Dressed Rydberg atoms in optical lattices are a promising platform for the quantum simulation of intriguing phenomena emerging in strongly interacting systems. Relevant to such a setup, we investigate the phase diagram of hard-core bosons in a triangular ladder with next-to-nearest-neighbor interaction along each leg and nearest-neighbor interactions without hopping between the legs. For weak interactions, Abelian bosonization predicts a spin density wave and a fully gapless Luttinger liquid phase. Such liquids transition to a ``spin-locked'' cluster Luttinger liquid at strong interactions along each leg, as predicted by cluster bosonization. Interestingly, the competition with the zigzag interaction generates a charge density wave, a ``polarized holonic'' phase, and a crystalline phase at the filling 2/5, that we address via a semiclassical perturbative approach. Exact diagonalization and density matrix renormalization group simulations confirm the predictions and further characterize the phases and their transitions.
Dressed Rydberg atoms in optical lattices are a promising platform for the quantum simulation of intriguing phenomena emerging in strongly interacting systems. Relevant to such a setup, we investigate the phase diagram of hard-core bosons in a triangular ladder with next-to-nearest-neighbor interaction along each leg and nearest-neighbor interactions without hopping between the legs. For weak interactions, Abelian bosonization predicts a spin density wave and a fully gapless Luttinger liquid phase. Such liquids transition to a spin-locked'' cluster Luttinger liquid at strong interactions along each leg, as predicted by cluster bosonization. Interestingly, the competition with the zigzag interaction generates a charge density wave, a polarized holonic'' phase, and a crystalline phase at the filling 2/5, that we address via a semiclassical perturbative approach. Exact diagonalization and density matrix renormalization group simulations confirm the predictions and further characterize the phases and their transitions.
We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and nonlocal terms gives rise to a phase diagram with liquid phases with dominant cluster, spin-, and density-wave quasi-long-range ordering. These phases are separated by Berezinskii-Kosterlitz-Thouless, Gaussian, and supersymmetric (SUSY) quantum critical transitions. For the latter, we provide a phenomenological description of coupled SUSY conformal field theories, whose predictions are confirmed by matrix product state simulations. Our results are motivated by, and directly relevant to, recent experiments with Rydberg-dressed atoms in optical lattices, where ladder dynamics has already been demonstrated, and emphasize the capabilities of these setups to investigate exotic quantum phenomena such as cluster liquids and coupled SUSY conformal field theories.
One-dimensional free fermions and hard-core bosons are often considered to be equivalent. Indeed, when restricted to nearest-neighbor hopping on a chain, the particles cannot exchange themselves, and therefore hardly experience their own statistics. Apart from the off-diagonal correlations which depend on the so-called Jordan-Wigner string, real-space observables are similar for free fermions and hard-core bosons on a chain. Interestingly, by coupling only two chains, thus forming a two-leg ladder, particle exchange becomes allowed and leads to a totally different physics between free fermions and hard-core bosons. Using a combination of analytical (strong coupling, field theory, renormalization group) and numerical (quantum Monte Carlo, density-matrix renormalization group) approaches, we study the apparently simple but nontrivial model of hard-core bosons hopping in a two-leg ladder geometry. At half filling, while a band insulator appears for fermions at large interchain hopping ${t}_{\ensuremath{\perp}}>2t$ only, a Mott gap opens up for bosons as soon as ${t}_{\ensuremath{\perp}}\ensuremath{\ne}0$ through a Kosterlitz-Thouless transition. Away from half filling, the situation is even more interesting since a gapless Luttinger liquid mode emerges in the symmetric sector with a nontrivial filling-dependent Luttinger parameter $1/2\ensuremath{\leqslant}{K}_{s}\ensuremath{\leqslant}1$. Consequences for experiments in cold atoms and spin ladders in a magnetic field, as well as disorder effects, are discussed. In particular, a quantum phase transition is expected at finite disorder strength between a one-dimensional superfluid and an insulating Bose glass phase.
Rydberg and Rydberg-dressed atomic gases have recently emerged as a promising quantum simulator for a variety of models in condensed matter physics. Here we investigate one-dimensional bosons with soft-core Rydberg-dressed interactions using exact path-integral quantum Monte Carlo simulations. The finite-range and the negative Fourier component of the interaction potential generate a roton mode at finite momentum, while particle-hole backscattering processes enhance the susceptibility of one-dimensional systems at twice the Fermi momentum. The competition between the corresponding length scales yields a rich phase diagram, featuring a conventional Tomonaga-Luttinger liquid (TLL) regime, a beyond-TLL regime, and commensurate cluster phases. In the TLL regime, the system transitions from Lieb-Liniger-like bnehavior with Luttinger parameter K>1 to hard-rod-like behavior with K<1, with a quasi-supersolid phase emerging for K<1/2. For strong interactions and high densities, deviations from TLL theory appear as precursors for the onset of cluster phases, where particles aggregate into stable clusters of several particles. The properties of each phase is discussed in detail.
We study hard-core bosons with unfrustrated nearest-neighbor hopping t and repulsive interaction V on a zigzag ladder. As a function of the boson density $\ensuremath{\rho}$ and V/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/t. At commensurate densities $\ensuremath{\rho}=1/3$, 1/2, and 2/3 insulating (crystalline) phases are stabilized for a sufficiently large interaction V. For intermediate densities $1/3<\ensuremath{\rho}<2/3$ and large V/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 symmetry breaking has been predicted.
Kinetically frustrated bosons at half filling in the presence of a competing nearest-neighbor repulsion support a wide supersolid regime on the two-dimensional triangular lattice. We study this model on a two-leg ladder using the finite-size density-matrix renormalization-group method, obtaining a phase diagram which contains three phases: a uniform superfluid (SF), an insulating charge density wave (CDW) crystal, and a bond ordered insulator (BO). We show that the transitions from SF to CDW and SF to BO are continuous in nature, with critical exponents varying continuously along the phase boundaries, while the transition from CDW to BO is found to be first order. The phase diagram is also found to contain an exactly solvable Majumdar Ghosh point, and reentrant SF to CDW phase transitions.
We explore the ground-state phase diagram of the S=1/2 two-leg ladder with different leg interactions. The xy and z components of the leg interactions between nearest-neighbor spins in the a (b) leg are respectively denoted by Jl,a and ΔlJl,a (Jl,b and ΔlJl,b). On the other hand, the xy and z components of the uniform rung interactions are respectively denoted by ΓrJr and Jr. In the above, Δl and Γr are the XXZ-type anisotropy parameters for the leg and rung interactions, respectively. This system has a frustration when Jl,aJl,b<0 irrespective of the sign of Jr. The phase diagram on the Δl (∣Δl∣≤1.0) versus Jl,b (−2.0≤Jl,b≤3.0) plane in the case where Jl,a=0.2, Jr=−1.0, and Γr=0.5 is determined numerically. We employ the physical consideration, and the level spectroscopy and phenomenological renormalization-group analyses of the numerical date obtained by the exact diagonalization method. The resultant phase diagram contains the ferromagnetic, Haldane, N{é}el, nematic Tomonaga-Luttinger liquid (TLL), partial ferrimagnetic, and XY1 phases. Interestingly enough, the nematic TLL phase appears in the strong-rung unfrustrated region as well as in the strong-rung frustrated one. We perform the first-order perturbational calculations from the strong rung coupling limit to elucidate the characteristic features of the phase diagram. Furthermore, we make the density-matrix renormalization-group calculations for some physical quantities such as the energy gaps, the local magnetization, and the spin correlation functions to supplement the reliability of the phase diagram.