Quantum collision theory in flat bands

Valiente, Manuel; Zinner, N. T.

doi:10.1088/1361-6455/aa60de

Cited by 10 publications

(10 citation statements)

References 67 publications

(86 reference statements)

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“…As Ω approaches Ω * , the bottom of the relative dispersion curve becomes "flatter", thereby leading to a larger density of states or degeneracy. In terms of the Bose-Fermi duality [54,55], one can interpret the fact that the effective odd-z coupling constant goes to infinity as a signature of bosonization, which is facilitated by the enhanced degeneracy [56]. Figure 11 shows the energy-dependent s-wave scattering length a s (E th ) at which the divergence for the scattering energy E = E th and (k so ) −1 = (0.2 √ 2) −1 a ho occurs as a function of Ω.…”

Section: A Scattering Properties At the Lowest Scattering Thresholdmentioning

confidence: 99%

“…Instead, we present the total reflection coefficient R, which is obtained by combining the individual K-matrix elements [see Eqs. (50), (52), (54), and (56)]. From a physical point of view, R tells one the fraction of the incoming flux that is reflected, provided the incoming flux populates the energetically open channels equally.…”

Section: B Scattering Properties As a Function Of The Energymentioning

confidence: 99%

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K -matrix formulation of two-particle scattering in a waveguide in the presence of one-dimensional spin-orbit coupling

2018

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The creation of artificial gauge fields in neutral ultracold atom systems has opened the possibility to study the effects of spin-orbit coupling terms in clean environments. This work considers the multi-channel scattering properties of two atoms confined by a wave guide in the presence of spinorbit coupling terms within a K-matrix scattering framework. The tunability of resonances, induced by the interplay of the external wave guide geometry, the interactions, and the spin-orbit coupling terms, is demonstrated. Our results for the K-matrix elements as well as partial and total reflection coefficients for two identical fermions interacting through a finite-range interaction potential in the singlet channel only are compared with those obtained for a strictly one-dimensional effective lowenergy Hamiltonian, which uses the effective coupling constant derived in Zhang et al. [Scientific Reports 4, 1 (2014)] and Zhang et al. [Phys. Rev. A 88, 053605 (2013)] as input. In the regime where the effective Hamiltonian is applicable, good agreement is obtained, provided the energydependence of the coupling constant is accounted for. Our approach naturally describes the energy regime in which the bands associated with excited transverse modes lie below a subset of the bands associated with the lowest transverse modes. The threshold behavior is discussed and scattering observables are linked to bound state properties.PACS numbers:

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Section: A Scattering Properties At the Lowest Scattering Thresholdmentioning

confidence: 99%

Section: B Scattering Properties As a Function Of The Energymentioning

confidence: 99%

K -matrix formulation of two-particle scattering in a waveguide in the presence of one-dimensional spin-orbit coupling

2018

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“…[22] by using a different (variational) approach. Scattering states in flat bands have instead been discussed in [46], but can also be obtained by adapting the formalism below, as done in Ref. [47].…”

Section: B Two-body Problemmentioning

confidence: 99%

Pairs, trimers and BCS-BEC crossover near a flat band: the sawtooth lattice

Orso,

Singh

2021

Preprint

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We investigate pairing and superconductivity in the attractive Hubbard model on the onedimensional sawtooth lattice. This is a periodic lattice with two sites per unit cell, which exhibits a flat band (FB) by fine-tuning the hopping rates. We first discuss the formation of pairs in vacuum, showing that there is a broad region of hopping rates values around the FB point, for which both the binding energy and the effective mass of the bound state are strongly affected even by weak interactions. Based on the DMRG method, we then address the ground-state properties of a system with equal spin populations as a function of the interaction strength and the hopping rates. We compare our results with those available for a linear chain, where the model is integrable by Bethe ansatz, and show that the multiband nature of the system substantially modifies the physics of the BCS-BEC crossover. The chemical potential of a system near the FB point remains always close to its zero-density limit predicted by the two-body physics. In contrast, the pairing gap exhibits a remarkably strong density dependence and, differently from the binding energy, it is no longer peaked at the FB point. We show that these results can be interpreted in terms of polarization screening effects, due to an anomalous attraction between pairs in the medium and single fermions. In particular, we find that three-body bound states (trimers) are allowed in the sawtooth lattice, in sharp contrast with the linear chain geometry.

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“…For simplicity, we will assume the trivial case of a system with a single flat band, but note that the results that follow apply when there are other, dispersive bands [35]. We set a single particle on the flat band interacting with a probe impurity, and study the scattering states.…”

Section: Flat Bandsmentioning

confidence: 99%

From Few to Many Body Degrees of Freedom

Valiente¹

2018

Few-Body Syst

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Here, I focus on the use of microscopic, few-body techniques that are relevant in the many-body problem. These methods can be divided into indirect and direct. In particular, indirect methods are concerned with the simplification of the many-body problem by substituting the full, microscopic interactions by pseudopotentials which are designed to reproduce collisional information at specified energies, or binding energies in the few-body sector. These simplified interactions yield more tractable theories of the many-body problem, and are equivalent to effective field theory of interactions. Direct methods, which so far are most useful in one spatial dimension, have the goal of attacking the many-body problem at once by using few-body information only. Here, I will present non-perturbative direct methods to study one-dimensional fermionic and bosonic gases in one dimension. IntroductionStrongly interacting quantum many-body ensembles are among the most intriguing and difficult to describe systems in nature. Standard methods such as direct perturbation theory or mean-field approaches are doomed to fail in this regime. Some of these problems, however, can be approximately recast into the form of effective theories which may be either exactly solvable (e.g. integrable quantum systems in one dimension) or weaklyinteracting (e.g. dilute Bose gases). The process of obtaining a microscopically accurate effective theory usually involves solving few-body problems, starting with the two-body sector, exactly, in a certain regime of scattering energies or for either weak or strong binding. These constitute what we may call indirect methods: after the simplified theory is obtained, this still needs to be solved, whether exactly or approximately. More recently, renewed interest in the study of strongly interacting one-dimensional systems has arised, especially due to the possibility of preparing and manipulating these using trapped ultracold atoms. In these settings it has been shown recently that few-body solutions can sometimes be used to extract many-body information directly without having to solve a many-body problem at any stage. Examples of direct methods include the recently developed machinery for trapped multicomponent systems, or a few-body method to obtain non-perturbative approximations to the speed of sound in Luttinger liquids. Indirect MethodsWe assume throughout these notes that we have a non-relativistic many-body system with N particles, interacting via two-body potentials V , and possibly under the influence of an external trapping (single-

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Quantum collision theory in flat bands

Cited by 10 publications

References 67 publications

K -matrix formulation of two-particle scattering in a waveguide in the presence of one-dimensional spin-orbit coupling

K -matrix formulation of two-particle scattering in a waveguide in the presence of one-dimensional spin-orbit coupling

Pairs, trimers and BCS-BEC crossover near a flat band: the sawtooth lattice

From Few to Many Body Degrees of Freedom

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