论文标题
用于横向场ISING模型的量子指数家族的标量曲率和量子相变
Scalar Curvature of the Quantum Exponential Family for the Transverse-Field Ising Model and the Quantum Phase Transition
论文作者
论文摘要
与经典的多体系统不同，量子多体系统的指数家族的标态曲率并未得到研究，其物理含义尚不清楚。在本文中，我们分析研究了属于量子指数家族的吉布斯热状态空间的标量曲率，该家族配备了零和高温下的零和一维横向ISISING模型的Bogoliubov-Kubo-Mori度量。我们发现，这些标量曲率在高温极限下趋于零，而它们的温度呈指数分化。这种差异是量子性的结果。此外，如果我们可以重新考虑在零温度下标量曲率的关键性，则可以认为它们以1指数为1的临界行为，并且该关键指数与Ising模型的量子古典对应关系一致。
Unlike for classical many-body systems, the scalar curvature of the exponential family for quantum many-body systems has been not so investigated, and its physical meaning remains unclear. In this paper, we analytically study the scalar curvature of the space of Gibbs thermal states, belonging to the quantum exponential family, equipped with the Bogoliubov-Kubo-Mori metric for the zero- and one-dimensional transverse-field Ising model at low and high temperatures. We find that these scalar curvatures converge to zero in the high-temperature limit whereas they exponentially diverge approaching zero temperature. This divergence is a consequence of quantumness. Furthermore, if we can reconsider the criticality of the scalar curvatures at zero temperature, they both can be considered to show a critical behavior with an exponent of 1, and this critical exponent is consistent with the quantum-classical correspondence of the Ising model.
