Anisotropic Harper-Hofstadter-Mott model: Competition between condensation and magnetic fields

Hügel, Dario; Strand, Hugo U. R.; Werner, Philipp; Pollet, Lode

doi:10.1103/physrevb.96.054431

Cited by 24 publications

(39 citation statements)

References 60 publications

(126 reference statements)

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“…t x = 0) instead, the cylinder reduces to an infinite set of decoupled 4-site rings which-depending on the filling -can exhibit gapped phases. The phase diagram therefore strongly differs at negative anisotropies from the one observed in the fully two-dimensional model [22]. The fact that the phases discussed in the following are in part entirely related to the quasi-one-dimensional geometry of the lattice is further evidenced by the fact that the situation changes drastically as soon as L y is changed from 4 to 8 with two unit cells in the y-direction, as discussed in appendix B, where the L y =8 results are much closer to the fully two-dimensional results than the ones for L y =4.…”

Section: Resultsmentioning

confidence: 68%

“…The main method we employ for the analysis of the model is RCMF [22], whose results we will further support by ED. It is defined in the thermodynamic limit and variationally approaches both condensed and uncondensed phases in models with multiorbital unit-cells and non-trivial dispersions, while preserving the translational symmetry of the lattice.…”

Section: Rcmf Theorymentioning

confidence: 71%

“…which can be solved iteratively. For a more detailed derivation of the method and technical details, see [22].…”

Section: Rcmf Theorymentioning

confidence: 99%

“…where ε GS and ε 1 are the energies of the ground-state(s) and the first excited state, respectively. In addition, by analyzing the behavior of the quasi-one-dimensional h-vector [22] as a function of the twisting angle θ x we can extrapolate the topological properties of the system. If the h-vector shows a closed-loop as a function of θ x , and the ground-state does not mix with the excited states such that (11) stays finite, it implies that the many-body ground-state is adiabatically translated by a single site in y-direction during one charge-pump cycle, resulting in different quantized Hall conductances depending on the filling.…”

Section: U(1)-symmetry Preserving Phasesmentioning

confidence: 99%

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Quasi-one-dimensional Hall physics in the Harper–Hofstadter–Mott model

2018

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We study the ground-state phase diagram of the strongly interacting Harper-Hofstadter-Mott model at quarter flux on a quasi-one-dimensional lattice consisting of a single magnetic flux quantum in ydirection. In addition to superfluid phases with various density patterns, the ground-state phase diagram features quasi-one-dimensional analogs of fractional quantum Hall phases at fillings ν=1/2 and 3/2, where the latter is only found thanks to the hopping anisotropy and the quasi-onedimensional geometry. At integer fillings-where in the full two-dimensional system the ground-state is expected to be gapless-we observe gapped non-degenerate ground-states: at ν=1 it shows an odd 'fermionic' Hall conductance, while the Hall response at ν=2 consists of the transverse transport of a single particle-hole pair, resulting in a net zero Hall conductance. The results are obtained by exact diagonalization and in the reciprocal mean-field approximation. system in question. Furthermore, the restriction of the y-direction to just a few sites (in our case four) enables us to benchmark our RCMF results against ED, where it suffices to scale the system-size in the x-direction only.In this work we analyze the properties of the HHMm on a quasi-one-dimensional lattice, consisting of just a single flux quantum along the y-direction, while the x-direction is treated in the thermodynamical limit. For the flux of Φ=π/2 considered here, this consists of 4 plaquettes in y-direction with periodic boundaries. Such a thin-torus limit has been previously investigated in fermionic systems in the lowest Landau level, where onedimensional analogs of quantum Hall states were observed, which are predicted to continuously develop into their two-dimensional counterparts for increasing y-direction [23][24][25]. For interacting bosons an effective ladder model realizing the thin-torus limit with 2 sites in y-direction has been proposed, predicting a charge density wave analog of the two-dimensional ν=1/2 fQH phase [26].The quasi-one-dimensional limit in combination with anisotropic hopping amplitudes leads to larger many-body gaps due to the finite size in y-direction, and therefore to more stable topological phases than in in the fully two-dimensional limit. This can be a useful insight in the experimental search for bosonic topologically non-trivial phases, where robustness against the expected strong heating processes is of great importance [27]. Equally important, fillings which are expected to be always gapless in the fully two-dimensional limit [28,29] can become gapped as a consequence of the finite size, leading to unexpected new ground-states. Another feature of the quasi-one-dimensional geometry lies in its low number of sites in y-direction, which makes it possible to map the spatial y-direction onto a finite number of internal degrees of freedom (in this case 4), rewriting the system as a one-dimensional multi-component system, which in the future could be simulated by cold atoms in the synthetic dimensions concept [30][31][32][33], o...

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Section: Resultsmentioning

confidence: 68%

Section: Rcmf Theorymentioning

confidence: 71%

“…which can be solved iteratively. For a more detailed derivation of the method and technical details, see [22].…”

Section: Rcmf Theorymentioning

confidence: 99%

Section: U(1)-symmetry Preserving Phasesmentioning

confidence: 99%

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Quasi-one-dimensional Hall physics in the Harper–Hofstadter–Mott model

2018

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“…Stripe phases are also well-known in high-temperature superconductivity, where it arises due to the interplay between antiferromagnetic interactions among the magnetic ions and the Coulomb interactions between the carriers [28]. The stripe phase has also been predicted in Bose-Hubbard model in a triangular optical lattice [29], quantum Hall system [30], core-corona system [31], Harper-Hofstadter-Mott model [32,33] etc.…”

Section: Introductionmentioning

confidence: 98%

Lattice and quintic nonlinearity induced stripe phase in Bose–Einstein condensate under non-inertial and inertial motion

Das

2018

J. Phys. Commun.

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We consider a parametrically forced Bose-Einstein condensate in the combined presence of an optical lattice and harmonic oscillator potential in the mean field approach. A spatial symmetry broken Bosecondensed phase in non-inertial and inertial frame yields a stripe phase in the presence of both cubic and quintic nonlinearities. We show that the existence of such stripe phase solely depends on the interplay between the quintic nonlinearity and the lattice potential. Furthermore, we observe that a time-dependent harmonic oscillator frequency destroys such stripe ordering. A linear stability analysis of the obtained solution is performed and we found that the solution is stable. In order to gain a better understanding of the underlying physics, we compute the energy, showing nonlinear compression of the condensate in some parameter domain.

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Quantum Hall States for $$\alpha = 1/3$$ α = 1 / 3 in Optical Lattices

Bai

Bandyopadhyay

Pal

et al. 2019

Springer Proceedings in Physics

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We examine the quantum Hall (QH) states of the optical lattices with square geometry using Bose-Hubbard model (BHM) in presence of artificial gauge field. In particular, we focus on the QH states for the flux value of α = 1/3. For this, we use cluster Gutzwiller mean-field (CGMF) theory with cluster sizes of 3 × 2 and 3 × 3. We obtain QH states at fillings ν = 1/2, 1, 3/2, 2, 5/2 with the cluster size 3 × 2 and ν = 1/3, 2/3, 1, 4/3, 5/3, 2, 7/3, 8/3 with 3 × 3 cluster. Our results show that the geometry of the QH states are sensitive to the cluster sizes. For all the values of ν, the competing superfluid (SF) state is the ground state and QH state is the metastable state.

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Anisotropic Harper-Hofstadter-Mott model: Competition between condensation and magnetic fields

Cited by 24 publications

References 60 publications

Quasi-one-dimensional Hall physics in the Harper–Hofstadter–Mott model

Quasi-one-dimensional Hall physics in the Harper–Hofstadter–Mott model

Lattice and quintic nonlinearity induced stripe phase in Bose–Einstein condensate under non-inertial and inertial motion

Quantum Hall States for $$\alpha = 1/3$$ α = 1 / 3 in Optical Lattices

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