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Journal of Physics Conference Series

Mott insulator and superfluid phases in bosonic superlattices

Greis J. Cruz, R Franco, Jereson Silva-Valencia

Published Feb 1, 2016• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/687/1/012065

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Physical review. B, Condensed matter•Jul 1, 1989•3,511 citations
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.
We analyze various quantum phases of ultracold bosonic atoms in a periodic one-dimensional optical superlattice. Our studies have been performed using the finite-size density-matrix renormalization group method in the framework of the Bose-Hubbard model. Calculations have been carried out for a wide range of densities and the energy shifts due to the superlattice potential. At commensurate fillings, we find the Mott insulator and the superfluid phases as well as Mott insulators induced by the superlattice. At a particular incommensurate density, the system is found to be in the superfluid phase coexisting with density oscillations for a certain range of parameters of the system.
We study the superfluid to Mott-insulator transition of hardcore bosons in commensurate superlattices in two and three dimensions. We focus on the special case where the superlattice has period two and the system is at half-filling. We obtain numerical results by using the stochastic series expansion algorithm, and compute various properties of the system, such as the ground-state energy, the density of bosons in the zero-momentum mode, the superfluid density, and the compressibility. We employ finite-size scaling to extrapolate the thermodynamic limit, and find the critical points of the phase transition. We also explore the extent to which several approximate solutions such as mean-field theory, with and without spin-wave corrections, can help one gain analytical insight into the behavior of the system in the vicinity of the phase transition.
We investigate the ground-state properties of a nonlocally coupled bosonic system in a bilayer optical superlattice by considering bosons in one layer to be of soft core in nature and separately allowing two- and three-body hard-core constraints on the other layer. We find that the presence of different constraints on bosons in one layer influences the overall phase diagram exhibiting various Mott insulator phases at incommensurate densities due to the presence of the superlattice potential apart from the usual Mott insulators at commensurate densities. Moreover, the presence of two- or three-body constraints significantly modifies the Mott insulator to superfluid phase transition points as a function of the superlattice potential. Due to the various competing interactions, constraints, and superlattice potential, the phase diagrams exhibit significantly different features. We obtain the complete phase diagrams by using the cluster mean-field-theory approach. We further extend this work to a coupled two-leg ladder superlattice where we obtain similar physics using the density-matrix renormalization-group method.
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 $({t}_{\ensuremath{\perp}})$ 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.
"We studied the one-dimensional Bose-Hubbard model, by means of the Density Matrix Renormalization Group (DMRG). The U parameter, which contains the Coulombian repulsion information, is fixed to U = 1 and it is performed a swept over the hopping parameter t. The entanglement is investigated by implementing the one-site, two-site and block von Neumann entropy looking for which of these measures give account of the quantum phase transition from Mott insulator to superfluid. The one-site and two-site entropy do not give information of the phase transition of the system. In contrast, the block entropy shows, in the Mott insulator phase a behavior that saturates rapidly to a finite value and in the superfluid phase shows a logarithmic behavior that agrees with the mean field theory. From the derivative of the block entropy average as a function of t we found the phase transition takes place at tc =0.15."
The phase diagrams and phase transitions of bosons with short-ranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluid-insulator transition induced by varying a parameter such as the density. Bosons in periodic potentials (e.g., on a lattice) at T=0 exhibit two types of phases: a superfluid phase and Mott insulating phases characterized by integer (or commensurate) boson densities, by the existence of a gap for particle-hole excitations, and by zero compressibility. Generically, the superfluid onset transition in d dimensions from a Mott insulator to superfluidity is ``ideal,'' or mean field in character, but at special multicritical points with particle-hole symmetry it is in the universality class of the (d+1)-dimensional XY model. In the presence of disorder, a third, ``Bose glass'' phase exists. This phase is insulating because of the localization effects of the randomness and analogous to the Fermi glass phase of interacting fermions in a strongly disordered potential.The Bose glass phase is characterized by a finite compressibility, no gap, but an infinite superfluid susceptibility. In the presence of disorder the transition to superfluidity is argued to occur only from the Bose glass phase, and never directly from the Mott insulator. This zero-temperature superfluid-insulator transition is studied via generalizations of the Josephson scaling relation for the superfluid density at the ordinary \ensuremath{\lambda} transition, highlighting the crucial role of quantum fluctuations. The transition is found to have a dynamic critical exponent z exactly equal to d and correlation length and order-parameter correlation exponents \ensuremath{\nu} and \ensuremath{\eta} which satisfy the bounds \ensuremath{\nu}\ensuremath{\ge}2/d and \ensuremath{\eta}\ensuremath{\le}2-d, respectively. It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension dc{d}_{c}dc​ which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed. Many of these conclusions are verified by explicit calculations on a model of one-dimensional bosons in the presence of both random and periodic potentials. The general results are applied to experiments on 4He^{4}\mathrm{He}4He absorbed in porous media such as Vycor. Some measurable properties of the superfluid onset are predicted exactly [e.g., the exponent x relating the \ensuremath{\lambda} transition temperature to the zero-temperature superfluid density is found to be d/2(d-1)], while stringent bounds are placed on others. Analysis of preliminary data is consistent with these predictions.