Renormalization of One-Dimensional Semirelativistic Bosons with Contact Interactions

Abstract:We study one-dimensional spinless bosons with semirelativistic spinless-Salpeter dispersion and attractive pairwise contact interactions. Because the dispersion becomes linear at large momentum, the contact interaction is marginal by power counting and produces a logarithmic ultraviolet divergence. We construct the renormalized many-body theory using an enlarged Fock space and a Schur-complement representation of the resolvent, eliminating the bare coupling in favor of the physical zero-total-momentum two-body bound-state energy. The resulting cutoff-independent resolvent defines a self-adjoint Hamiltonian in each fixed particle-number sector. We treat the two-body problem explicitly and show, in the norm-resolvent sense, that the nonrelativistic limit reproduces the attractive Lieb--Liniger Hamiltonian. We also formulate a mean-field approximation directly within the renormalized theory. In the massless and deeply bound large-particle-number regimes, it predicts an exponentially increasing binding scale whose exponent is determined by a one-dimensional variational problem.

Quantum Gases (cond-mat.quant-gas); Mathematical Physics (math-ph); Quantum Physics (quant-ph)

arXiv:2609.09068 [cond-mat.quant-gas]

(or arXiv:2609.09068v1 [cond-mat.quant-gas] for this version)

https://doi.org/10.48550/arXiv.2609.09068 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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