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arXiv:cond-mat/0404562 · Physical Review B

Topological phase separation in a two-dimensional quantum lattice Bose-Hubbard system away from half-filling

Alexander S. Moskvin

Published Jun 11, 2004• 18 citations
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Abstract

We suppose that the doping of the two-dimensional (2D) hard-core (hc) boson system away from half-filling may result in the formation of a multicenter topological inhomogeneity (defect), such as charge order (CO) bubble domain(s) with Bose superfluid (BS) and extra bosons both localized in domain wall(s), or else in a topological $\text{CO}+\text{BS}$ phase separation rather than a uniform mixed $\text{CO}+\text{BS}$ supersolid phase. Starting from the classical model, we predict the properties of the respective quantum system. The long-wavelength behavior of the system is believed to be reminiscent of that of granular superconductors, charge-density wave materials, Wigner crystals, and multi-Skyrmion systems akin to the quantum Hall ferromagnetic state of a 2D electron gas. To elucidate the role played by quantum effects and that of the lattice discreteness, we have addressed the simplest nanoscopic counterpart of the bubble domain in the checkerboard CO phase of a 2D hc Bose-Hubbard (BH) square lattice. It is shown that the relative magnitude and symmetry of a multicomponent order parameter are mainly determined by the sign of the nearest-neighbor and next-nearest-neighbor transfer integrals. In general, the topologically inhomogeneous phase of the hc-BH system away from the half-filling can exhibit the signatures of the $s$, $d$, and $p$ symmetries of the off-diagonal order.

DOI
10.1103/physrevb.69.214505

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We suppose that the doping of the two-dimensional (2D) hard-core (hc) boson system away from half-filling may result in the formation of a multicenter topological inhomogeneity (defect), such as charge order (CO) bubble domain(s) with Bose superfluid (BS) and extra bosons both localized in domain wall(s), or else in a topological CO+BS\text{CO}+\text{BS}CO+BS phase separation rather than a uniform mixed CO+BS\text{CO}+\text{BS}CO+BS supersolid phase. Starting from the classical model, we predict the properties of the respective quantum system. The long-wavelength behavior of the system is believed to be reminiscent of that of granular superconductors, charge-density wave materials, Wigner crystals, and multi-Skyrmion systems akin to the quantum Hall ferromagnetic state of a 2D electron gas. To elucidate the role played by quantum effects and that of the lattice discreteness, we have addressed the simplest nanoscopic counterpart of the bubble domain in the checkerboard CO phase of a 2D hc Bose-Hubbard (BH) square lattice. It is shown that the relative magnitude and symmetry of a multicomponent order parameter are mainly determined by the sign of the nearest-neighbor and next-nearest-neighbor transfer integrals. In general, the topologically inhomogeneous phase of the hc-BH system away from the half-filling can exhibit the signatures of the sss, ddd, and ppp symmetries of the off-diagonal order.
We suppose that the doping of the 2D hard-core boson system away from half-filling may result in the formation of a multicenter topological defect such as charge order (CO) bubble domain(s) with Bose superfluid (BS) and extra bosons both localized in domain wall(s), or a topological CO + BS phase separation , rather than a uniform mixed CO + BS supersolid phase. Starting from the classical model, we predict the properties of the respective quantum system. The long-wavelength behavior of the system is believed to resemble that of granular superconductors, CDW materials, Wigner crystals, and multiskyrmion system akin in a quantum Hall ferromagnetic state of a 2D electron gas.
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.
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.
We study the ground-state phase diagram of the hard-core extended boson Hubbard model on the square lattice with both nearest- and next-nearest-neighbor hoppings and repulsions, using Gutzwiller mean-field theory and quantum Monte Carlo simulations. We observe the formation of supersolid states with checkerboard, striped, and quarter-filled crystal structures when the system is doped away from commensurate fillings. In the striped supersolid phase, a strong anisotropy in the superfluid density is obtained from the simulations; however, the transverse component remains finite, indicating a true two-dimensional superflow. We find that upon doping, the striped supersolid transitions directly into the supersolid with quarter-filled crystal structure, via a first-order stripe melting transition.
We investigate the extended hard-core Bose-Hubbard model on the triangular lattice as a function of spatial anisotropy with respect to both hopping and nearest-neighbor interaction strength. At half-filling the system can be tuned from decoupled one-dimensional chains to a two-dimensional solid phase with alternating density order by adjusting the anisotropic coupling. At intermediate anisotropy, however, frustration effects dominate and an incommensurate supersolid phase emerges, which is characterized by incommensurate density order as well as an anisotropic superfluid density. We demonstrate that this intermediate phase results from the proliferation of topological defects in the form of quantum bosonic domain walls. Accordingly, the structure factor has peaks at wave vectors, which are linearly related to the number of domain walls in a finite system in agreement with extensive quantum Monte Carlo simulations. We discuss possible connections with the supersolid behavior in the high-temperature superconducting striped phase.
The two-dimensional square lattice hard-core boson Hubbard model with near-neighbor interactions has a ``checkerboard'' charge density wave insulating phase at half filling and sufficiently large intersite repulsion. When doped, rather than forming a supersolid phase in which long-range charge density wave correlations coexist with a condensation of superfluid defects, the system instead phase separates. However, it is known that there are other lattice geometries and interaction patterns for which such coexistence takes place. In this paper we explore the possibility that anisotropic hopping or anisotropic near-neighbor repulsion might similarly stabilize the square lattice supersolid. By considering the charge density wave structure factor and superfluid density for different ratios of interaction strength and hybridization in the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{x}$ and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{y}$ directions, we conclude that phase separation still occurs.