Boundary-Sensitive Quantum Order on Non-Amenable Lattices
Abstract
We show that quantum systems on non-amenable lattices, whose boundaries constitute an extensive fraction of the system, host novel forms of bulk ordering with no Euclidean counterpart. Combining boundary-retaining iDMRG with an exact symmetry-fixing duality, we investigate p<5 state clock models on the coordination-3 infinite Cayley tree. We find that between the ordered and disordered phases lies an emergent intermediate phase with bulk order induced by an arbitrarily weak boundary field rather than by conventional spontaneous symmetry-breaking. This establishes boundary-sensitive order as a distinct quantum ordering mechanism defying Landau's spontaneous symmetry-breaking paradigm. The intermediate phase realizes a bulk-boundary correspondence in which the unpolarized boundary selects a specific ordered bulk state.
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BibTeX
@misc{wang2026boundarysensitive,
title = {{Boundary-Sensitive Quantum Order on Non-Amenable Lattices}},
author = {Xingzhi Wang and Zohar Nussinov and Gerardo Ortiz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26859},
eprint = {2610.26859},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26859},
}
RIS
TY - UNPB
TI - Boundary-Sensitive Quantum Order on Non-Amenable Lattices
AU - Xingzhi Wang
AU - Zohar Nussinov
AU - Gerardo Ortiz
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26859
UR - https://arxiv.org/abs/2610.26859
AB - We show that quantum systems on non-amenable lattices, whose boundaries constitute an extensive fraction of the system, host novel forms of bulk ordering with no Euclidean counterpart. Combining boundary-retaining iDMRG with an exact symmetry-fixing duality, we investigate p<5 state clock models on the coordination-3 infinite Cayley tree. We find that between the ordered and disordered phases lies an emergent intermediate phase with bulk order induced by an arbitrarily weak boundary field rather than by conventional spontaneous symmetry-breaking. This establishes boundary-sensitive order as a distinct quantum ordering mechanism defying Landau's spontaneous symmetry-breaking paradigm. The intermediate phase realizes a bulk-boundary correspondence in which the unpolarized boundary selects a specific ordered bulk state.
ER -