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arXiv:1903.04103 · Physical review. B./Physical review. B

Pair hopping in systems of strongly interacting hard-core bosons

Alvin J. R. Heng, Wenan Guo, Anders W. Sandvik, Pinaki Sengupta

Published Sep 26, 2019• 5 citations
arXivHTMLPDF

Abstract

We have used the stochastic series expansion quantum Monte Carlo method to study interacting hard-core bosons on the square lattice with pair-hopping processes supplementing the standard single-particle hopping. Such pair hopping arises in effective models for frustrated quantum magnets. Our goal is to investigate the effects of the pair-hopping process on the commonly observed superfluid, insulating (Mott), and supersolid ground-state phases in the standard hard-core boson model with various interaction terms. The model is specifically motivated by the observation of finite dispersion of two-magnon bound states in neutron-diffraction experiments ${\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}$. Our results show that the pair hopping has different effects on Mott phases at different filling fractions, ``melting'' them at different critical pair-hopping amplitudes. Thus, it appears that pair hopping may play an important role in determining which out of a potentially large number of Mott phases (stabilized by details of the charge-diagonal interaction terms) actually survive the totality of quantum fluctuations present.

DOI
10.1103/physrevb.100.104433

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We have used the stochastic series expansion quantum Monte Carlo method to study interacting hard-core bosons on the square lattice with pair-hopping processes supplementing the standard single-particle hopping. Such pair hopping arises in effective models for frustrated quantum magnets. Our goal is to investigate the effects of the pair-hopping process on the commonly observed superfluid, insulating (Mott), and supersolid ground-state phases in the standard hard-core boson model with various interaction terms. The model is specifically motivated by the observation of finite dispersion of two-magnon bound states in neutron-diffraction experiments SrCu2(BO3)2{\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}SrCu2​(BO3​)2​. Our results show that the pair hopping has different effects on Mott phases at different filling fractions, ``melting'' them at different critical pair-hopping amplitudes. Thus, it appears that pair hopping may play an important role in determining which out of a potentially large number of Mott phases (stabilized by details of the charge-diagonal interaction terms) actually survive the totality of quantum fluctuations present.
We investigate the consequences of correlated hopping on the ground state properties of hard-core bosons on a square lattice as revealed by extensive exact diagonalizations and quantum Monte Carlo simulations. While for noninteracting hard-core bosons the effective attraction induced by the correlated hopping leads to phase separation at low density, we show that a modest nearest-neighbor repulsion suppresses phase separation, leading to a remarkable low-density pairing phase with no single particle Bose-Einstein condensation but long-range two-particle correlations, signaling a condensation of pairs. We also explain why the unusual properties of the pairing phase are a real challenge for standard one-worm quantum Monte Carlo simulations.
We study a model for interacting spinless bosons in one dimension. The bosons are under a hard-core condition, which does not allow two or more bosons in the same site. However, nearestneighbor interactions between bosons ( V ) and hoppings to the nearest empty site ( t ) are allowed. As V increases from a large negative value, the system undergoes a quantum phase transition from a phase-separation (PS) phase to a superfluid (SF) phase because the hopping term overcomes the attractive energy. When V becomes positive and is increased more, the superfluid phase becomes a charge-density-wave (CDW) phase because the repulsive energy blocks the movements of bosons. Via exact diagonalizations, we calculated the ground-state energies, the correlation energies, and the kinetic energies to obtain signatures of the quantum phase transitions. We adopted a fast stateseeking algorithm that enabled us to calculate the ground states and the ground-state energies up to L = 32 more efficiently. Some results are compared with those of quantum Monte Carlo simulations by using stochastic series expansion for the Heisenberg point, and the momentum distribution functions for the three phases are discussed.
By using an unbiased quantum Monte Carlo method, we investigate the hard-core Bose-Hubbard model on a square lattice with the anisotropic dipole-dipole interaction. To study the effect of the anisotropy, dipole moments are assumed to be polarized in the yyy direction on the two-dimensional xyxyxy plane. To perform efficient simulations of long-range interacting systems, we use the worm algorithm with an O(N)O(N)O(N) Monte Carlo method. We obtain the ground-state phase diagram that includes a superfluid phase and a striped solid phase at half-filling as two main phases. In addition to these two main phases, we find a small region where there are multiple plateaus in the particle density for small hopping amplitudes. In this region, the number of plateaus increases as the system size increases. This indicates the appearance of numerous competing ground states due to frustrated interactions. In our simulations, we find no evidence of a supersolid phase.
We have systematically studied the hard-core Bose-Hubbard model with correlated hopping on a triangular lattice using the density-matrix renormalization group method. A rich ground-state phase diagram is determined. In this phase diagram there is a supersolid phase and a pair superfluid phase due to the interplay between the ordinary frustrated boson hopping and an unusual correlated hopping. In particular, we find that the quantum phase transition between the supersolid phase and the pair superfluid phase is continuous.
One-dimensional free fermions and hard-core bosons are often considered to be equivalent. Indeed, when restricted to nearest-neighbor hopping on a chain, the particles cannot exchange themselves, and therefore hardly experience their own statistics. Apart from the off-diagonal correlations which depend on the so-called Jordan-Wigner string, real-space observables are similar for free fermions and hard-core bosons on a chain. Interestingly, by coupling only two chains, thus forming a two-leg ladder, particle exchange becomes allowed and leads to a totally different physics between free fermions and hard-core bosons. Using a combination of analytical (strong coupling, field theory, renormalization group) and numerical (quantum Monte Carlo, density-matrix renormalization group) approaches, we study the apparently simple but nontrivial model of hard-core bosons hopping in a two-leg ladder geometry. At half filling, while a band insulator appears for fermions at large interchain hopping ${t}_{\ensuremath{\perp}}>2t$ only, a Mott gap opens up for bosons as soon as ${t}_{\ensuremath{\perp}}\ensuremath{\ne}0$ through a Kosterlitz-Thouless transition. Away from half filling, the situation is even more interesting since a gapless Luttinger liquid mode emerges in the symmetric sector with a nontrivial filling-dependent Luttinger parameter $1/2\ensuremath{\leqslant}{K}_{s}\ensuremath{\leqslant}1$. Consequences for experiments in cold atoms and spin ladders in a magnetic field, as well as disorder effects, are discussed. In particular, a quantum phase transition is expected at finite disorder strength between a one-dimensional superfluid and an insulating Bose glass phase.