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arXiv:1903.01766 · Physical review. B./Physical review. B

Interacting bosons in generalized zigzag and railroad-trestle models

Sebastian Greschner, Tapan Mishra

Published Oct 2, 2019• 9 citations
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Abstract

We theoretically study the ground-state phase diagram of strongly interacting bosons on a generalized zigzag ladder model, the railroad-trestle (RRT) model. By means of analytical arguments in the limits of decoupled chains and the case of vanishing fillings as well as extensive DMRG calculations, we examine the rich interplay between frustration and interaction for various parameter regimes. We distinguish three different cases, the fully frustrated RRT model where the dispersion relation becomes doubly degenerate and an extensive chiral superfluid regime is found, the antisymmetric RRT with alternating $\ensuremath{\pi}$ and 0 fluxes through the ladder plaquettes and the sawtooth limit, which is closely related to the latter case. We study detailed phase diagrams which include besides different single-component superfluids, the chiral superfluid phases, the two component superfluids, and different gaped phases, with dimer and a charge-density wave order.

DOI
10.1103/physrevb.100.144405

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We theoretically study the ground-state phase diagram of strongly interacting bosons on a generalized zigzag ladder model, the railroad-trestle (RRT) model. By means of analytical arguments in the limits of decoupled chains and the case of vanishing fillings as well as extensive DMRG calculations, we examine the rich interplay between frustration and interaction for various parameter regimes. We distinguish three different cases, the fully frustrated RRT model where the dispersion relation becomes doubly degenerate and an extensive chiral superfluid regime is found, the antisymmetric RRT with alternating \ensuremathπ\ensuremath{\pi}\ensuremathπ and 0 fluxes through the ladder plaquettes and the sawtooth limit, which is closely related to the latter case. We study detailed phase diagrams which include besides different single-component superfluids, the chiral superfluid phases, the two component superfluids, and different gaped phases, with dimer and a charge-density wave order.
We study the ground state phase diagram of a frustrated spin tube in a strong external magnetic field. This model can be viewed as two coupled zigzag spin chains, or as a two-leg spin ladder with frustrating next-nearest-neighbor couplings along the legs, and its study is motivated by the physics of such materials as sulfolane-Cu2Cl4{\mathrm{Cu}}_{2}{\mathrm{Cl}}_{4}Cu2​Cl4​ and BiCu2PO6{\mathrm{BiCu}}_{2}{\mathrm{PO}}_{6}BiCu2​PO6​. In magnetic fields right below the saturation, the system can be effectively represented as a dilute gas of two species of bosonic quasiparticles that correspond to magnons with inequivalent incommensurate momenta at two degenerate minima of the magnon dispersion. Using the method previously proposed and tested for frustrated spin chains, we calculate effective interactions in this two-component Bose gas. On this basis, we establish the phase diagram of nearly saturated frustrated spin tube, which is shown to include the two-component Luttinger liquid, two types of vector chiral phases, and phases whose physics is determined by the presence of bound magnons. We study the phase diagram of the model numerically by means of the density matrix renormalization group technique, and find a good agreement with our analytical predictions.
We consider interacting bosonic particles on a two-leg triangular ladder in the presence of an artificial gauge field. We employ density matrix renormalization group numerical simulations and analytical bosonization calculations to study the rich phase diagram of this system. We show that the interplay between the frustration induced by the triangular lattice geometry and the interactions gives rise to multiple chiral quantum phases. Phase transitions between superfluid to Mott-insulating states occur, which can have Meissner or vortex character. Furthermore, a state that explicitly breaks the symmetry between the two legs of the ladder, the biased chiral superfluid, is found for values of the flux close to $\ensuremath{\pi}$. In the regime of hard-core bosons, we show that the extension of the bond order insulator beyond the case of the fully frustrated ladder exhibits Meissner-type chiral currents. We discuss the consequences of our findings for experiments in cold atomic systems.
Using the bosonization and level spectroscopy methods, we study the ground-state phase diagram of a XXZ antiferromagnet on a railroad-trestle lattice with asymmetric leg interactions. It is shown that the asymmetry does not change the dimer/Neel transition line significantly, which agrees with the expectation based on a naive bosonization procedure, but it does change the dimer/spin-fluid transition line. To understand this observation, we analyze eigenvectors of the ground state, dimer excitation, doublet excitation and Neel excitation, and find that only the doublet excitation is affected by the asymmetric interaction.
We study hard-core bosons with unfrustrated nearest-neighbor hopping ttt and repulsive interaction VVV on a zigzag ladder. As a function of the boson density $\ensuremath{\rho}$ and V/tV/tV/t, the ground state displays different quantum phases. A standard one-component Tomonaga-Luttinger liquid is stable for $\ensuremath{\rho}<1/3$ (and $\ensuremath{\rho}>2/3$) at any value of V/tV/tV/t. At commensurate densities $\ensuremath{\rho}=1/3$, 1/21/21/2, and 2/32/32/3 insulating (crystalline) phases are stabilized for a sufficiently large interaction VVV. For intermediate densities $1/3<\ensuremath{\rho}<2/3$ and large V/tV/tV/t, the ground state shows a clear evidence of a bound state of two bosons, implying gapped single-particle excitations but gapless excitations of boson pairs. These properties can be understood by the fact that the antisymmetric sector acquires a gap and a single gapless mode survives. Finally, for the same range of boson densities and weak interactions, the system is again a one-component Tomonaga-Luttinger liquid with no evidence of any breaking of discrete symmetries, in contrast to the frustrated case, where a Z2{\mathcal{Z}}_{2}Z2​ symmetry breaking has been predicted.
We investigate a metallic zigzag carbon nanotube by means of a Hubbard model, which includes both on-site and nearest-neighbor interactions. Assuming weak interactions, a renormalization group analysis of the equivalent two-leg ladder followed by bosonization and refermionization results in a Gross-Neveu model with an enlarged symmetry relative to the original Hamiltonian. For the undoped case the symmetry of the Gross-Neveu model is SO(8), but for the doped case the particle-hole symmetry is broken and the symmetry reduces to SO(6). Four ground-state phases are found in the undoped carbon nanotube with repulsive interactions, a ddd-wave Mott insulator, an sss-wave Mott insulator, a ppp-density wave, and a charge density wave. The doped case has two ground-state phases, a ddd-wave superconductor and a phase where a ppp density wave and a charge density wave coexist. We also explore the global phase diagram with a general interaction profile and find several additional states, including a chiral current phase where current flows around the nanotube along the zigzag bonds.
The origin of metallic ferromagnetism is a long-standing problem in condensed matter physics, because it is a strong coupling phenomenon essentially. It was also known that one dimensional systems have a lesser chance of showing ferromagnetism in the ground states. In fact, for a class of one-dimensional correlated electron systems including the simple Hubbard chain, the ground state was proved to be nonmagnetic. Several authors have been studied whether ferromagnetism is stabilized or not by taking neglected terms in the simple Hubbard chain into account. It was shown that a positive next-nearest neighbor hopping leads to ferromagnetism for less-than-half filled systems in strong correlation regime on the basis of DMRG calculations. We call this model the railroad–trestle-lattice Hubbard model below. The railroad–trestle lattice is graphically shown in Fig. 1. In this article, we treat the problem of ferromagnetism of the nearly half-filled extended Hubbard ladder with an additional intersite repulsion V . The Hamiltonian is H 1⁄4 t P hi; ji; ðc y i cj þ c y j ci Þ þU P i nini# þV P hi; ji ninj, where ci represent electron creation operators, ni 1⁄4 P c y i ci , and hi; ji denotes nearest-neighbor pairs of the sites on the two-leg ladder. Vojta et al. made a DMRG study of this model in strong coupling region. Tsuchiizu and Suzumura recently studied this model by using the weakcoupling bosonization method, motivated by the experimental observation of a charge-density-wave in the selfdoped ladder compound Sr14 xCaxCu24O41. 7,8) We first mention the half-filled case, i.e., electron density n 1⁄4 1. When U < 3V , the ground state has the checkerboard-type charge-ordering shown in Fig. 2 due to the intersite repulsion. (The sublattice consisting of doubly occupied sites is defined as A-sublattice.) Our main concern is what happens when holes are doped into this chargeordered insulating state. By using the DMRG method, Vojta et al. calculated the checkerboard-type charge-ordering correlation function from quarter-filling to half-filling, 1=2 n 1, where U 1⁄4 8t was chosen. They confirmed that the long-range charge-order correlation is obtained for V VcðnÞ ’ U=3. They also found that the total spin of the doped charge-ordering state is not zero, i.e., the charge ordering coexists with ferromagnetism. However, the origin of this ferromagnetism was not clarified. The main purpose of this paper is to get intuitive understanding of the ferromagnetism in the doped charge-ordered state. In order to attack this issue, we assume t U, V and use strong coupling expansion. Then, we calculate the effective Hamiltonian for holes doped into the charge-ordered state at half-filling. When holes are introduced, they enter the A-sublattice sites [see Fig. 3(a)]. If we totally neglect the bare hopping term in H, then we have the ground state degeneracy concerned with the way of arrangement of doped holes. The introduction of the bare hopping term resolves this degeneracy and is expected to induce an ordering of the doped holes. In order to write down the second-order effective Hamiltonian with respect to t, it is convenient to carry out the particle–hole transformation for the A-sublattice according to c‘ 1⁄4 a‘ , where a y ‘ are the creation operators of the A-sublattice holes. Within the two-hole approximation, we obtain the following effective Hamiltonian: