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arXiv:1204.1175 · Journal of the Physical Society of Japan

Mott Transition and Spin Structures of Spin-1 Bosons in Two-Dimensional Optical Lattice at Unit Filling

Yuta Toga, Hiroki Tsuchiura, Makoto Yamashita, Kensuke Inaba, Hisatoshi Yokoyama

Published May 2, 2012• 13 citations
arXivHTMLPDF

Abstract

We study the ground state properties of spin-1 bosons in a two-dimensional optical lattice, by applying a variational Monte Carlo method to the S=1 Bose-Hubbard model on a square lattice at unit filling. A doublon-holon binding factor introduced in the trial state provides a noticeable improvement in the variational energy over the conventional Gutzwiller wave function and allows us to deal effectively with the inter-site correlations of particle densities and spins. We systematically show how spin-dependent interactions modify the superfluid-Mott insulator transitions in the S=1 Bose-Hubbard model due to the interplay between the density and spin fluctuations of bosons. Furthermore, regarding the magnetic phases in the Mott region, the calculated spin structure factor elucidates the emergence of nematic and ferromagnetic spin orders for antiferromagnetic ($U_2>0$) and ferromagnetic ($U_2<0$) couplings, respectively.

DOI
10.1143/jpsj.81.063001

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We study the ground state properties of spin-1 bosons in a two-dimensional optical lattice, by applying a variational Monte Carlo method to the S=1 Bose-Hubbard model on a square lattice at unit filling. A doublon-holon binding factor introduced in the trial state provides a noticeable improvement in the variational energy over the conventional Gutzwiller wave function and allows us to deal effectively with the inter-site correlations of particle densities and spins. We systematically show how spin-dependent interactions modify the superfluid-Mott insulator transitions in the S=1 Bose-Hubbard model due to the interplay between the density and spin fluctuations of bosons. Furthermore, regarding the magnetic phases in the Mott region, the calculated spin structure factor elucidates the emergence of nematic and ferromagnetic spin orders for antiferromagnetic (U2>0U_2>0U2​>0) and ferromagnetic (U2<0U_2<0U2​<0) couplings, respectively.
We study, using quantum Monte Carlo (QMC) simulations, the ground state properties of spin-1 bosons trapped in a square optical lattice. The phase diagram is characterized by the mobility of the particles (Mott insulating or superfluid phase) and by their magnetic properties. For ferromagnetic on-site interactions, the whole phase diagram is ferromagnetic and the Mott insulators-superfluid phase transitions are second order. For antiferromagnetic on-site interactions, spin nematic order is found in the odd Mott lobes and in the superfluid phase. Furthermore, the superfluid-insulator phase transition is first or second order depending on whether the density in the Mott is even or odd. Inside the even Mott lobes we observe a singlet-to-nematic transition for certain values of the interactions. This transition appears to be first order.
To understand the mechanism of Mott transitions in case of no magnetic influence, superfluid-insulator (Mott) transitions in the S=0 Bose Hubbard model at unit filling are studied on the square and triangular lattices, using a variational Monte Carlo method. In trial many-body wave functions, we introduce various types of attractive correlation factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), which play a central role for Mott transitions, in addition to the onsite repulsive (Gutzwiller) factor. By optimizing distance-dependent parameters, we study various properties of this type of wave functions. With a hint from the Mott transition arising in a completely D-H bound state, we propose an improved picture of Mott transitions, by introducing two characteristic length scales, the D-H binding length ξdhξ_{\rm dh}ξdh​ and the minimum D-D exclusion length ξddξ_{\rm dd}ξdd​. Generally, a Mott transition occurs when ξdhξ_{\rm dh}ξdh​ becomes comparable to ξddξ_{\rm dd}ξdd​. In the conductive (superfluid) state, domains of D-H pairs overlap with each other (ξdh>ξddξ_{\rm dh}>ξ_{\rm dd}ξdh​>ξdd​); thereby D and H can propagate independently as density carriers by successively exchanging the partners. In contrast, intersite repulsive Jastrow (D-D and H-H) factors have little importance for the Mott transition.
We describe the ground state of a gas of bosonic atoms with two coherently coupled internal levels in a deep optical lattice in a one-dimensional geometry. In the single-band approximation this system is described by a Bose-Hubbard Hamiltonian. The system has a superfluid and a Mott insulating phase that can be either paramagnetic or ferromagnetic. We characterize the quantum phase transitions at unit filling by means of a density-matrix renormalization-group technique and compare the results with a mean-field approach and an effective spin Hamiltonian. The presence of the ferromagnetic Ising-like transition modifies the Mott lobes. In the Mott insulating region the system maps to the ferromagnetic spin-1/2 XXZXXZXXZ model in a transverse field and the numerical results compare very well with the analytical results obtained from the spin model. In the superfluid regime quantum fluctuations strongly modify the phase transition with respect to the well-established mean-field three-dimensional classical bifurcation.
We study, using quantum Monte Carlo simulations, the bosonic Kondo-Hubbard model in a two-dimensional square lattice. We explore the phase diagram and analyze the mobility of particles and magnetic properties. At unit filling, the transition from a paramagnetic Mott insulator to a ferromagnetic superfluid appears continuous, contrary to what was predicted with mean field. For double occupation per site, both the Mott insulating and superfluid phases are ferromagnetic and the transition is still continuous. Multiband tight-binding Hamiltonians can be realized in optical lattice experiments, which offer not only the possibility of tuning the different energy scales over wide ranges, but also the option of loading the system with either fermionic or bosonic atoms.
We investigate the Mott transition in a two-dimensional two-orbital Hubbard model on a square lattice at half filling by using the variational Monte Carlo method. As a variational trial wave function, we consider Gutzwiller's on-site correlations and nearest-neighbor doublon-holon correlations. We calculate the ground-state energy and the other physical quantities, all of which clearly signal a first-order Mott transition. We thus obtain the phase diagram at zero temperature, where we find the coexistence region of the metal and the Mott insulator. We discuss how Hund's coupling affects the nature of the Mott transition in this system.
We study the physics of interacting spin-1 bosons in an optical lattice using a variational Gutzwiller technique. We compute the mean-field ground state wave function and discuss the evolution of the condensate, spin, nematic, and singlet order parameters across the superfluid-Mott transition. We then extend the Gutzwiller method to derive the equations governing the dynamics of low energy excitations in the lattice. Linearizing these equations, we compute the excitation spectra in the superfluid and Mott phases for both ferromagnetic and antiferromagnetic spin-spin interactions. In the superfluid phase, we recover the known excitation spectrum obtained from Bogoliubov theory. In the nematic Mott phase, we obtain gapped, quadratically dispersing particle and hole-like collective modes, whereas in the singlet Mott phase, we obtain a nondispersive gapped mode, corresponding to the breaking of a singlet pair. For the ferromagnetic Mott insulator, the Gutzwiller mean-field theory only yields particle-hole-like modes but no Goldstone mode associated with long-range spin order. To overcome this limitation, we supplement the Gutzwiller theory with a Schwinger boson mean-field theory which captures superexchange-driven fluctuations. In addition to the gapped particle-hole-like modes, we obtain a gapless quadratically dispersing ferromagnetic spin-wave Goldstone mode. We discuss the evolution of the singlet gap, particle-hole gap, and the effective mass of the ferromagnetic Goldstone mode as the superfluid-Mott phase boundary is approached from the insulating side. We discuss the relevance and validity of Gutzwiller mean-field theories to spinful systems, and potential extensions of this framework to include more exotic physics which appears in the presence of spin-orbit coupling or artificial gauge fields.