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Physical Review B

Collective excitations of hard-core bosons at half filling on square and triangular lattices

Tyler Bryant, Rajiv R. P. Singh

Published Aug 15, 2007• 5 citations
Publisher

Abstract

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 $XXZ$ 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.

DOI
10.1103/physrevb.76.064520

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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.
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 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.
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.
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.
Understanding the microscopic mechanism of coexisting long-range orders (such as lattice supersolidity) in strongly correlated systems is a subject of immense interest. We study the possible manifestations of long-range orders, including lattice-supersolid phases with differently broken symmetry, in a two-dimensional square lattice system of hard-core bosons (HCBs) coupled to archetypal cooperative/coherent normal-mode distortions such as those in perovskites. At strong HCB-phonon coupling, using a duality transformation to map the strong-coupling problem to a weak-coupling one, we obtain an effective Hamiltonian involving nearest-neighbor, next-nearest-neighbor, and next-to-next-nearest-neighbor hoppings and repulsions. Using stochastic series expansion quantum Monte Carlo, we construct the phase diagram of the system. As coupling strength is increased, we find that the system undergoes a first-order quantum phase transition from a superfluid to a checkerboard solid at half-filling and from a superfluid to a diagonal striped solid [with crystalline ordering wave vector $\stackrel{P\vec}{Q}=(2\ensuremath{\pi}/3,2\ensuremath{\pi}/3)$ or $(2\ensuremath{\pi}/3,4\ensuremath{\pi}/3)]$ at one-third filling without showing any evidence of supersolidity. On tuning the system away from these commensurate fillings, checkerboard supersolid is generated near half-filling whereas a rare diagonal striped supersolid is realized near one-third filling. Interestingly, there is an asymmetry in the extent of supersolidity about one-third filling. Within our framework, we also provide an explanation for the observed checkerboard and stripe formations in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{NiO}}_{4}$ at x=1/2x=1/2x=1/2 and x=1/3x=1/3x=1/3.