Bethe states for the two-site Bose–Hubbard model: A binomial approach

Santos, G.; Ahn, Changrim; Foerster, Angela; Roditi, I.

doi:10.1016/j.physletb.2015.05.003

Cited by 4 publications

(6 citation statements)

References 53 publications

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“…which is a polynomial of order L. It follows from (24) that S(z 2 j ) = 0, j = 1, ..., L which, along with the consideration of the asymptotic behaviour of (25) as u → ∞, establishes that…”

Section: N-species Casementioning

confidence: 82%

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Solution of the classical Yang–Baxter equation with an exotic symmetry, and integrability of a multi-species boson tunnelling model

Links¹

2017

Nuclear Physics B

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Solutions of the classical Yang-Baxter equation provide a systematic method to construct integrable quantum systems in an algebraic manner. A Lie algebra can be associated with any solution of the classical Yang-Baxter equation, from which commuting transfer matrices may be constructed. This procedure is reviewed, specifically for solutions without skew-symmetry. A particular solution with an exotic symmetry is identified, which is not obtained as a limiting expansion of the usual Yang-Baxter equation. This solution facilitates the construction of commuting transfer matrices which will be used to establish the integrability of a multi-species boson tunneling model. The model generalises the well-known two-site Bose-Hubbard model, to which it reduces in the one-species limit. Due to the lack of an apparent reference state, application of the algebraic Bethe Ansatz to solve the model is prohibitive. Instead, the Bethe Ansatz solution is obtained by the use of operator identities and tensor product decompositions.

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Section: N-species Casementioning

confidence: 82%

“…When L = 1 (1) reduces to the two-site Bose-Hubbard model, which endures as the subject of widespread investigation, e.g. [4,5,13,24,26,40]. Thus (1) represents an L-species generalisation.…”

Section: Introductionmentioning

confidence: 99%

Solution of the classical Yang–Baxter equation with an exotic symmetry, and integrability of a multi-species boson tunnelling model

Links¹

2017

Nuclear Physics B

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“…The expansion of Bethe vectors [30,31] into Fock space was performed in Ref. [49]. Since in the present paper we work mostly with the auxillary Hamiltonian (8), it is slightly more convenient to use another representation of the Bethe vectors which is given in Ref.…”

Section: Expectation Valuesmentioning

confidence: 99%

“…For the two-site Bose-Hubbard model, the determinant representation for time-dependent correlation functions has been developed [48], and the expansion of the eigenfunctions of the model into Fock space was been performed in Ref. [49].…”

Section: Introductionmentioning

confidence: 99%

High-accuracy energy formulas for the attractive two-site Bose-Hubbard model

2018

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The attractive two-site Bose-Hubbard model is studied within the framework of the analytical solution obtained by the application of Quantum Inverse Scattering Method. The structure of the ground and excited states is analyzed in terms of solutions of Bethe equations, and an approximate solution for the Bethe roots are given. This yields approximate formulas for the ground state and for the first excited state energies. The obtained formulas work with remarkable precision for a wide range of parameters of the model, and confirmed numerically. An expansion of the Bethe state vectors into a Fock space is also provided for evaluation of expectation values, although this does not have the similar accuracy to the energies.

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“…However, these kinds of models are important in condensed matter physics and their dynamical and thermodynamical properties are rich and varied. For example, few-body and effectively one-dimensional single-well and few-well systems have already been used to investigate magnetism and quantum phase transitions in Heisenberg spin chain models [7][8][9][10][11][12][13] and to check the consistency of the approximations used to solve Hubbard-type models [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Infinite barriers and symmetries for a few trapped particles in one dimension

Harshman

2017

Phys. Rev. A

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This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are dependent on the specific shapes of the traps and the interactions, this article applies symmetry analysis to identify generic features in the spectrum of stationary states of few-particle, few-well systems. Extended attention is given to a simple but flexible threeparameter model of two particles in two wells in one dimension. A key insight is that two limiting cases, hard-core repulsion and no inter-well tunneling, can both be treated as emergent symmetries of the few-particle Hamiltonian. These symmetries are the mathematical consequences of infinite barriers in configuration space. They are necessary to explain the pattern of degeneracies in the energy spectrum, to understand how degeneracies are broken for models away from limiting cases, and to explain separability and integrability. These symmetry methods are extendable to more complicated models and the results have practical consequences for stable state control in fewparticle, few-well systems with ultracold atoms in optical traps.

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Bethe states for the two-site Bose–Hubbard model: A binomial approach

Cited by 4 publications

References 53 publications

Solution of the classical Yang–Baxter equation with an exotic symmetry, and integrability of a multi-species boson tunnelling model

Solution of the classical Yang–Baxter equation with an exotic symmetry, and integrability of a multi-species boson tunnelling model

High-accuracy energy formulas for the attractive two-site Bose-Hubbard model

Infinite barriers and symmetries for a few trapped particles in one dimension

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