Phase diagram of hard-core bosons on clean and disordered two-leg ladders: Mott insulator–Luttinger liquid–Bose glass

Abstract

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 depends 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 twoleg 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 non-trivial 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 ⊥ > 2t only, a Mott gap opens up for bosons as soon as t ⊥ = 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 non-trivial filling-dependent Luttinger parameter 1/2 ≤ Ks ≤ 1. Consequences for experiments in cold atoms, 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 1D superfluid and an insulating Bose glass phase.

Bose metals and insulators on multileg ladders with ring exchange

“…Furthermore, our confirmation of the central charge of c 2 for the DBL [3,0] and the compelling results of the VMC/ED comparison for small system sizes serve to reinforce our proposed realization of this phase in our model. We also carefully considered finite-size effects using DMRG, and, although we can never rule out eventual small gaps appearing on very long length scales, 56 we believe the data presented strongly supports identification of the remarkable phase found in our ring model as an exotic gapless Mott insulator.…”

“…In these works, it was shown that at halffilling the system enters a rung Mott insulating phase for any finite J ⊥ , although the charge gap grows exponentially slowly with J ⊥ , i.e., as exp(−aJ/J ⊥ ), and is extremely difficult to deal with numerically due to a large value of the constant factor a in the exponential. 56 In our DMRG study of the two-leg half-filled system, we observed what looked like a superfluid on finite-size systems for small K; however, we did not perform an extensive finite-size analysis of this system as in Ref. 56.…”

“…For example, we have been unable to extract a meaningful central charge with the DMRG data, which points to c 2-3 for a 24×3 system, while the quasi-1D BCSF phase described above should lead to a Luttinger liquid with c = 1 gapless mode. It may be that the DMRG entanglement entropy Finally, we note that two very recent works 55,56 have considered in detail hard-core bosons hopping on the twoleg ladder without ring exchange, i.e., our J-J ⊥ -K model with K = 0. In these works, it was shown that at halffilling the system enters a rung Mott insulating phase for any finite J ⊥ , although the charge gap grows exponentially slowly with J ⊥ , i.e., as exp(−aJ/J ⊥ ), and is extremely difficult to deal with numerically due to a large value of the constant factor a in the exponential.…”

“…56 In our DMRG study of the two-leg half-filled system, we observed what looked like a superfluid on finite-size systems for small K; however, we did not perform an extensive finite-size analysis of this system as in Ref. 56. It is therefore possible that the apparent superfluid is a rung Mott phase on long length scales, and there are only direct transitions between the rung Mott phase and the staggered rung current and (π, π) CDW phases mentioned above.…”

Geometry of system-bath coupling and gauge fields in bosonic ladders: Manipulating currents and driving phase transitions

“…two connected chains. This geometry has been extensively studied both in Josephson junctions arrays and bosonic atoms in optical lattices also in presence of interactions [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. To be highlighted is the emergence of a quantum phase transition for bosonic FIG.…”