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arXiv:1406.5849 · Physical Review B

Quantum phases of hardcore bosons in two coupled chains: A density matrix renormalization group study

Bradraj Pandey, Subhasis Sinha, Swapan Kumar Pati

Published Jun 26, 2015• 9 citations
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Abstract

We consider hardcore bosons in two coupled chains of one dimensional lattices at half filling with repulsive intrachain interaction and interchain attraction. This can be mapped onto a coupled chain of spin-1/2 $XXZ$ model with interchain ferromagnetic coupling. We investigate various phases of hardcore bosons (and related spin model) at zero temperature by a density matrix renormalization group method. Apart from the usual superfluid and density wave phases, pairing of interchain bosons leads to the formation of phases like pair superfluid and density wave of strongly bound pairs. We discuss the possible experimental realization of such correlated phases in the context of cold dipolar gas.

DOI
10.1103/physrevb.91.214432

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We consider hardcore bosons in two coupled chains of one dimensional lattices at half filling with repulsive intrachain interaction and interchain attraction. This can be mapped onto a coupled chain of spin-1/2 XXZXXZXXZ model with interchain ferromagnetic coupling. We investigate various phases of hardcore bosons (and related spin model) at zero temperature by a density matrix renormalization group method. Apart from the usual superfluid and density wave phases, pairing of interchain bosons leads to the formation of phases like pair superfluid and density wave of strongly bound pairs. We discuss the possible experimental realization of such correlated phases in the context of cold dipolar gas.
We investigate the phase diagram of two coupled quantum spin-1/2 chains, a square ladder, allowing for anisotropies both in the interchain and intrachain coupling, using the recently introduced density-matrix renormalization-group (DMRG) algorithm. We consider open chains up to a length of 2\ifmmode\times\else\texttimes\fi{}200, while retaining up to 120 states in the truncated basis of the Hilbert space. The phase diagram is discussed in connection with exact results and bosonization analysis. Numerically, we show that the crossover from the critical behavior of the uncoupled disordered spin-1/2 chain to a gapped quantum liquid sets in for infinitesimal interchain coupling, both for ferromagnetic and antiferromagnetic interchain coupling. The Haldane phase of the coupled chains is, even for small interchain couplings, generically described by the Affleck-Kennedy-Lieb-Tasaki model. We also discuss typical shortcomings of the DMRG for some choices of the interaction parameters. \textcopyright{} 1996 The American Physical Society.
The phase diagram of two bosonic chains coupled by interchain hopping and interchain boson-boson repulsion is investigated by means of bosonization and renormalization-group techniques. It comprises two types of charge-density waves, a conventional superfluid phase, and a superfluid phase made of condensed boson pairs. The effect of a random potential on that system is also derived. Compared with the one-chain case, interchain hopping strongly stabilizes the conventional superfluid phase with respect to Anderson localization. By contrast, the superfluid phase made of condensed boson pairs is much more unstable with respect to Anderson localization than the superfluid phase of the one-chain system. An exact mapping of the two strongly correlated bosonic chains onto two coupled vortex planes gives us the phase diagram of the latter system without any further calculation. The vortex system exhibits two types of vortex lattice phase (one with entanglement and another one without entanglement), a normal phase and a phase with bound pairs of vortices. The results for Anderson localization of the bosons allow us to study vortex pinning by columnar defects or twin boundaries and obtain the correlation length of the pinned vortex lattice. We show that interplane vortex hopping strongly reduces vortex pinning by columnar defects but not by twin boundaries. We obtain the melting temperature of the entangled solid. We also derive the critical current by modified Larkin-Ovchinnikov arguments and find a very sharp decrease of critical currents when the system moves into the entangled phase in the case of columnar pins. For strong columnar pins, there is a transition into a pinned solid phase with dislocations. We argue that two multicritical points may exist in the phase diagram.
We calculate the zero-temperature phase diagram of the disordered Bose-Hubbard model in one dimension using the density matrix renormalization group. For integer filling the Mott insulator is always separated from the superfluid by a Bose glass phase. There is a re-entrance of the Bose glass both as a function of the repulsive interaction and of disorder. At half-filling where no Mott insulator exists, the superfluid density has a maximum where the kinetic and repulsive energies are about the same. Superfluidity is suppressed both for small and very strong repulsion but is always monotonic in disorder.
We consider a periodic lattice loaded with pairs of bosonic atoms tightly bound to each other via strong attractive on-site interaction that exceeds the intersite tunneling rate. An ensemble of such lattice dimers is accurately described by an effective Hamiltonian of hard-core bosons with strong nearest-neighbor repulsion, which is equivalent to the XXZXXZXXZ model with Ising-like anisotropy. We calculate the ground-state phase diagram for a one-dimensional system, which exhibits incompressible phases, corresponding to an empty and a fully filled lattice (ferromagnetic phases) and a half-filled alternating density crystal (antiferromagnetic phase), separated from each other by compressible phases. In a finite lattice the compressible phases show characteristic oscillatory modulations on top of the antiferromagnetic density profile and in density-density correlations. We derive a kink model that provides simple quantitative explanation of these features. To describe the long-range correlations of the system, we employ the Luttinger-liquid theory with the relevant Luttinger parameter KKK obtained exactly using the Bethe-ansatz solution. We calculate the density-density as well as first-order correlations and find excellent agreement with numerical results obtained with density-matrix renormalization-group methods.
We study the phase diagram of two weakly coupled one-dimensional dipolar boson chains at half-odd-integer fillings. We find that the system contains a rich phase diagram. Four different phases are found. They are the Mott insulators, the single-particle resonant superfluid, the paired superfluid, and the bond-density or interchain density waves. Moreover, the Mott insulating phase can be further classified according to a hidden string order parameter, which is analogous to the one investigated recently in the one-dimensional boson Mott insulator at integer fillings.
We investigate a system of two- and three-body constrained dipolar bosons in a pair of one-dimensional optical lattices coupled to each other by nonlocal dipole-dipole interactions. Assuming attractive dipole-dipole interactions, we obtain the ground-state phase diagram of the system by employing the cluster mean-field theory. The competition between the repulsive on-site and attractive nearest-neighbor interactions between the chains yields three kinds of superfluids, namely, the trimer superfluid, the pair superfluid, and the usual single-particle superfluid along with the insulating Mott phase at the commensurate density. Additionally, we realize the simultaneous existence of Mott insulator and superfluid phases for the two- and three-body constrained bosons, respectively. We also analyze the stability of these quantum phases in the presence of a harmonic trap potential.