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On evidence for quantum Berezinskii-Kosterlitz-Thouless transition in one-dimensional Bose-Hubbard model from on-site atom number fluctuations

Mateusz Łącki, Bogdan Damski

Published Jul 13, 2021• 0 citations
OpenAlex

Abstract

We study the one-dimensional Bose-Hubbard model describing the superfluid-Mott insulator quantum phase transition of cold atoms in optical lattices. We show that derivatives of the variance of the on-site atom number occupation, computed with respect to the parameter driving the transition, have extrema that are located off the critical point even in the thermodynamic limit. We discuss whether such extrema provide solid evidence of the quantum Berezinskii-Kosterlitz-Thouless transition taking place in this system. The calculations are done for systems with the mean number of atoms per lattice site equal to either one or two. They also characterize the nearest-neighbor correlation function, which is typically discussed in the context of time-of-flight images of cold atoms.

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We study the one-dimensional Bose-Hubbard model describing the superfluid-Mott insulator quantum phase transition of cold atoms in optical lattices. We show that derivatives of the variance of the on-site atom number occupation, computed with respect to the parameter driving the transition, have extrema that are located off the critical point even in the thermodynamic limit. We discuss whether such extrema provide solid evidence of the quantum Berezinskii-Kosterlitz-Thouless transition taking place in this system. The calculations are done for systems with the mean number of atoms per lattice site equal to either one or two. They also characterize the nearest-neighbor correlation function, which is typically discussed in the context of time-of-flight images of cold atoms.
We study the one-dimensional Bose-Hubbard model describing the superfluid-Mott insulator quantum phase transition of cold atoms in optical lattices. We show that derivatives of the variance of the on-site atom number occupation, computed with respect to the parameter driving the transition, have extrema that are located off the critical point even in the thermodynamic limit. We discuss whether such extrema provide solid evidence of the quantum Berezinskii-Kosterlitz-Thouless transition taking place in this system. The calculations are done for systems with the mean number of atoms per lattice site equal to either one or two. They also characterize the nearest-neighbor correlation function, which is typically discussed in the context of time-of-flight images of cold atoms.
We discuss how positions of critical points of the three-dimensional Bose-Hubbard model can be accurately obtained from variance of the on-site atom number operator, which can be experimentally measured. The idea that we explore is that the derivative of the variance, with respect to the parameter driving the transition, has a pronounced maximum close to critical points. We show that Quantum Monte Carlo studies of this maximum lead to precise determination of critical points for the superfluid-Mott insulator transition in systems with mean number of atoms per lattice site equal to one, two, and three. We also extract from such data the correlation-length critical exponent through the finite-size scaling analysis and discuss how the derivative of the variance can be reliably computed from numerical data for the variance. The same conclusions apply to the derivative of the nearest-neighbor correlation function, which can be obtained from routinely measured time-of-flight images.
We show that the critical point of the two-dimensional Bose-Hubbard model can be easily found through studies of either on-site atom number fluctuations or the nearest-neighbor two-point correlation function (the expectation value of the tunnelling operator). Our strategy to locate the critical point is based on the observation that the derivatives of these observables with respect to the parameter that drives the superfluid-Mott insulator transition are singular at the critical point in the thermodynamic limit. Performing the quantum Monte Carlo simulations of the two-dimensional Bose-Hubbard model, we show that this technique leads to the accurate determination of the position of its critical point. Our results can be easily extended to the three-dimensional Bose-Hubbard model and different Hubbard-like models. They provide a simple experimentally-relevant way of locating critical points in various cold atomic lattice systems.
The Bose–Hubbard model with an effective off-site three-body tunneling, characterized by jumps towards one another, between one atom on a site and a pair atoms on the neighborhood site, is studied systematically on a one-dimensional (1D) lattice, by using the density matrix renormalization group method. The off-site trimer superfluid, condensing at momentum k = 0 , emerges in the softcore Bose–Hubbard model but it disappears in the hardcore Bose–Hubbard model. Our results numerically verify that the off-site trimer superfluid phase derived in the momentum space from [ Phys. Rev. A 81 , 011601(R) (2010)] is stable in the thermodynamic limit. The off-site trimer superfluid phase, the partially off-site trimer superfluid phase and the Mott insulator phase are found, as well as interesting phase transitions, such as the continuous or first-order phase transition from the trimer superfluid phase to the Mott insulator phase. Our results are helpful in realizing this novel off-site trimer superfluid phase by cold atom experiments.
We study the superfluid-insulator transition in Bose-Hubbard models in one-, two-, and three-dimensional cubic lattices by means of a recently proposed variational wave function. In one dimension, the variational results agree with the expected Berezinskii-Kosterlitz-Thouless scenario of the interaction-driven Mott transition. In two and three dimensions, we find evidence that, across the transition, most of the spectral weight is concentrated at high energies, suggestive of preformed Mott-Hubbard sidebands. This result is compatible with the experimental data by Stoferle et al. [Phys. Rev. Lett. 92, 130403 (2004)].
Motivated by a recent experiment that realizes nearest-neighbor dipolar couplings in an optical lattice [C. Lagoin et al., Nature (London) 609, 485 (2022)], we study a one-dimensional version of the two-component extended Bose-Hubbard model via the density-matrix renormalization group method. By using the nearest-neighbor and on-site interaction parameters from the experiment, we start by mapping the quantum phase diagram in the hopping parameter ${t}_{A}\text{\ensuremath{-}}{t}_{B}$ plane with boson densities ${\ensuremath{\rho}}_{A}={\ensuremath{\rho}}_{B}=1/2$. In addition to the density-wave phase reported in the experiment, we find several regimes of superfluidity when one or both hopping parameters are large enough, and interestingly there is a supercounterfluid phase at moderate and comparable hopping parameters. The universality classes of these phase transitions are analyzed from the correlation functions, excitation gaps, and entanglement entropy. In particular, a Berezinskii-Kosterlitz-Thouless type is recognized for several gapped-to-gapless transitions. In addition, we also study the quantum phase transitions by varying ${\ensuremath{\rho}}_{B}$ from 0 to 1 while keeping ${\ensuremath{\rho}}_{A}=1/2$. We identify a supersolid phase in a wide range of $1/2<{\ensuremath{\rho}}_{B}<1$. Our work paves the way for realizing exotic many-body phases in cold-atom experiments upon proper tuning of experimental parameters.