Quantum geometric bounds at finite temperature for one-dimensional chiral systems
Abstract
The geometry and topology of quantum states are intimately related at zero temperature through exact bounds that constrain geometric quantities from below by topological invariants. At finite-temperature, however, the analogous relations remain unclear. Here we establish rigorous geometric lower bounds for one-dimensional (1D) chiral-symmetric systems at finite temperature within the Uhlmann's framework for mixed states. We show that the Bures length is bounded by a continuous geometric phase angle. We further derive a temperature-dependent bound that interpolates between the zero-temperature limit and a trivial high-temperature regime. Our results are verified analytically and numerically using the Su-Schrieffer-Heeger (SSH) model and the spinless Kitaev chain model. Finally, we discuss potential ways to detect the geometry of the density matrix in quantum circuits, with the quantum imaginary time evolution (QITE) method.
Related
- Information-Geometric Representation of Upper Bounds on Fluctuation Growth in Open Quantum Systems
- Multiscale Schmidt-Spectrum Bounds for High-Dimensional Entanglement: Geometric Measures and Schmidt-Number Witnesses
- Information-geometric bounds on nonequilibrium relaxation in quantum Markov dynamics
- Three-Dimensional Coulomb Discrete Spectrum via Symplectic Geometry and Phase-Space Constraints: A Geometric Framework for Condensed-Matter Coulomb-Like Systems
- Quantum gravity phenomenology in quadrupolar Bose-Einstein condensates: Finite-temperature thermodynamics and projected bounds
BibTeX
@misc{he2026quantum,
title = {{Quantum geometric bounds at finite temperature for one-dimensional chiral systems}},
author = {Peng He and Hai-Tao Ding and Yu-Guo Liu},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27944},
eprint = {2608.27944},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27944},
}
RIS
TY - UNPB
TI - Quantum geometric bounds at finite temperature for one-dimensional chiral systems
AU - Peng He
AU - Hai-Tao Ding
AU - Yu-Guo Liu
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.27944
UR - https://arxiv.org/abs/2608.27944
AB - The geometry and topology of quantum states are intimately related at zero temperature through exact bounds that constrain geometric quantities from below by topological invariants. At finite-temperature, however, the analogous relations remain unclear. Here we establish rigorous geometric lower bounds for one-dimensional (1D) chiral-symmetric systems at finite temperature within the Uhlmann's framework for mixed states. We show that the Bures length is bounded by a continuous geometric phase angle. We further derive a temperature-dependent bound that interpolates between the zero-temperature limit and a trivial high-temperature regime. Our results are verified analytically and numerically using the Su-Schrieffer-Heeger (SSH) model and the spinless Kitaev chain model. Finally, we discuss potential ways to detect the geometry of the density matrix in quantum circuits, with the quantum imaginary time evolution (QITE) method.
ER -