Quantum Mechanics of One-Dimensional Three-Body Contact Interactions

2024-2-13

JPS Hot Topics 4, 007

https://doi.org/10.7566/JPSHT.4.007

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Topologically nontrivial three-body contact interaction in one dimension
(PTEP Editors' Choice)

Satoshi Ohya
Prog. Theor. Exp. Phys. 2024, 013A01 (2024) .

The quantum mechanical description of topologically nontrivial three-body contact interactions in one dimension is not well understood. This study explores the Hamiltonian description of these interactions using the path-integral formalism.

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Quantum contact interactions in low energy regime are one of the most fundamental type of interactions in nature. In these interactions, the wavelengths of particles are longer than the characteristic range of the interactions, and particles are no longer able to resolve their microscopic details. Consequently, short-range interactions can be described as contact or point-like interactions.

In this context, recent studies have shown that three-body contact interactions of non-identical particles in one dimension are particularly unique. They can be topologically nontrivial, and so, can be classified by unitary irreducible representations of the pure twin group. The pure twin group is a set of trajectories of particles in spacetime, allowing only two particles to interact simultaneously. However, the description of these interactions within the framework of quantum mechanics, especially in the Hamiltonian formalism, remains unknown.

Addressing this gap, a new study published in Progress of Theoretical and ExperimentalPhysics explores the Hamiltonian descriptions of the topologically nontrivial three-body contact interactions by using the path-integral formalism. The study revealed that these interactions can be described by fictitious, infinitely thin magnetic fluxes in the many-body configuration space. When the trajectories of the particles wind around these fluxes, they acquire the Aharonov–Bohm phases, which can solely be determined by topology and group theory. Additionally, the study also introduces a new special parameter to describe the contact interactions of more than three non-identical particles.

In summary, this topological description of three-body contact interactions expands our understanding of quantum contact interactions. Moreover, owing to its similarity to particles called anyons in two dimensions, these findings hold great potential for quantum computing.

Topologically nontrivial three-body contact interaction in one dimension
(PTEP Editors' Choice)

Satoshi Ohya
Prog. Theor. Exp. Phys. 2024, 013A01 (2024) .