Hypergeometric analytic continuation of the strong-coupling perturbation series for the 2d Bose-Hubbard model

Sanders, Sören; Heinisch, Christoph; Holthaus, Martin

doi:10.1209/0295-5075/111/20002

Cited by 7 publications

(20 citation statements)

References 28 publications

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“…In conclusion, we have applied a very recently developed hypergeometric resummation 53,54,56 to the calculation of physical observables in nonequilibrium steadystate electron-boson quantum many-body system. In particular, we have considered the hypergeometric resummation of the non-crossing self-consistent sunset diagrammatic series (comprising Fock-SCBA) for the NEGF of electrons interacting with phonons in the presence of applied bias voltage which can drive this system far from equilibrium.…”

Section: Discussionmentioning

confidence: 99%

“…53,54 The same approach was subsequently utilized for the calculation of field-assisted ionization in transition metal dichalcogenides 55 as well as in Ref. 56 for the calculation of the critical exponents in the two-dimensional Bose-Hubbard model -where higherorder hypergeometric functions p F q were also considered. In these cases hypergeometric resummation revealed itself as a method superior to widely used resummation approaches, such as Shanks transformation, 57 Padé approximants 58 and Borel-Padé resummation.…”

Section: -56mentioning

confidence: 99%

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Hypergeometric resummation of self-consistent sunset diagrams for steady-state electron-boson quantum many-body systems out of equilibrium

2016

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A newly developed hypergeometric resummation technique [H. Mera et al., Phys. Rev. Lett. 115, 143001 (2015)] provides an easy-to-use recipe to obtain conserving approximations within the self-consistent nonequilibrium many-body perturbation theory. We demonstrate the usefulness of this technique by calculating the phonon-limited electronic current in a model of a single-molecule junction within the self-consistent Born approximation for the electron-phonon interacting system, where the perturbation expansion for the nonequilibrium Green function in powers of the free bosonic propagator typically consists of a series of non-crossing sunset diagrams. Hypergeometric resummation preserves conservation laws and it is shown to provide substantial convergence acceleration relative to more standard approaches to self-consistency. This result strongly suggests that the convergence of the self-consistent sunset series is limited by a branch-cut singularity, which is accurately described by Gauss hypergeometric functions. Our results showcase an alternative approach to conservation laws and self-consistency where expectation values obtained from conserving divergent perturbation expansions are summed to their self-consistent value by analytic continuation functions able to mimic the convergence-limiting singularity structure.

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Section: Discussionmentioning

confidence: 99%

Section: -56mentioning

confidence: 99%

Hypergeometric resummation of self-consistent sunset diagrams for steady-state electron-boson quantum many-body systems out of equilibrium

2016

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“…For the sake of the argument, let us for the moment assume that for certain m U we may neglect terms of order  y ( ) 6 in the full effective potential (17). This assumption reduces the effective potential to the archetypal form(1) reviewed in the introduction.…”

Section: Evaluation Of the Critical Exponentmentioning

confidence: 99%

“…In summary, if terms of order  y ( ) 8 can be neglected in the effective potential (17), the exponent β is bounded by…”

Section: Evaluation Of the Critical Exponentmentioning

confidence: 99%

Hypergeometric continuation of divergent perturbation series: I. Critical exponents of the Bose–Hubbard model

Sanders

Holthaus

2017

New J. Phys.

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We study the connection between the exponent of the order parameter of the Mott insulator-tosuperfluid transition occurring in the two-dimensional Bose-Hubbard model, and the divergence exponents of its one-and two-particle correlation functions. We find that at the multicritical points all divergence exponents are related to each other, allowing us to express the critical exponent in terms of one single divergence exponent. This approach correctly reproduces the critical exponent of the threedimensional XY universality class. Because divergence exponents can be computed in an efficient manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems.

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“…It is easy to check that our perturbative expansions-(8), (12), and (27) for n = 1; (9), (13), and (30) for n = 2; and (10), (14), and (33) for n = 3-satisfy this identity. Combining this result with the Feynman-Hellmann theorem,…”

Section: Ground State Identities and Sum Rulementioning

confidence: 78%

Properties of the one-dimensional Bose–Hubbard model from a high-order perturbative expansion

Damski

Zakrzewski

2015

New J. Phys.

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We employ a high-order perturbative expansion to characterize the ground state of the Mott phase of the one-dimensional Bose-Hubbard model. We compute for different integer filling factors the energy per lattice site, the two-point and density-density correlations, and expectation values of powers of the on-site number operator determining the local atom number fluctuations (variance, skewness, kurtosis). We compare these expansions to numerical simulations of the infinite-size system to determine their range of applicability. We also discuss a new sum rule for the density-density correlations that can be used in both equilibrium and non-equilibrium systems. ( )= á ñ -The ground state energy per lattice site E for the unit filling factor is E J J J J J J J J 4 68 9 while for n = 2 it is given by E J J J J J J 4 and finally for n = 3 it reads E J J J J J J This quantity is experimentally accessible due to the spectacular recent progress in the quantum gas microscopy [26]. We find that for the unit filling factor n J J J J J J J J var 8 24 2720 9 + for the filling factor n = 2 n J J J J J J var 24 192 396832 63 + and finally for n=3 n J J J J J J var 48 744 2946560 63 22414210034 1289925 Q J J J J J J J J Q J J J J J J J J 4 56 72 22784 9 Q J J J J J J J J Q J J J J J J + Q J J J J J J + Q J J J J J J + Finally, for three atoms per site we derive 2 18 320 3 1826 9 234862 243 + C J J J J J J + and for the filling factor n = 2 they are C J J J 6 8 1 0 12 and finally for n = 3 they can be written as D J J J J J J -+ D J J J J J + -D J J J J 3 9 12148432 135 246576902129764 14586075 D J J J J J

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Hypergeometric analytic continuation of the strong-coupling perturbation series for the 2d Bose-Hubbard model

Cited by 7 publications

References 28 publications

Hypergeometric resummation of self-consistent sunset diagrams for steady-state electron-boson quantum many-body systems out of equilibrium

Hypergeometric resummation of self-consistent sunset diagrams for steady-state electron-boson quantum many-body systems out of equilibrium

Hypergeometric continuation of divergent perturbation series: I. Critical exponents of the Bose–Hubbard model

Properties of the one-dimensional Bose–Hubbard model from a high-order perturbative expansion

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