Mean-field study of the Bose-Hubbard model in Penrose lattice

Ghadimi, Rasoul; Sugimoto, Takanori; Tohyama, Takami

doi:10.48550/arxiv.2005.04885

Cited by 3 publications

(3 citation statements)

References 59 publications

(64 reference statements)

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“…It is to be expected that the mean-field phase diagrams would converge between periodic and quasicrystalline lattices with no random onsite disorder as shown in figure 10(a) [88,89]. When random disorder is included, we observe the same features as expected from previous results on disorder in periodic lattices [1].…”

Section: Disordered Vertex Modelsupporting

confidence: 85%

The mean-field Bose glass in quasicrystalline systems

Johnstone

Öhberg

Duncan

2021

J. Phys. A: Math. Theor.

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We confirm the presence of a mean-field Bose glass (BG) in 2D quasicrystalline Bose-Hubbard models. We focus on two models where the aperiodic component is present in different parts of the problem. First, we consider a 2D generalisation of the Aubry-André (AA) model, where the lattice geometry is that of a square with a quasiperiodic onsite potential. Second, we consider the randomly disordered vertex model, which takes aperiodic tilings with non-crystalline rotational symmetries, and forms lattices from the vertices and lengths of the tiles. For the disordered vertex models, the mean-field BG forms across large ranges of the chemical potential, and we observe no significant differences from the case of a square lattice with uniform random disorder. Small variations in the critical points in the presence of random disorder between quasicrystalline and crystalline lattice geometries can be accounted for by the varying coordination number and the different rotational symmetries present. In the 2D AA model, substantial differences are observed from the usual phase diagrams of crystalline disordered systems. We show that weak modulation lines can be predicted from the underlying potential and may stabilise or suppress the mean-field BG in certain regimes. This results in a lobe-like structure for the mean-field BG in the 2D AA model, which is significantly different from the case of random disorder. Together, the two quasicrystalline models studied in this work show that the mean-field BG phase is present, as expected for

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Section: Disordered Vertex Modelsupporting

confidence: 85%

The mean-field Bose glass in quasicrystalline systems

Johnstone

Öhberg

Duncan

2021

J. Phys. A: Math. Theor.

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“…Beyond the MI critical points, the system is otherwise in the SF phase, with homogenous transport across the lattice. From the phase diagrams, we can also immediately see that the critical points for the square lattice and quasicrystalline tilings are almost identical, which is in agreement with previous results [90,91]. In other words, the local structure of the quasicrystals does not play a significant role in the phase transition of a MI to SF.…”

Section: B Disordered Vertex Modelsupporting

confidence: 89%

The Mean-Field Bose Glass in Quasicrystalline Systems

Johnstone,

Öhberg,

Duncan

2020

Preprint

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We study the ground state phases of the Bose-Hubbard model with disordered potentials for quasicrystalline systems, with a focus on the Bose-Glass phase. Generally speaking, disorder can lead to the formation of a Bose-Glass, which is characterised by the lack of global phase coherence across the lattice. Here, we will look at two models; the interacting 2D Aubry-Andre model and disordered vertex models from quasicrystalline tiling patterns. Unlike typical disorder in homogeneous, periodic systems, quasicrystalline models possess self-similarity. This leads to a fascinating interplay between correlated, quasiperiodic order and uncorrelated, random disorder. In this work, we combine Gutzwiller mean-field theory with a percolation analysis of superfluid clusters, allowing the critical points and phase regions of these disordered systems to be mapped. When the longrange order is separate to the random disorder, as is the case for the disordered vertex models, then the physics reflects that of periodic lattices with disorder. However, we find that long-range order present in the disorder term of the 2D Aubry-Andre model can result in some peculiarities to the physics of the Bose-Glass. These peculiarities include stabilisation from weak disorder lines and intricate, ordered structures of the phase itself that may provide fruitful areas of future study.

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“…The existence of a BG and the regime of strong interactions remain, however, largely unexplored. On the theoretical side, mean field phase diagrams have been found using inhomogeneous Gutzwiller-like ansatz on simplified quasiperiodic graphs [53][54][55]. Such approaches, however, ignore beyond-mean field effects in the vicinity of critical points as well as the exact connectivity of optical qua-sicrystals.…”

mentioning

confidence: 99%

Strongly-Interacting Bosons in a Two-Dimensional Quasicrystal Lattice

Gautier,

Yao,

Sanchez-Palencia

2020

Preprint

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Quasicrystals exhibit exotic properties inherited from the self-similarity of their long-range ordered, yet aperiodic, structure. The recent realization of an optical quasicrystal lattice for ultracold atoms paves the way to the study of correlated bosons in such structures, but the regime of strong interactions remains largely unexplored. Here, we determine the quantum phase diagram of two-dimensional correlated bosons in a quasicrystal potential. Using large-scale Monte Carlo calculations, we find evidence of a superfluid-to-Bose glass transition, and determine the critical line. Moreover, we show that strong interactions can stabilize a Mott insulator phase, possibly with spontaneously broken eightfold symmetry. Our results drive prospects to experimental investigation and, in particular, to the observation of the still elusive Bose glass phase in two dimensions.

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Mean-field study of the Bose-Hubbard model in Penrose lattice

Cited by 3 publications

References 59 publications

The mean-field Bose glass in quasicrystalline systems

The mean-field Bose glass in quasicrystalline systems

The Mean-Field Bose Glass in Quasicrystalline Systems

Strongly-Interacting Bosons in a Two-Dimensional Quasicrystal Lattice

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