It was known that by a duality transformation, interacting bosons at filling factor f = p/q hopping on a lattice can be mapped to interacting vortices hopping on the dual lattice subject to a fluctuating dual " magnetic field" whose average strength through a dual plaquette is equal to the boson density f = p/q. So the kinetic term of the vortices is the same as the Hofstadter problem of electrons moving in a lattice in the presence of f = p/q flux per plaquette. Motivated by this mapping, we study the Hofstadter bands of vortices hopping in the presence of magnetic flux f = p/q per plaquette on 5 most common bipartite and frustrated lattices namely square, honeycomb, triangular, dice and Kagome lattices. We count the total number of bands, determine the number of minima and their locations in the lowest band. We also numerically calculate the bandwidths of the lowest Hofstadter bands in these lattices that directly measure the mobility of the dual vortices. The less mobil the dual vortices are, the more likely in a superfluid state the bosons are. We find that except the Kagome lattice at odd q, they all satisfy the exponential decay law W = Ae −cq even at the smallest q. At given q, the bandwidth W decreases in the order of Triangle, Square and Honeycomb lattice. This indicates that the domain of the superfluid state of the original bosons increases in the order of the corresponding direct lattices: Honeycome, Square and Triangular. When q = 2, we find that the the lowest Hofstadter band is completely flat for both Kagome and dice lattices. There is a gap on Kagome lattice, but no gap on dice lattice. This indicates that the boson ground state at half filling with nearest neighbor hopping on Kagome lattice is always a superfluid state. The superfluid state remains stable slightly away from the half filling. Our results show that the behaviours of bosons at or near half filling on Kagome lattice are quite distinct from those in square, honeycomb and triangular lattices studied previously.
There have been experimental and theoretical studies on Photoluminescence (PL) from possible exciton superfluid in semiconductor electron-hole bilayer systems. However, the PL contains no phase information and no photon correlations, so it can only lead to suggestive evidences. It is important to identify smoking gun experiments which can lead to convincing evidences. Here we study two mode phase sensitive squeezing spectrum and also two photon correlation functions. We find the emitted photons along all tilted directions are always in a two mode squeezed state between k and − k. There are always two photon bunching, the photon statistics is super-Poissonian. Observing these unique features by possible future phase sensitive homodyne experiment and HanburyBrown-Twiss type of experiment could lead to conclusive evidences of exciton superfluid in these systems.
We construct a quantum Ginsburg-Landau theory to study the quantum phase transition from the excitonic superfluid to a possible pseudospin density wave (PSDW) at some intermediate distances driven by the magnetoroton minimum collapsing at a finite wave vector. We explicitly show that the PSDW takes a square lattice structure. We suggest the existence of zero-point quantum fluctuation generated vacancies in the PSDW and that correlated hopping of vacancies in the active and passive layers in the PSDW state leads to very large and temperature dependent drag consistent with the experimental data. Comparisons with previous numerical calculations are made. Further experimental implications are given.
Starting from the Ginzburg-Landau free energy describing the normal state to LarkinOvchinnikov-Fulde-Ferrell (LOFF) state transition, we evaluate the free energy of seven most common lattice structures such as stripe, square, triangular, Simple Cubic (SC), Face centered Cubic (FCC), Body centered Cubic (BCC) and Quasi-crystal (QC). We find that the stripe phase which is the original LO state, is the most stable phase. This result maybe relevant to the detection of LOFF state in some heavy fermion compounds and the pairing lattice structure of fermions with unequal populations in the BCS side of Feshbach resonance in ultra-cold atoms.
Bilayer quantum Hall system (BLQH) differ from its single layer counterparts (SLQH) by its symmetry breaking ground state and associated neutral gapless mode in the pseudo-spin sector. Due to the gapless mode, qualitatively good groundstate and low energy excited state wavefunctions at any finite distance is still unknown. We investigate this important open problem by the Composite Boson (CB) theory developed by one of the authors to study BLQH systematically. We derive the ground state, quasi-hole and a pair of quasihole wavefunctions from the CB theory and its dual action. We find that the ground state wavefunction is the product of two parts, one in the charge sector which is the well known Halperin's (111) wavefunction and the other in the spin sector which is non-trivial at any finite d due to the gapless mode. So the total groundstate wavefunction differs from the well known (111) wavefunction at any finite d. In addition to commonly known multiplicative factors, the quasi-hole and a pair of quasi-holes wavefunctions also contain non-trivial normalization factors multiplying the correct ground state wavefunction. We expect that the quasi-hole and pair wave function not only has logarithmically divergent energy, well localized charge distribution, but also correct interlayer correlations. All the distance dependencies in all the wavefunctions are encoded in the spin part of the ground state wavefunction. The instability encoded in the spin part of the groundstate wavefunction leads to the pseudo-spin density wave formation proposed previously by one of the authors. Some subtleties related to the Lowest Landau Level (LLL) projection of the CB theory are also noted.
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