Pseudo-Riemannian metric: a new perspective on the quantum realm

Fuente: arXiv
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Main Authors: Wei, Miaomiao, Xiang, Longjun, Xu, Fuming, Wang, Baigeng, Wang, Jian
Format: Preprint
Published: 2024
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author Wei, Miaomiao
Xiang, Longjun
Xu, Fuming
Wang, Baigeng
Wang, Jian
author_facet Wei, Miaomiao
Xiang, Longjun
Xu, Fuming
Wang, Baigeng
Wang, Jian
contents As a fundamental concept in condensed matter physics, quantum geometry within the Riemannian metric elucidates various exotic phenomena, including the Hall effects driven by Berry curvature and quantum metric. In this work, we propose novel quantum geometries within a pseudo-Riemannian framework to explore unique characteristic of quantum matter. By defining distinct distances on pseudo-Riemannian manifolds and incorporating spin degree of freedom, we introduce the Pauli quantum geometric tensor. The imaginary part of this tensor corresponds to the Pauli Berry curvature, leading to the discovery a novel quantum phase: Pauli semimetal in PT-symmetric systems. This phase, characterized by the topological Pauli Chern number, manifests as a two-dimensional Pauli Chern insulator with helical edge states. These topological phases, uniquely revealed by the Pauli-Riemannian metric, go beyond the familiar Riemannian metric, where Berry curvature vanishes due to PT-symmetry. Pauli Chern number can classify helical topological insulator with or without time reversal symmetry. Pseudo-Riemannian metrics offer new insights into quantum materials and extend the scope of quantum geometry.
format Preprint
id arxiv_https___arxiv_org_abs_2409_19551
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Pseudo-Riemannian metric: a new perspective on the quantum realm
Wei, Miaomiao
Xiang, Longjun
Xu, Fuming
Wang, Baigeng
Wang, Jian
Mesoscale and Nanoscale Physics
Quantum Physics
As a fundamental concept in condensed matter physics, quantum geometry within the Riemannian metric elucidates various exotic phenomena, including the Hall effects driven by Berry curvature and quantum metric. In this work, we propose novel quantum geometries within a pseudo-Riemannian framework to explore unique characteristic of quantum matter. By defining distinct distances on pseudo-Riemannian manifolds and incorporating spin degree of freedom, we introduce the Pauli quantum geometric tensor. The imaginary part of this tensor corresponds to the Pauli Berry curvature, leading to the discovery a novel quantum phase: Pauli semimetal in PT-symmetric systems. This phase, characterized by the topological Pauli Chern number, manifests as a two-dimensional Pauli Chern insulator with helical edge states. These topological phases, uniquely revealed by the Pauli-Riemannian metric, go beyond the familiar Riemannian metric, where Berry curvature vanishes due to PT-symmetry. Pauli Chern number can classify helical topological insulator with or without time reversal symmetry. Pseudo-Riemannian metrics offer new insights into quantum materials and extend the scope of quantum geometry.
title Pseudo-Riemannian metric: a new perspective on the quantum realm
topic Mesoscale and Nanoscale Physics
Quantum Physics
url https://arxiv.org/abs/2409.19551