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Chinese Physics B

Quantum Monte Carlo study of hard-core bosons in Creutz ladder with zero flux

Yang Lin, Weichang Hao, Huaiming Guo

Published Jan 1, 2018• 1 citation
Publisher

Abstract

The quantum phase of hard-core bosons in Creutz ladder with zero flux is studied. For a specific regime of the parameters ( t x = t p , t y < 0), the exact ground-state is found analytically, which is a dimerized insulator with one electron bound in each rung of the ladder. For the case t x , t y , t p > 0, the system is exactly studied using quantum Monte Carlo (QMC) method without a sign problem. It is found that the system is a Mott insulator for small t p and a quantum phase transition to a superfluid phase is driven by increasing t p . The critical t p c is determined precisely by a scaling analysis. Since it is possible that the Creutz ladder is realized experimentally, the theoretical results are interesting to the cold-atom experiments.

DOI
10.1088/1674-1056/27/1/010204

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The quantum phase of hard-core bosons in Creutz ladder with zero flux is studied. For a specific regime of the parameters ( t x = t p , t y < 0), the exact ground-state is found analytically, which is a dimerized insulator with one electron bound in each rung of the ladder. For the case t x , t y , t p > 0, the system is exactly studied using quantum Monte Carlo (QMC) method without a sign problem. It is found that the system is a Mott insulator for small t p and a quantum phase transition to a superfluid phase is driven by increasing t p . The critical t p c is determined precisely by a scaling analysis. Since it is possible that the Creutz ladder is realized experimentally, the theoretical results are interesting to the cold-atom experiments.
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.
We introduce two quantum Monte Carlo algorithms and employ them to study the superfluid-insulator transition in a two-dimensional system of hard-core bosons. One of the algorithms is appropriate for zero temperature and is based upon the Green's function Monte Carlo method; the other is an extension of the finite-temperature world-line cluster method. In each case we find that the dynamical exponent is consistent with the theoretical prediction of z=2z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2z=2 by Fisher and co-workers.
We study hard-core bosons on the checkerboard lattice with nearest-neighbor unfrustrated hopping ttt and ``tetrahedral'' plaquette charging energy UUU. Analytical arguments and quantum Monte Carlo simulations lead us to the conclusion that the system undergoes a zero temperature (T)(T)(T) quantum phase transition from a superfluid phase at small U∕tU∕tU∕t to a large U∕tU∕tU∕t Mott insulator phase with $\ensuremath{\rho}=1∕4$ for a range of values of the chemical potential $\ensuremath{\mu}$. Further, the quarter-filled insulator breaks lattice translation symmetry in a characteristic fourfold ordering pattern and occupies a lobe of finite extent in the $\ensuremath{\mu}\text{\ensuremath{-}}U∕t$ phase diagram. A quantum Monte Carlo study slightly away from the tip of the lobe provides evidence for a direct weakly first-order superfluid insulator transition away from the tip of the lobe. While analytical arguments lead us to conclude that the transition at the tip of the lobe belongs to a different Landau-forbidden second-order universality class, an extrapolation of our numerical results suggests that the size of the first-order jump does not go to zero even at the tip of the lobe.
We study the superfluid density of hard-core bosons on quasi-one-dimensional lattices using the quantum Monte Carlo method. Because of phase slippage, the superfluid density drops quickly to zero at finite temperatures with increasing the system length $\ensuremath{\ell}$ and the superfluid transition temperature is zero in one spatial dimension and also in quasi-one dimension in the limit of $\ensuremath{\ell}\ensuremath{\rightarrow}\ensuremath{\infty}$. We calculate the superfluid density of a model where no phase slippage is allowed and show that the superfluid density remains finite at finite temperatures even in the one-dimensional limit. We also discuss how finite superfluid density can be observed in a quasi-one-dimensional system using a torsional oscillator.
We study the hard-core bosons in one-dimensional (1D) interacting topological bands at different filling factors using exact diagonalization. At the filling factor $\ensuremath{\nu}=1$ and in the presence of the on-site Hubbard interaction, we find no sign of the existence of the bosonic topological phase, which is in contrast to the fermionic case. Instead by studying the momentum distribution and the condensate fraction we find a superfluid to Mott-insulator transition driven by the Hubbard interaction. At the filling factor $\ensuremath{\nu}=1/3$ and in the presence of longer-ranged interactions, we identify the bosonic fractional topological phase whose ground states are characterized by a threefold degeneracy and a quantized total Berry phase, which is very similar to the fermionic case. Finally we discuss the reason for the different behaviors of hard-core bosons at different filling factors by mapping them to spinless fermions. Our results can be realized in cold-atom experiments.
By means of Monte Carlo techniques, we study the role of disorder on a system of hard-core bosons in a two-leg ladder with both intrachain (ttt) and interchain (${t}^{\ensuremath{'}}$) hoppings. We find that the phase diagram as a function of the boson density, disorder strength, and ${t}^{\ensuremath{'}}/t$ is far from being trivial. This contrasts with the case of spinless fermions where standard localization arguments apply and an Anderson-localized phase pervades the whole phase diagram. A compressible Bose-glass phase always intrudes between the Mott insulator with zero (or one) bosons per site and the superfluid that is stabilized for weak disorder. At half-filling, there is a direct transition between a (gapped) rung-Mott insulator and a Bose glass, which is driven by exponentially rare regions where disorder is suppressed. Finally, by doping the rung-Mott insulator, a direct transition to the superfluid is possible only in the clean system, whereas the Mott phase is always surrounded by the a Bose glass when disorder is present. The phase diagram based on our numerical evidence is finally reported.