Exact Rokhsar-Kivelson points hosting first-order phase transitions in S=1 compass models
Abstract
We study S=1 compass models on the square and kagome lattices with bond-dependent bilinear and biquadratic interactions parametrized by an angle θ. For compatible geometries, we determine the exact ground-state manifolds throughout the interval π/4≤θ≤3π/4. At each endpoint, a product of on-site unitaries maps the Hamiltonian to the Laplacian of a configuration graph 𝒢 in the S=1 Cartesian basis. These endpoints are exact Rokhsar-Kivelson (RK) points, with one ground state per dynamically connected component of 𝒢. Each such state is an equal-amplitude superposition in the transformed basis and acquires configuration-dependent phases upon transforming back to the original basis. Both models possess m=O(L) independent and mutually commuting conserved ℤ2 line charges, where L is the linear system size, forcing a ground-state degeneracy of at least 2m at the RK endpoints. Throughout the interior region, π/4<θ<3π/4, the ground-state manifold on each lattice is instead spanned by two product states, both annihilated by the Hamiltonian. On both lattices, each RK endpoint also hosts a first-order transition into this intervening interior phase spanned by the two product states with long-range order.
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BibTeX
@misc{pandey2026exact,
title = {{Exact Rokhsar-Kivelson points hosting first-order phase transitions in $S=1$ compass models}},
author = {Jay Pandey},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05326},
eprint = {2611.05326},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05326},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact Rokhsar-Kivelson points hosting first-order phase transitions in S=1 compass models
AU - Jay Pandey
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05326
UR - https://arxiv.org/abs/2611.05326
AB - We study S=1 compass models on the square and kagome lattices with bond-dependent bilinear and biquadratic interactions parametrized by an angle θ. For compatible geometries, we determine the exact ground-state manifolds throughout the interval π/4≤θ≤3π/4. At each endpoint, a product of on-site unitaries maps the Hamiltonian to the Laplacian of a configuration graph 𝒢 in the S=1 Cartesian basis. These endpoints are exact Rokhsar-Kivelson (RK) points, with one ground state per dynamically connected component of 𝒢. Each such state is an equal-amplitude superposition in the transformed basis and acquires configuration-dependent phases upon transforming back to the original basis. Both models possess m=O(L) independent and mutually commuting conserved ℤ_2 line charges, where L is the linear system size, forcing a ground-state degeneracy of at least 2^m at the RK endpoints. Throughout the interior region, π/4<θ<3π/4, the ground-state manifold on each lattice is instead spanned by two product states, both annihilated by the Hamiltonian. On both lattices, each RK endpoint also hosts a first-order transition into this intervening interior phase spanned by the two product states with long-range order.
ER -