集成电路的发展对电子器件的热管理提出了越来越高的要求，热界面材料、电子封装材料和热电材料的热管理性能都依赖于其热导率。对称性在材料的热导率中扮演着重要角色，然而目前对称性对晶格热输运的影响机理尚不清晰，研究中存在如下问题：声子散射选择定则的影响范围不明确，第一性原理晶格热输运计算对算力要求过高，相变点附近热导率计算不准确。本论文围绕以上问题进行了算法改进，并利用改进后的算法研究了二维材料 MoS2 和 PtS2，钙钛矿材料 BaBiO3和 SrTiO3 中晶体对称性与晶格热输运的关联，为高性能热电材料的设计提供了理论依据。针对第一性原理晶格热传输计算对算力要求过高的问题，本研究结合了全主元高斯-约当消元法和压缩感知晶格动力学法，在显著降低计算资源消耗的同时保证了数值稳定性。针对声子散射选择定则的影响范围不明确的问题，本研究将空间群选择定则应用到晶格热输运领域，开发了选择定则代码，并明确了只有平移对称性与二维材料中的镜面对称性可以通过选择定则显著影响热输运。利用这些方法，计算分析了单层、多层和块体结构中 MoS2 与 PtS2 的晶格热导率，其中单层 MoS2 具有镜面对称性，而 PtS2 没有镜面对称性。镜面对称性不仅限制了单层结构中面外振动模式的散射，还影响了热导率对层数的依赖关系。MoS2 晶格热导率随层数增加单调降低，PtS2 晶格热导率随层数增加先升高后降低。本研究实现了自洽第一性原理晶格动力学算法，消除了高温相 BaBiO3 的声子谱虚频。基于空间群分析，将 BaBiO3 的多个相变划分为平移对称性的破缺与旋转对称性的破缺，从而分别研究了平移、旋转对称性对晶格热输运的影响。当平移对称性降低时，散射通道的数目增加，弛豫时间降低，而旋转对称性降低时，散射强度增强，中低频声子群速度降低。针对相变点附近热导率计算不准确的问题，本研究结合深度势能模型与量子热浴分子动力学，改进了自洽第一性原理晶格动力学的算法，研究了 SrTiO3 在随温度变化产生的对称性破缺前后的晶格热导率。计算结果解释了 SrTiO3 晶格热输运的反常，其主要来自于对二阶力常数的重整化。在对称性破缺前后热导率的局部最大值来源于群速度，而高温相热导率随温度的弱依赖，是因为当温度升高时有效二阶力常数的变化导致散射强度降低，归一化弛豫时间升高。

The development of integrated circuits has put increasingly high demands on the thermal management of electronic devices. The thermal management performance of thermal interface materials, electronic packaging materials, and thermoelectric materials all depend on their thermal conductivity. Symmetry plays an important role in the thermal conductivity of materials. However, the current understanding of the impact mechanism of symmetry on lattice thermal transport is not clear. The following issues exist in the research: the scope of influence of phonon scattering selection rules is unclear, first-principles lattice thermal transport calculations have excessive computational requirements, and thermal conductivity calculations near phase transition points are inaccurate. This thesis focuses on these issues and proposes algorithm improvements, and uses the improved algorithm to study the relationship between crystal symmetry and lattice thermal transport in two-dimensional materials MoS2 and PtS2, perovskite materials BaBi3 and SrTiO3, providing a theoretical basis for the design of high-performance thermoelectric materials.To address the issue of high computational requirements for first-principles lattice thermal transport calculations, this study combines the complete pivoting Gaussian-Jordan elimination method and compressive sensing lattice dynamics method, significantly reducing the consumption of computational resources while ensuring numerical stability. To clarify the scope of influence of phonon scattering selection rules, this study applies space group selection rules to the field of lattice thermal transport, develops selection rule codes, and clarifies that only translational symmetry and mirror symmetry in two-dimensional materials can significantly affect thermal transport through selection rules. Using these methods, the lattice thermal conductivity of MoS2 and PtS2 in single-layer, multi-layer, and bulk structures was calculated and analyzed. Single-layer MoS2 has mirror symmetry, while PtS2 does not have mirror symmetry. Mirror symmetry not only restricts the scattering of out-of-plane vibration modes in single-layer structures but also affects the dependence of thermal conductivity on the number of layers. The lattice thermal conductivity of MoS2 monotonically decreases with increasing number of layers, while that of PtS2 first increases and then decreases.This study implements a self-consistent ab initio lattice dynamics algorithm, eliminating the imaginary frequencies in the phonon spectrum of the high-temperature phase BaBiO3. Based on space group analysis, the multiple phase transitions of BaBiO3 are divided into the breaking of translational symmetry and rotational symmetry, and the effects of translational and rotational symmetry on lattice thermal transport are studied separately. When translational symmetry is reduced, the number of scattering channels increases, and the relaxation time decreases. When rotational symmetry is reduced, scattering intensity increases, and the group velocity of mid-to-low frequency phonons decreases.To address the issue of inaccurate thermal conductivity calculations near phase transition points, this study combines deep potential models with quantum thermal bath molecular dynamics, improving the self-consistent ab initio lattice dynamics algorithm, and investigates the lattice thermal conductivity of SrTiO3 before and after the symmetry breaking caused by temperature changes. The calculation results explain the anomaly of SrTiO3 lattice thermal transport. It mainly comes from the renormalization of the second-order force constant. The local maximum value of thermal conductivity before and after the symmetry breaking comes from the group velocity. And the weak temperature dependence of high-temperature phase thermal conductivity is due to the decrease in scattering intensity and the increase in normalized relaxation time when the temperature increases, as a result of the change in effective second-order force constant.