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arXiv:0802.0396 · Physical Review B

Phase diagram of a bosonic ladder with two coupled chains

Meetu Sethi Luthra, Tapan Mishra, Ramesh V. Pai, Bhanu Pratap Das

Published Oct 6, 2008• 16 citations
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Abstract

We study a bosonic ladder with two coupled chains using the finite-size density-matrix renormalization group method. We show that in a commensurate bosonic ladder the critical on-site interaction $({U}_{C})$ for the superfluid to Mott insulator transition gets larger as the interchain hopping $({t}_{\ensuremath{\perp}})$ increases. We analyze this quantum phase transition and obtain the phase diagram in the ${t}_{\ensuremath{\perp}}\ensuremath{-}U$ plane. We also consider the asymmetric case where the on-site interactions are different in the two chains and have shown that the system as a whole will not be in the Mott insulator phase unless both the chains have on-site interactions greater than the critical value.

DOI
10.1103/physrevb.78.165104

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We study a bosonic ladder with two coupled chains using the finite-size density-matrix renormalization group method. We show that in a commensurate bosonic ladder the critical on-site interaction (UC)({U}_{C})(UC​) for the superfluid to Mott insulator transition gets larger as the interchain hopping (t\ensuremath⊥)({t}_{\ensuremath{\perp}})(t\ensuremath⊥​) increases. We analyze this quantum phase transition and obtain the phase diagram in the t\ensuremath⊥\ensuremath−U{t}_{\ensuremath{\perp}}\ensuremath{-}Ut\ensuremath⊥​\ensuremath−U plane. We also consider the asymmetric case where the on-site interactions are different in the two chains and have shown that the system as a whole will not be in the Mott insulator phase unless both the chains have on-site interactions greater than the critical value.
We investigate the quantum phases of bosons in a two-chain-coupled ladder. This bosonic ladder is generally in a biased configuration, meaning that the two chains of the ladder can have dramatically different on-site interactions and potential energies. Adopting the numerical density-matrix renormalization-group method, we analyze the phase transitions in various parameter spaces. We find signatures of both insulating-to-superfluid and superfluid-to-insulating quantum phase transitions as the interchain tunneling is increased. Interestingly, tuning the interaction to some intermediate values, the system can exhibit a reentrant quantum phase transition between insulating and superfluid phases. We show that for infinite interaction bias the model is amenable to analytical treatment, predictions of which concerning the phase boundary are in great agreement with numerical results. We finally clarify some critical parameters which separate the system into regimes with distinct phase-transition behaviors, and we briefly compare typical properties of the biased and unbiased bosonic ladder systems. Our paper enriches Bose-Hubbard physics.
The Bose-Hubbard Hamiltonian describes the competition between superfluidity and Mott insulating behavior at zero temperature and commensurate filling as the strength of the on-site repulsion is varied. Gapped insulating phases also occur at noninteger densities as a consequence of longer ranged repulsive interactions. In this paper we explore the formation of gapped phases in coupled chains due instead to anisotropies ${t}_{x}\ensuremath{\ne}{t}_{y}$ in the bosonic hopping, extending the work of Crepin et al. [Phys. Rev. B 84, 054517 (2011).] on two coupled chains, where a gap was shown to occur at half filling for arbitrarily small interchain hopping ty{t}_{y}ty​. Our main result is that, unlike the two-leg chains, for three- and four-leg chains, a charge gap requires a finite nonzero critical ty{t}_{y}ty​ to open. However, these finite values are surprisingly small, well below the analogous values required for a fermionic band gap to open.
We study the superfluid and insulating phases of bosons in double-well optical lattices, and focus on the specific example of a two-legged ladder, which is currently accessible in experiments. We obtain the zero-temperature phase diagram using both mean-field and time-evolving block decimation techniques. We find that the mean-field approach describes the correct phase boundaries only when the intrachain hopping is sufficiently small in comparison to the on-site repulsion. We show the dependence of the phase diagram on the interchain hopping or tilt between double wells. We find that the Mott-insulator phase at unit filling exhibits a nonmonotonic behavior as a function of the tilt parameter, producing a reentrant phase transition between Mott insulator and superfluid phases. Finally, we determine the critical point separating the insulating and superfluid phases at commensurate fillings, where the Berezinskii-Kosterlitz-Thouless transition occurs.
We study the ground-state phase diagram of boson chains on a 2-period superlattice using the density matrix renormalization group method. New insulators for commensurate densities were found, differentiated by the arrangement of the particles in the unit cell, which was corroborated by analysis of the density versus the potential strength. Also, phase transitions between insulators for ρ ≥ 1 were seen, and a maximum in the behavior of the von Neumann entropy in the critical region was revealed, which suggests a superfluid phase between the insulators.
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.