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arXiv · 2610.13824

The Quasiparticle Ansatz for Relativistic Continuous Matrix Product States

Silviu S. Pufu·Benjamin T. Søgaard·Spyros Terlemes
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Abstract

The Relativistic Continuous Matrix Product State (RCMPS) ansatz introduced in arXiv:2102.07741 is a translation-invariant variational ansatz intended to approximate the ground states of gapped one-dimensional relativistic Quantum Field Theories directly in the continuum limit and in infinite volume. In this work, we develop an ansatz, referred to as the Relativistic Quasiparticle (RQP) ansatz, for the low-lying one-particle excitations of the RCMPS vacuum, as well as for solitons interpolating between two distinct degenerate vacua. The corresponding energies of these states can be obtained as the eigenvalues of an effective Hamiltonian. The RQP ansatz generalizes constructions used in the Matrix Product State and Continuous Matrix Product State literature. We apply the RQP ansatz to the sine-Gordon model and find good agreement with results from integrability for both the soliton and breather masses. We also apply the RQP ansatz to the $ϕ^4$ theory, in both its $\mathbb Z_2$-preserving and $\mathbb{Z}_2$-broken phases, and determine the spectrum of particles and solitons. This enables us to determine the parameter regime for which multiple stable particles exist.

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Silviu S. Pufu, Benjamin T. Søgaard, Spyros Terlemes. 2026-10-09. The Quasiparticle Ansatz for Relativistic Continuous Matrix Product States. https://arxiv.org/abs/2610.13824

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