Model hamiltonian for superfluidity

Moorad Alexanian

Nikolay N. Bogolubov

On the Theory of Superfluidity Quasi-Averages in Problems of Statistical Mechanics Hydrodynamics Equations in Statistical Mechanics On the Hydrodynamics of a Superfluid Liquid On the Model Hamiltonian of Superconductivity Model Hamiltonians with Fermion Interaction

Sanjoy Datta, Sudhakar Yarlagadda

We derive an effective d-dimensional Hamiltonian for a system of hard-core-bosons coupled to optical phonons in a lattice. Away from half-filling, we show that the presence of next-nearest-neighbor hopping in the effective Hamiltonian leads to a superfluid-to-supersolid transition at intermediate boson-phonon (b-p) couplings, while at strong-couplings the system phase separates. However, at half-filling and at a critical b-p coupling (as in the xxz-model), the system undergoes a superfluid-to-charge-density-wave transition without any signature of supersolidity. Our analyses is based on extensive calculations of the structure factor, the superfluid fraction, the Bose-Einstein condensate fraction, and the system energy at various fillings. We present a phase diagram for this system and compare it to that of the xxz-model. We also demonstrate explicitly that the next-nearest-neighbor hopping (in the absence of nearest-neighbor hopping) in the effective Hamiltonian leads only to a single transition, i.e., a first-order superfluid-to-supersolid transition.

F.W. Cummings, James R. Johnston

Jonathan D’Emidio, Ribhu K. Kaul

We consider the easy-plane limit of bipartite $\mathrm{SU}(N$) Heisenberg Hamiltonians, which have a fundamental representation on one sublattice and the conjugate to fundamental on the other sublattice. For $N=2$ the easy plane limit of the SU(2) Heisenberg model is the well-known quantum $XY$ model of a lattice superfluid. We introduce a logical method to generalize the quantum $XY$ model to arbitrary $N$, which keeps the Hamiltonian sign-free. We show that these quantum Hamiltonians have a world-line representation as the statistical mechanics of certain tightly packed loop models of $N$ colors in which neighboring loops are disallowed from having the same color. In this loop representation we design an efficient Monte Carlo cluster algorithm for our model. We present extensive numerical results for these models on the two dimensional square lattice, where we find the nearest neighbor model has superfluid order for $N\ensuremath{\le}5$ and valence-bond order for $N>5$. By introducing $\mathrm{SU}(N$) easy-plane symmetric four-spin couplings we are able to tune across the superfluid-VBS phase boundary for all $N\ensuremath{\le}5$. We present clear evidence that this quantum phase transition is first order for $N=2$ and $N=5$, suggesting that easy-plane deconfined criticality runs away generically to a first-order transition for small $N$.

Yongle Yu