A Statistical Approach to Quantum Many-Body Eigenstates near Criticality: Multifractality in Hilbert Space

接近临界点的量子多体本征态的统计方法:希尔伯特空间中的多重分形

基本信息

项目摘要

Certain isolated quantum many-body systems never reach equilibrium (defined via suitable single-particle observables) under their own unitary dynamics. Even at the single-particle level, the system retains information about its initial state encoded in local degrees of freedom for arbitrarily long times, due to that fact that many-particle interactions fail to provide a thermal bath for the system itself. Such behaviour is a reflection of the structure of the many-body excited eigenstates of the system, which exhibit localisation in Hilbert space. This occurs for example in interacting quantum systems subjected to strong disorder (many-body localisation), as well as in certain classically chaotic many-body systems. A deeper understanding of ergodicity, chaos and thermalisation in generic many-body quantum systems requires a detailed study of the nature of many-body wavefunctions and related observables in Hilbert space. In particular, wavefunction multifractality seems to be a generic feature of many-body systems that plays a key role in this phenomenology. Multifractal wavefunctions occupy an infinite volume in the thermodynamic limit -like extended states do-, but at the same time a vanishing fraction of the whole space -inheriting the non-ergodicity of localised states. The structure of many-body wavefunctions, and the quantification of their multifractal fluctuations and how these evolve as the system flows from ergodic to localised is not fully understood, yet this determines crucially the behaviour of physical observables. We propose to tackle the study of multifractality in Hilbert space using a numerical beyond-standard generalised multifractal analysis in combination with finite-size scaling. This powerful technique enlarges the applicability of multifractal analysis to describe regions of extended, multifractal and localised states and the scaling between these. With our innovative approach we aim to: (a) Give a clear perspective of the many-body localisation phenomenology in Hilbert space for disordered interacting fermions. We will provide unambiguous evidence of the existence (or not) of ergodic, truly localised, and multifractal intermediate phases of the many-body eigenstates. This will lead to a high-precision phase diagram of localisation and multifractality for interacting fermions, as a function of energy density, interaction strength and disorder.(b) Unravel multifractality in Fock space for interacting bosons in the absence of disorder. Our preliminary investigations reveal multifractality in the ground state of such a system. We will study the evolution of multifractality as a function of the inter-particle interaction strength, in relation with the Mott to superfluid phase transition. By adding a tilt to the local chemical potential, we will investigate the multifractal properties of robust (parametric solitonic) states in the excitation energy spectrum, and relate them to those of the system's ground state.
某些孤立的量子多体系统在它们自己的幺正动力学下永远不会达到平衡(通过合适的单粒子可观测量定义)。即使在单粒子水平上,系统也会在任意长的时间内保留关于其初始状态的信息,这些信息被编码在局部自由度中,这是因为多粒子相互作用无法为系统本身提供热浴。这种行为是多体激发本征态的系统,表现出在希尔伯特空间中的局部化的结构的反映。例如,这发生在受到强无序(多体局域化)的相互作用量子系统中,以及某些经典混沌多体系统中。要更深入地理解一般多体量子系统中的遍历性、混沌和热化,需要详细研究希尔伯特空间中多体波函数和相关观测量的性质。特别是,波函数多重分形似乎是多体系统的一个通用功能,在这种现象学中起着关键作用。多重分形波函数在热力学极限中占据了无限大的体积--就像扩展态一样--但同时也是整个空间的一小部分--继承了局域态的非遍历性。多体波函数的结构,多重分形涨落的量化,以及这些涨落如何随着系统从遍历流到局域流而演变,还没有完全理解,但这决定了物理观测量的行为。我们建议使用数值超越标准的广义多重分形分析结合有限尺寸标度来解决希尔伯特空间中多重分形的研究。这种强大的技术扩大了多重分形分析的适用性,以描述区域的扩展,多重分形和本地化的状态和这些之间的缩放。通过我们的创新方法,我们的目标是:(a)给出一个清晰的视角在希尔伯特空间的无序相互作用费米子的多体局域化现象。我们将提供明确的证据的存在(或不)的遍历,真正本地化,和多重分形中间阶段的多体本征态。这将导致相互作用费米子的局部化和多重分形的高精度相图,作为能量密度,相互作用强度和无序的函数。(b)在没有无序的情况下,解开Fock空间中相互作用玻色子的多重分形。我们的初步研究揭示了这样一个系统的基态多重分形。我们将研究多重分形的演变作为粒子间相互作用强度的函数,与莫特超流相变。通过添加一个倾斜的本地化学势,我们将调查的多重分形性质的强大的(参数孤子)状态的激发能谱,并将它们与系统的基态。

项目成果

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Professor Dr. Andreas Buchleitner其他文献

Professor Dr. Andreas Buchleitner的其他文献

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{{ truncateString('Professor Dr. Andreas Buchleitner', 18)}}的其他基金

Transport and entanglement of orbital angular momentum photonic states in turbulent atmosphere
湍流大气中轨道角动量光子态的传输和纠缠
  • 批准号:
    289382917
  • 财政年份:
    2015
  • 资助金额:
    --
  • 项目类别:
    Research Grants
Matter wave spectroscopy of the many-body physics in optical lattices
光学晶格中多体物理的物质波谱
  • 批准号:
    201192159
  • 财政年份:
    2011
  • 资助金额:
    --
  • 项目类别:
    Research Grants
Pump-probe approach to multiple scattering of intense laser light from cold atoms
泵浦探针方法对来自冷原子的强激光进行多次散射
  • 批准号:
    193945900
  • 财政年份:
    2011
  • 资助金额:
    --
  • 项目类别:
    Research Grants
Coherent transport of waves in disordered systems with nonlinearity and interactions
具有非线性和相互作用的无序系统中波的相干传输
  • 批准号:
    163842026
  • 财政年份:
    2010
  • 资助金额:
    --
  • 项目类别:
    Research Grants
Coherent backscattering of light by saturated atoms
饱和原子对光的相干反向散射
  • 批准号:
    118966434
  • 财政年份:
    2009
  • 资助金额:
    --
  • 项目类别:
    Research Grants
Decay, scattering, and decoherence in many-body quanum systems
多体量子系统中的衰变、散射和退相干
  • 批准号:
    40341746
  • 财政年份:
    2007
  • 资助金额:
    --
  • 项目类别:
    Research Units
Spectral properties of interacting cold atoms in optical lattices
光学晶格中相互作用的冷原子的光谱特性
  • 批准号:
    5454459
  • 财政年份:
    2005
  • 资助金额:
    --
  • 项目类别:
    Priority Programmes

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EnSite array指导下对Stepwise approach无效的慢性房颤机制及消融径线设计的实验研究
  • 批准号:
    81070152
  • 批准年份:
    2010
  • 资助金额:
    10.0 万元
  • 项目类别:
    面上项目

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职业:量子态复杂性理论:表征量子计算机科学的新方法
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    2023
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The limits of Quantum Computing: an approach via Post-Quantum Cryptography
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    EP/W02778X/2
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