双曲晶格几何上量子自旋系统的面积律研究

Tensor Networks: Phase transition phenomena on hyperbolic and fractal geometries

One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several numerical simulation methods have been proposed in recent years. Amongst all of them, the Tensor Network algorithms have become increasingly popular in recent years, especially for their adaptability to simulate strongly correlated systems. The current work focuses on the generalization of such Tensor-Network-based algorithms, which are sufficiently robust …

Free Energy Analysis of Spin Models on Hyperbolic Lattice Geometries

We investigate relations between spatial properties of the free energy and the radius of Gaussian curvature of the underlying curved lattice geometries. For this purpose we derive recurrence relations for the analysis of the free energy normalized per lattice site of various multistate spin models in the thermal equilibrium on distinct non-Euclidean surface lattices of the infinite sizes. Whereas the free energy is calculated numerically by means of the Corner Transfer Matrix Renormalization Group algorithm, the radius of curvature has an analytic expression. Two tasks are considered in this w…

Study of classical and quantum phase transitions on non-Euclidean geometries in higher dimensions

The investigation of the behavior of both classical and quantum systems on non-Euclidean surfaces near the phase transition point represents an interesting research area of modern physics. In the case of classical spin systems, a generalization of the Corner Transfer Matrix Renormalization Group algorithm has been developed and successfully applied to spin models on infinitely many regular hyperbolic lattices. In this work, we extend these studies to specific types of lattices. It is important to say that no suitable algorithms for numerical analysis of ground-states of quantum systems in simi…

双曲张量网络的顶点表示

Vertex Representation of Hyperbolic Tensor Networks

本文提出双曲晶格经典自旋系统的顶点型张量网络表示，证明纠缠熵可区分双曲几何，并验证其在各级相变中的数值精度与量子基态应用潜力。

广义几何中Boltzmann方程的最大对称性Boost不变解

Maximally Symmetric Boost-Invariant Solutions of the Boltzmann Equation in Foliated Geometries

本文研究了在静态最大对称背景dS_3×R上，Boost不变的共形气体的相对论动力学，通过分析各常曲率切片及其对称群，推导出Boltzmann方程的统一精确解，涵盖各常曲率切片，并讨论了新解的物理意义。

Analysis of quantum spin models on hyperbolic lattices and Bethe lattice

The quantum XY, Heisenberg, and transverse field Ising models on hyperbolic lattices are studied by means of the Tensor Product Variational Formulation algorithm. The lattices are constructed by tessellation of congruent polygons with coordination number equal to four. The calculated ground-state energies of the XY and Heisenberg models and the phase transition magnetic field of the Ising model on the series of lattices are used to estimate the corresponding quantities of the respective models on the Bethe lattice. The hyperbolic lattice geometry induces the mean-field-like universality of the…