Adiabatic landscape and optimal paths in ergodic systems
Adiabatic landscape and optimal paths in ergodic systems
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DOI：
10.1103/physrevresearch.3.013102
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
S. Sugiura;P. W. Claeys;A. Dymarsky;A. Polkovnikov
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文献类型：
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作者：
S. Sugiura;P. W. Claeys;A. Dymarsky;A. Polkovnikov
无论是对量子态制备还是对高效热机的设计感兴趣，绝热（可逆）变换在最小化计算复杂性和能量损失方面都起着关键作用。因此，理解这些转换的结构并确定可以有效和快速地执行这些转换的系统是至关重要的。在本文中，我们专注于寻找最佳路径控制系统的哈密顿空间中的耦合。更具体地说，从一个本地的哈密顿量，我们分析方向的耦合空间中的沿着绝热变换可以准确地产生的本地运营商，这是既可实现的实验和易于数值模拟。我们考虑一个不可积的一维伊辛模型参数化的两个独立的耦合，对应的纵向和横向磁场。我们发现在空间中的耦合区域的特点是一个非常强的各向异性的变分绝热规范位（AGP），产生的绝热变换，这使我们能够定义最佳的绝热路径。我们发现，这些路径一般终止于奇异点，其特征在于广泛的退化的能量谱，分裂的参数空间成不连续的区域。的各向异性遵循从奇异的AGP，我们确定了特殊的强大的弱热化和非吸收多体“暗”的状态被湮灭的奇异部分的AGP，并表明它们的存在延伸到深入遍历制度。
Whether one is interested in quantum state preparation or in the design of efficient heat engines, adiabatic (reversible) transformations play a pivotal role in minimizing computational complexity and energy losses. Understanding the structure of these transformations and identifying the systems for which such transformations can be performed efficiently and quickly is therefore of primary importance. In this paper we focus on finding optimal paths in the space of couplings controlling the system's Hamiltonian. More specifically, starting from a local Hamiltonian we analyze directions in the space of couplings along which adiabatic transformations can be accurately generated by local operators, which are both realizable in experiments and easy to simulate numerically. We consider a non-integrable 1D Ising model parametrized by two independent couplings, corresponding to longitudinal and transverse magnetic fields. We find regions in the space of couplings characterized by a very strong anisotropy of the variational adiabatic gauge potential (AGP), generating the adiabatic transformations, which allows us to define optimal adiabatic paths. We find that these paths generally terminate at singular points characterized by extensive degeneracies in the energy spectrum, splitting the parameter space into adiabatically disconnected regions. The anisotropy follows from singularities in the AGP, and we identify special robust weakly-thermalizing and non-absorbing many-body "dark" states which are annihilated by the singular part of the AGP and show that their existence extends deep into the ergodic regime.