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.
The zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with nearestneighbor 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.PACS numbers: 05.30. Jp, 05.70.Jk, 67.40.Db Quantum phase transitions in strongly correlated systems have attracted a lot of interest in recent years. Usually the basic particles are electrons, but in some interesting cases the relevant particles are not fermions but bosons. Examples of experimental systems with superfluid and insulating phases are Cooper pairs in thin granular superconducting films 1 and cooper pairs or fluxes in Josephson junction arrays 2 . While in dimensions greater than one the existence of supersolids 3 , i.e. phases with simultaneous superfluid and crystalline order, has been established in theoretical work, the situation in one dimension is less clear. Recently normal phases that are neither crystalline nor superfluid have been found in a one-dimensional model of Josephson junction arrays 4 in the region where supersolids are found in higher dimensions. In this paper we will verify whether supersolids or normal phases exist in the more general Bose-Hubbard model in one dimension.The Bose-Hubbard model contains the basic physics of interacting bosons on a lattice. It is a minimal bosonic many-particle model that cannot be reduced to a single particle model. The bosons have repulsive interactions, and they can gain energy by hopping to neighboring sites on the lattice. The Hamiltonian with on-site and nearestneighbor interactions iswhere b i are the annihilation operators of bosons on site i,n i = b † i b i the number of particles on site i, t is the hopping matrix element. U and V are on-site and nearestneighbor repulsion, and µ is the chemical potential. The energy scale is set by choosing U = 1.The range of the interactions depends on the individual experimental situation. In general the lattice underlying the system is not an atomic lattice, but a larger structure like a Josephson-junction or a grain in a superconductor. In Josephson-junctions the relevant bosons can be cooper pairs or fluxes, resulting in different interactions.As a starting point we first consider the case of onsite repulsion only. In the (µ, t)-plane Mott-insulating regions are surrounded by the superfluid phase 5 . These phases are separated by two types of phase transitions. On the constant density line the transition is driven by phase fluctuations and is of the Berezinskii-KosterlitzThouless (BKT...
The density matrix renormalization group ͑DMRG͒ method allows for very precise calculations of ground state properties in low-dimensional strongly correlated systems. We investigate two methods to expand the DMRG to calculations of dynamical properties. In the Lanczos vector method the DMRG basis is optimized to represent Lanczos vectors, which are then used to calculate the spectra. This method is fast and relatively easy to implement, but the accuracy at higher frequencies is limited. Alternatively, one can optimize the basis to represent a correction vector for a particular frequency. The correction vectors can be used to calculate the dynamical correlation functions at these frequencies with high accuracy. By separately calculating correction vectors at different frequencies, the dynamical correlation functions can be interpolated and pieced together from these results. For systems with open boundaries we discuss how to construct operators for specific wave vectors using filter functions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.