The Quasiparticle Ansatz for Relativistic Continuous Matrix Product States
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 ϕ4 theory, in both its ℤ2-preserving and ℤ2-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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BibTeX
@misc{pufu2026quasiparticle,
title = {{The Quasiparticle Ansatz for Relativistic Continuous Matrix Product States}},
author = {Silviu S. Pufu and Benjamin T. Søgaard and Spyros Terlemes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13824},
eprint = {2610.13824},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13824},
}
RIS
TY - UNPB
TI - The Quasiparticle Ansatz for Relativistic Continuous Matrix Product States
AU - Silviu S. Pufu
AU - Benjamin T. Søgaard
AU - Spyros Terlemes
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13824
UR - https://arxiv.org/abs/2610.13824
AB - 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 ℤ_2-preserving and 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.
ER -