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arXiv:1605.01237 · Physical Review Letters

Quantum Domain Walls Induce Incommensurate Supersolid Phase on the Anisotropic Triangular Lattice

Xue‐Feng Zhang, Shijie Hu, Axel Pelster, Sebastian Eggert

Published Nov 3, 2016• 25 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.117.193201

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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.
We investigate the interplay between commensurate lock-in and incommensurate supersolid phases of the hard-core bosons at half-filling with anisotropic nearest-neighbor hopping and repulsive interactions on triangular lattice. We use numerical quantum and variational Monte Carlo as well as analytical Schwinger boson mean-field analysis to establish the ground states and phase diagram. It is shown that, for finite-size systems, there exist a series of jumps between different supersolid phases as the anisotropy parameter is changed. The density ordering wave vectors are locked to commensurate values and jump between adjacent supersolids. In the thermodynamic limit, however, the magnitude of these jumps vanishes leading to a continuous set of novel incommensurate supersolid phases.
We study the extended hard-core Bose-Hubbard model with nearest-neighbor interactions on a triangular lattice with spatial anisotropy by quantum Monte Carlo simulations. The effects of the geometric frustration or the anisotropic strength, represented by the ratio ${t}^{\ensuremath{'}}/t$ between the intrachain nearest-neighbor hopping ${t}^{\ensuremath{'}}$ and the interchain hopping ttt, are studied. We find that for small values of anisotropy ratio ${t}^{\ensuremath{'}}/t$, a solid state emerges at $\ensuremath{\rho}=1/2$ and a supersolid is unstable toward phase separation; for large values of anisotropy ratio ${t}^{\ensuremath{'}}/t$, solid states emerge at $\ensuremath{\rho}=1/3$, 2/3, and a supersolid phase is stable in the region $\ensuremath{\rho}<2/3$; for intermediate values of anisotropy ratio ${t}^{\ensuremath{'}}/t$, three kinds of solid states at fillings $\ensuremath{\rho}=1/3$, 1/2, and $\ensuremath{\rho}=2/3$ coexist and no stable supersolid phase is observed. At half filling, we find that with increasing frustration ${t}^{\ensuremath{'}}/t$, the $\ensuremath{\rho}=1/2$ solid transitions indirectly into the supersolid via an intervening superfluid.
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 study the ground state properties of the extended hard-core Bose–Hubbard model in a two-dimensional anisotropic triangular lattice by quantum Monte Carlo simulations. We present the ground state phase diagram at half filling. Four kinds of phases, including two solid phases, a superfluid phase and a supersolid phase, are observed. The supersolid phase exists only in a narrow region close to the isotropic limit. Away from half filling, we find that the results are strongly dependent on the phase at half filling. No supersolid phase exists if the ground state at half filling is a superfluid or a solid.
We study a system of hard-core boson on a one-dimensional lattice with frustrated next-nearest-neighbor hopping and nearest-neighbor interaction. At half filling, for equal magnitude of nearest- and next-nearest-neighbor hopping, the ground state of this system exhibits a first-order phase transition from a bond-ordered solid to a charge-density-wave solid as a function of the nearest-neighbor interaction. Moving away from half filling we investigate the system at incommensurate densities, where we find a supersolid phase which has concurrent off-diagonal long-range order and density-wave order which is unusual in a system of hard-core bosons in one dimension. Using the finite-size density-matrix renormalization group method, we obtain the complete phase diagram for this model.
We study the soft-core extended Bose-Hubbard model in a two-dimensional triangular lattice by using the quantum Monte Carlo methods. The ground-state phase diagram of the system exhibits a very fruitful structure and is much intriguing. Aside from the Mott insulating state, four kinds of solid states with respect to the commensurate filling factors $\ensuremath{\rho}=1∕3,2∕3$ and $\ensuremath{\rho}=1$ are identified. In incommensurate fillings, superfluid, supersolid, as well as phase-separation states are detected. As in the case of the hard-core bosons, a supersolid phase exists in $1∕3<\ensuremath{\rho}<2∕3$ while it is unstable toward the phase separation in $\ensuremath{\rho}<1∕3$. However, this instability is refrained in $2∕3<\ensuremath{\rho}<1$ due to the softening of the bosons, and then a supersolid phase survives.