Commensurate-incommensurate transition of cold atoms in an optical lattice

An atomic gas subject to a commensurate periodic potential generated by an optical lattice undergoes a superfluid--Mott insulator transition. Confining a strongly interacting gas to one dimension generates an instability where an arbitrary weak potential is sufficient to pin the atoms into the Mott state; here, we derive the corresponding phase diagram. The commensurate pinned state may be detected via its finite excitation gap and the Bragg peaks in the static structure factor.Comment: 4 pages, 2 figure

The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction

We study the one-dimensional Bose-Hubbard model using the Density-Matrix Renormalization Group (DMRG).For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott-insulators and charge density wave phases are determined. We find a direct phase transition between the charge density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. It is known from Luttinger liquid theory that a single impurity causes the system to be insulating if the effective interactions are repulsive, and that an even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac-conductivity in the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.Comment: 19 pages, 30 figure

One-dimensional phase transitions in a two-dimensional optical lattice

A phase transition for bosonic atoms in a two-dimensional anisotropic optical lattice is considered. If the tunnelling rates in two directions are different, the system can undergo a transition between a two-dimensional superfluid and a one-dimensional Mott insulating array of strongly coupled tubes. The connection to other lattice models is exploited in order to better understand the phase transition. Critical properties are obtained using quantum Monte Carlo calculations. These critical properties are related to correlation properties of the bosons and a criterion for commensurate filling is established.Comment: 14 pages, 8 figure

Mott-Superfluid transition in bosonic ladders

We show that in a commensurate bosonic ladder, a quantum phase transition occurs between a Mott insulator and a superfluid when interchain hopping increases. We analyse the properties of such a transition as well as the physical properties of the two phases. We discuss the physical consequences for experimental systems such as Josephson Junction arrays.Comment: 4 pages, 2 figures, revtex

Time dependent mean field theory of the superfluid-insulator phase transition

We develop a time-dependent mean field approach, within the time-dependent variational principle, to describe the Superfluid-Insulator quantum phase transition. We construct the zero temperature phase diagram both of the Bose-Hubbard model (BHM), and of a spin-S Heisenberg model (SHM) with the XXZ anisotropy. The phase diagram of the BHM indicates a phase transition from a Mott insulator to a compressibile superfluid phase, and shows the expected lobe-like structure. The SHM phase diagram displays a quantum phase transition between a paramagnetic and a canted phases showing as well a lobe-like structure. We show how the BHM and Quantum Phase model (QPM) can be rigorously derived from the SHM. Based on such results, the phase boundaries of the SHM are mapped to the BHM ones, while the phase diagram of the QPM is related to that of the SHM. The QPM's phase diagram obtained through the application of our approach to the SHM, describes the known onset of the macroscopic phase coherence from the Coulomb blockade regime for increasing Josephson coupling constant. The BHM and the QPM phase diagrams are in good agreement with Quantum Monte Carlo results, and with the third order strong coupling perturbative expansion.Comment: 15 pages, 8 figures. To be published in Phys. Rev.

Phases of the one-dimensional Bose-Hubbard model

The zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with nearest-neighbor interaction is investigated using the Density-Matrix Renormalization Group. Recently normal phases without long-range order have been conjectured between the charge density wave phase and the superfluid phase in one-dimensional bosonic systems without disorder. Our calculations demonstrate that there is no intermediate phase in the one-dimensional Bose-Hubbard model but a simultaneous vanishing of crystalline order and appearance of superfluid order. The complete phase diagrams with and without nearest-neighbor interaction are obtained. Both phase diagrams show reentrance from the superfluid phase to the insulator phase.Comment: Revised version, 4 pages, 5 figure

Effect of Doublon-Holon Binding on Mott transition---Variational Monte Carlo Study of Two-Dimensional Bose Hubbard Models

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 $\xi_{\rm dh}$ and the minimum D-D exclusion length $\xi_{\rm dd}$. Generally, a Mott transition occurs when $\xi_{\rm dh}$ becomes comparable to $\xi_{\rm dd}$. In the conductive (superfluid) state, domains of D-H pairs overlap with each other ($\xi_{\rm dh}>\xi_{\rm dd}$); 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.Comment: 16 pages, 22 figures, submitted to J. Phys. Soc. Jp

The Lorentz Integral Transform (LIT) method and its applications to perturbation induced reactions

The LIT method has allowed ab initio calculations of electroweak cross sections in light nuclear systems. This review presents a description of the method from both a general and a more technical point of view, as well as a summary of the results obtained by its application. The remarkable features of the LIT approach, which make it particularly efficient in dealing with a general reaction involving continuum states, are underlined. Emphasis is given on the results obtained for electroweak cross sections of few--nucleon systems. Their implications for the present understanding of microscopic nuclear dynamics are discussed.Comment: 83 pages, 31 figures. Topical review. Corrected typo

Effects of Long-Range Correlations on Nonmagnetic Mott Transitions in Hubbard model on Square Lattice

The mechanism of Mott transition in the Hubbard model on the square lattice is studied without explicit introduction of magnetic and superconducting correlations, using a variational Monte Carlo method. In the trial wave functions, we consider various types of binding factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), like a long-range type as well as a conventional nearest-neighbor type, and add independent long-range D-D (H-H) factors. It is found that a wide choice of D-H binding factor leads to Mott transitions at critical values near the band width. We renew the D-H binding picture of Mott transitions by introducing two characteristic length scales, the D-H binding length l_{DH} and the minimum D-D distance l_{DD}, which we appropriately estimate. A Mott transition takes place at l_{DH}=l_{DD}. In the metallic regime (l_{DH}>l_{DD}), the domains of D-H pairs overlap with one another, thereby doublons and holons can move independently by exchanging the partners one after another. In contrast, the D-D factors give only a minor contribution to the Mott transition.Comment: 13 pages, 18 figures, submitted to J. Phys. Soc. Jp

Density-matrix renormalisation group approach to quantum impurity problems

A dynamic density-matrix renormalisation group approach to the spectral properties of quantum impurity problems is presented. The method is demonstrated on the spectral density of the flat-band symmetric single-impurity Anderson model. We show that this approach provides the impurity spectral density for all frequencies and coupling strengths. In particular, Hubbard satellites at high energy can be obtained with a good resolution. The main difficulties are the necessary discretisation of the host band hybridised with the impurity and the resolution of sharp spectral features such as the Abrikosov-Suhl resonance.Comment: 16 pages, 6 figures, submitted to Journal of Physics: Condensed Matte