热力学极限下有效的准粒子守恒林德布拉德算子
Effective quasiparticle conserving Lindbladians in the thermodynamic limit
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中文总结 AI 辅助
本研究针对热力学极限下开放量子多体系统林德布拉德算子的处理难题，提出pcst++与deepCST两种方法，将连续相似变换推广至多体系统，成功应用于耗散横场伊辛链并揭示了相互作用与耗散的竞争机制。
中文摘要 AI 辅助
开放量子多体系统通常由林德布拉德主方程描述，但热力学极限下林德布拉德算子的处理仍是重大挑战。我们开发了直接在热力学极限下构建有效准粒子守恒林德布拉德算子的框架，该方法将连续相似变换推广到非厄米开放量子系统，可针对准粒子（qp）数对林德布拉德算子进行系统块对角化。我们提出两种互补方法：第一种是投影连续相似变换（pcst++），将微扰连续幺正变换推广到林德布拉德算子，使 linked-cluster 展开能给出无限系统的高阶级数展开；第二种是 deepCST，通过结合相同的准粒子守恒生成元与微扰截断方案，直接扩展经评估的增强微扰连续幺正变换，从而直接在热力学极限下得到非微扰有效林德布拉德算子。我们将 pcst++ 和 deepCST 应用于具有局域耗散的耗散横场伊辛链，聚焦低伊辛 regime，通过将每个自旋拆分为两个位点来纯化林德布拉德，自旋翻转对应两个准粒子，我们推导并分析了0至2个准粒子 sector 中有效的准粒子守恒林德布拉德，结果表明伊辛相互作用会重整化基本自旋翻转激发的衰减率，并为相干相互作用与耗散的竞争提供微观机制。本工作确立了微扰与非微扰连续相似变换作为推导热力学极限下开放量子多体系统有效准粒子图像的通用工具。
英文摘要
Open quantum many-body systems are commonly described by Lindblad master equations, yet the treatment of Lindbladian operators in the thermodynamic limit remains a major challenge. We develop a framework for constructing effective quasiparticle-conserving Lindbladian operators directly in the thermodynamic limit. Our approach extends continuous similarity transformations to non-Hermitian open quantum systems and enables the systematic block diagonalization of Lindbladians with respect to the quasiparticle (qp) number. We formulate two complementary methods. The first, projective continuous similarity transformations (pcst++), generalizes perturbative continuous unitary transformations to Lindblad operators so that a linked-cluster expansion allows us to obtain high-order series expansions of the infinite system. The second, deepCST, extends directly evaluated enhanced perturbative continuous unitary transformations by combining the same qp-conserving generator with a perturbative truncation scheme that yields non-perturbative effective Lindbladian operators directly in thermodynamic limit. We apply pcst++ and deepCST to the dissipative transverse-field Ising chain with local dissipation. We focus on the low-Ising regime. We purify the Lindbladian by splitting each spin into two sites. A spin flip then corresponds to two qps. We derive and analyze the effective, qp-conserving Lindbladian in the sectors with zero to two qps. We show how the Ising interaction renormalizes the decay rates of elementary spin-flip excitations and provides the microscopic mechanism for a competition between coherent interactions and dissipation. Our work establishes perturbative and non-perturbative continuous similarity transformations as a versatile tool for deriving effective qp pictures of open quantum many-body systems in the thermodynamic limit.
发表机构
- Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）
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