotic cluster Mott insulator are discussed in light of candidate materials with partially filled bands on the pyrochlore lattice.
We study hard-core bosons with unfrustrated hopping (t) and nearest neighbor repulsion (U) (spin S=1/2 XXZ model) on the triangular lattice. At half filling, the system undergoes a zero temperature (T) quantum phase transition from a superfluid phase at small U to a supersolid at Uc approximately 4.45 in units of 2t. This supersolid phase breaks the lattice translation symmetry in a characteristic sqrt[3] x square root of 3 pattern, and is remarkably stable--indeed, a smooth extrapolation of our results indicates that the supersolid phase persists for arbitrarily large U/t.
We study hard-core bosons on the checkerboard lattice with nearest-neighbor unfrustrated hopping
t and ``tetrahedral'' plaquette charging energy
U. Analytical arguments and quantum Monte Carlo simulations lead us to the conclusion that the system undergoes a zero temperature
(T) quantum phase transition from a superfluid phase at small
U∕t to a large
U∕t Mott insulator phase with $\ensuremath{\rho}=1∕4$ for a range of values of the chemical potential $\ensuremath{\mu}$. Further, the quarter-filled insulator breaks lattice translation symmetry in a characteristic fourfold ordering pattern and occupies a lobe of finite extent in the $\ensuremath{\mu}\text{\ensuremath{-}}U∕t$ phase diagram. A quantum Monte Carlo study slightly away from the tip of the lobe provides evidence for a direct weakly first-order superfluid insulator transition away from the tip of the lobe. While analytical arguments lead us to conclude that the transition at the tip of the lobe belongs to a different Landau-forbidden second-order universality class, an extrapolation of our numerical results suggests that the size of the first-order jump does not go to zero even at the tip of the lobe.
We study hard-core bosons with unfrustrated nearest-neighbor hopping
t and repulsive interaction
V on a zigzag ladder. As a function of the boson density $\ensuremath{\rho}$ and
V/t, the ground state displays different quantum phases. A standard one-component Tomonaga-Luttinger liquid is stable for $\ensuremath{\rho}<1/3$ (and $\ensuremath{\rho}>2/3$) at any value of
V/t. At commensurate densities $\ensuremath{\rho}=1/3$,
1/2, and
2/3 insulating (crystalline) phases are stabilized for a sufficiently large interaction
V. For intermediate densities $1/3<\ensuremath{\rho}<2/3$ and large
V/t, the ground state shows a clear evidence of a bound state of two bosons, implying gapped single-particle excitations but gapless excitations of boson pairs. These properties can be understood by the fact that the antisymmetric sector acquires a gap and a single gapless mode survives. Finally, for the same range of boson densities and weak interactions, the system is again a one-component Tomonaga-Luttinger liquid with no evidence of any breaking of discrete symmetries, in contrast to the frustrated case, where a
Z2 symmetry breaking has been predicted.
We study a model of hard-core bosons on the kagome lattice with short-range hopping
(t) and repulsive interactions
(V). This model directly maps onto an easy-axis
S=1∕2 XXZ model on the kagome lattice and is also related, at large
V∕t, to a quantum dimer model on the triangular lattice. Using quantum Monte Carlo numerics, we map out the phase diagram of this model at half-filling. At
T=0, we show that this model exhibits a superfluid phase at small
V∕t and an insulating phase at large
V∕t, separated by a continuous quantum phase transition at ${V}_{c}∕t\ensuremath{\approx}19.8$. The insulating phase at
T=0 appears to have no conventional broken symmetries, and is thus a uniform Mott insulator (a ``spin liquid'' in magnetic language). We characterize this insulating phase as a uniform
Z2 fractionalized insulator from the topological order in the ground state and estimate its vison gap. Consistent with this identification, there is no apparent thermal phase transition upon heating the insulator. The insulating phase instead smoothly crosses over into the high temperature paramagnet via an intermediate cooperative paramagnetic regime. We also study the superfluid-to-normal thermal transition for
V<Vc. We find that this is a Kosterlitz-Thouless transition at small
V∕t but changes to a first order transition for
V closer to
Vc. We argue that this first order thermal transition is consistent with the presence of a nearby
Z2 insulating ground state obtained from the superfluid ground state by condensing double vortices.