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Physical Review B

Excitation spectra of hard-core bosons on square and triangular lattices in superfluid phase

Tatiana N. Antsygina, M. I. Poltavskaya, Igor Poltavsky, Konstantin A. Chishko

Published Oct 7, 2010• 2 citations
Publisher

Abstract

Excitation spectra of hard-core bosons with nearest- and next-nearest-neighbor interactions on square and triangular lattices in the superfluid phase are studied using the spin-wave theory. We go beyond the standard linear spin-wave approximation calculating corrections due to spin-wave interaction. Account for the spin-wave interaction considerably improves the quantitative description of the excitation spectra. The behavior of the spectra is analyzed in detail at different particle densities and relations between the interaction parameters. Particular attention is given to the spectrum minima with the aim to find out the conditions for instability of the superfluid phase. We show that for a triangular lattice at high enough next-nearest-neighbor repulsion there appears a true roton minimum inside the Brillouin zone located on the line connecting the zone center with the midpoint of the face of the zone boundary. The obtained analytical results are in excellent quantitative agreement with the numerical simulations known from literature.

DOI
10.1103/physrevb.82.144504

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Excitation spectra of hard-core bosons with nearest- and next-nearest-neighbor interactions on square and triangular lattices in the superfluid phase are studied using the spin-wave theory. We go beyond the standard linear spin-wave approximation calculating corrections due to spin-wave interaction. Account for the spin-wave interaction considerably improves the quantitative description of the excitation spectra. The behavior of the spectra is analyzed in detail at different particle densities and relations between the interaction parameters. Particular attention is given to the spectrum minima with the aim to find out the conditions for instability of the superfluid phase. We show that for a triangular lattice at high enough next-nearest-neighbor repulsion there appears a true roton minimum inside the Brillouin zone located on the line connecting the zone center with the midpoint of the face of the zone boundary. The obtained analytical results are in excellent quantitative agreement with the numerical simulations known from literature.
We study ground state properties and excitation spectra for hard-core Bosons on square and triangular lattices, at half filling, using series expansion methods. Nearest-neighbor repulsion between the Bosons leads to the development of short-range density order at the antiferromagnetic wavevector, and simultaneously a roton minima in the density excitation spectra. On the square-lattice, the model maps on to the well studied XXZ model, and the roton gap collapses to zero precisely at the Heisenberg symmetry point, leading to the well known spectra for the Heisenberg antiferromagnet. On the triangular-lattice, the collapse of the roton gap signals the onset of the supersolid phase. Our results suggest that the transition from the superfluid to the supersolid phase maybe weakly first order. We also find several features in the density of states, including two-peaks and a sharp discontinuity, which maybe observable in experimental realization of such systems.
We study ground state properties and excitation spectra for hard-core bosons on square and triangular lattices, at half filling, using series expansion methods. Nearest-neighbor repulsion between the bosons leads to the development of short-range density order at the antiferromagnetic wave vector, and simultaneously, a minimum in the density excitation spectra. On the square lattice, the model maps onto the well studied XXZXXZXXZ model, and the gap at the minimum collapses to zero precisely at the Heisenberg symmetry point, leading to the well known spectra for the Heisenberg antiferromagnet. On the triangular lattice, the collapse of the gap at the minimum signals the onset of the supersolid phase. Our results suggest that the transition from the superfluid to the supersolid phase may be weakly first order. We also find several features in the density of states, including two peaks and a sharp discontinuity, which may be observable in experimental realization of such systems.
Hard-core bosons on a triangular lattice with nearest-neighbor repulsion are a prototypical example of a system with supersolid behavior on a lattice. We show that in this model the physical origin of the supersolid phase can be understood quantitatively and analytically by constructing quasiparticle excitations of defects that are moving on an ordered background. The location of the solid to supersolid phase transition line is predicted from the effective model for both positive and negative (frustrated) hopping parameters. For positive hopping parameters the calculations agree very accurately with numerical quantum Monte Carlo simulations. The numerical results indicate that the supersolid to superfluid transition is first order.
We present the linear spin wave theory calculation of the superfluid phase of a hard-core boson J-K model with nearest neighbour exchange J and four-particle ring-exchange K at half filling on the triangular lattice, as well as the phase diagrams of the system at zero and finite temperatures. A similar analysis has been done on a square lattice (Schaffer et al. Phys. Rev. B, 80, 014503 (2009)). We find similar behaviour to that of a square lattice but with different spin wave values of the thermodynamic quantities. We also find that the pure J model (XY model), which has a well-known uniform superfluid phase with an ordered parameter [Formula: see text] at zero temperature is quickly destroyed by the inclusion of negative-K ring-exchange interactions, favouring a state with a (4π/3, 0) ordering wavevector. We further study the behaviour of the finite-temperature Kosterlitz–Thouless phase transition (TKT) in the uniform superfluid phase, by forcing the universal quantum jump condition on the finite-temperature spin wave superfluid density. We find that for K < 0, the phase boundary monotonically decreases to T = 0 at K/J = −4/3, where a phase transition is expected and TKT decreases rapidly, while for positive K, TKT reaches a maximum at some K ≠ 0. It has been shown on a square lattice using quantum Monte Carlo (QMC) simulations that for small K > 0 away from the XY point, the zero-temperature spin stiffness value of the XY model is decreased (Melko and Sandvik. Ann. Phys. 321, 1651 (2006)). Our result seems to agree with this trend found in QMC simulations for two-dimensional systems.
We determine the phase diagram of hard-core bosons on a triangular lattice with nearest-neighbor repulsion, paying special attention to the stability of the supersolid phase. Similar to the same model on a square lattice we find that for densities rho<1/3 or rho>2/3 a supersolid phase is unstable and the transition between a commensurate solid and the superfluid is of first order. At intermediate fillings 1/3<rho<2/3 we find an extended supersolid phase even at half filling rho=1/2. The emergence of the supersolid on the triangular lattice reflects a novel and interesting way for a quantum system to avoid classical frustration, similar to an order-by-disorder mechanism. It also offers an exciting possibility of realizing such phenomena in ultracold atoms on optical lattices.
In this Brief Report, we study phase structure of a system of hard-core bosons with a nearest-neighbor (NN) repulsive interaction in a stacked triangular lattice. The Hamiltonian of the system contains two parameters, one of which is the hopping amplitude ttt between NN sites and the other is the NN repulsion VVV. We investigate the system by means of the Monte Carlo simulations and clarify the low- and high-temperature phase diagrams. Phase diagrams contain various phases, e.g., solid, superfluid, supersolid, and phase-separated states. The result is compared with the phase diagram of the two-dimensional system in a triangular lattice at vanishing temperature.