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arXiv:cond-mat/0304657 · Physical Review Letters

Melting of Bosonic Stripes

Guido Schmid, Matthias Troyer

Published Aug 5, 2004• 24 citations
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Abstract

We use quantum Monte Carlo simulations to determine the finite temperature phase diagram and to investigate the thermal and quantum melting of stripe phases in a two-dimensional hard-core boson model. At half filling and low temperatures the stripes melt at a first order transition. In the doped system, the melting transitions of the smectic phase at high temperatures and the superfluid smectic (supersolid) phase at low temperatures are either very weakly first order, or of second order with no clear indications for an intermediate nematic phase.

DOI
10.1103/physrevlett.93.067003

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We use quantum Monte Carlo simulations to determine the finite temperature phase diagram and to investigate the thermal and quantum melting of stripe phases in a two-dimensional hard-core boson model. At half filling and low temperatures the stripes melt at a first order transition. In the doped system, the melting transitions of the smectic phase at high temperatures and the superfluid smectic (supersolid) phase at low temperatures are either very weakly first order, or of second order with no clear indications for an intermediate nematic phase.
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.
The supersolid phase of soft-core bosons in two dimensions is investigated using the self-consistent Hartree-Fock and quantum Monte Carlo methods. An approximate phase diagram at finite temperatures is initially constructed using the mean-field approach, which is subsequently validated through precise path-integral simulations, enabling a microscopic characterization of the various phases. Superfluid and melting/freezing transitions are analyzed through the superfluid density and the long-range behavior of correlation functions associated with positional and orientational order, in accordance with the general picture of Berezinskii-Kosterlitz-Thouless transitions. A broad region at low temperatures is identified where the supersolid phase exists, separating the uniform superfluid phase from the normal quasicrystal phase. Additionally, a potential intermediate hexatic phase with quasi-long-range orientational order is identified in a narrow region between the normal solid and fluid phases. These findings establish self-consistent Hartree-Fock theory beyond the local density approximation as an effective tool, complementary to computationally intensive quantum Monte Carlo simulations, for investigating the melting of the supersolid phase and the possible emergence of the hexatic superfluid phase in bosonic systems with various interaction potentials.
We study the ground-state properties of repulsively interacting bosons on the honeycomb lattice using large-scale quantum Monte Carlo simulations. In the hard-core limit, the half-filled system develops long-ranged diagonal order for sufficiently strong nearest-neighbor repulsion. This staggered solid melts at a first-order quantum phase transition into the superfluid phase, without the presence of any intermediate supersolid phase. Within the superfluid phase, both the superfluid density and the compressibility exhibit local minima near the particle (hole) density of one quarter, while the density and the condensate fraction show inflection points in this region. Relaxing the hard-core constraint, supersolid phases emerge for soft-core bosons. The suppression of the superfluid density is found to persist for sufficiently large, finite on-site repulsion.
We use two quantum Monte Carlo algorithms to map out the phase diagram of the two-dimensional hardcore boson Hubbard model with near (V1){(V}_{1})(V1​) and next near (V2){(V}_{2})(V2​) neighbor repulsion. At half filling we find three phases: superfluid (SF), checkerboard solid, and striped solid depending on the relative values of V1,V2,{V}_{1}{,V}_{2},V1​,V2​, and the kinetic energy. Doping away from half filling, the checkerboard solid undergoes phase separation: The superfluid and solid phases coexist but not as a single thermodynamic phase. As a function of doping, the transition from the checkerboard solid is therefore first order. In contrast, doping the striped solid away from half filling instead produces a striped supersolid phase: coexistence of density order with superfluidity as a single phase. One surprising result is that the entire line of transitions between the SF and checkerboard solid phases at half filling appears to exhibit dynamical O(3)O(3)O(3) symmetry restoration. The transitions appear to be in the same universality class as the special Heisenberg point even though this symmetry is explicitly broken by the V2{V}_{2}V2​ interaction.
Using large scale quantum Monte Carlo simulations and dual vortex theory, we analyze the ground state phase diagram of hard-core bosons on the kagome lattice with nearest-neighbor repulsion. In contrast with the case of a triangular lattice, no supersolid emerges for strong interactions. While a uniform superfluid prevails at half filling, two novel solid phases emerge at densities rho=1/3 and rho=2/3. These solids exhibit an only partial ordering of the bosonic density, allowing for local resonances on a subset of hexagons of the kagome lattice. We provide evidence for a weakly first-order phase transition at the quantum melting point between these solid phases and the superfluid.
Liquid crystals are phases of matter intermediate between crystals and liquids. Whereas classical liquid crystals have been known for a long time and are used in electro-optical displays, much less is known about their quantum counterparts. There is growing evidence that quantum liquid crystals play a central role in many electron systems including high temperature superconductors, but a quantitative understanding is lacking due to disorder and other complications. Here, we analyse the quantum phase diagram of a two-dimensional dipolar gas, which exhibits stripe, nematic and supersolid phases. We calculate the stiffness constants determining the stability of the nematic and stripe phases, and the melting of the stripes set by the proliferation of topological defects is analysed microscopically. Our results for the critical temperatures of these phases demonstrate that a controlled study of the interplay between quantum liquid and superfluid phases is within experimental reach for the first time, using dipolar gases.