全息异化：系统方法揭示强关联非离子系统的物理特性

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"全息异化：系统方法"是一篇发表于2016年6月的Open Access论文，由Matthias Ihl、Niko Jokela和Tobias Zingg合作撰写，发表在《Journal of High Energy Physics》(JHEP)第6期，卷号为076。该研究探讨了理论和实验领域中任何子粒子（anyons）的广泛兴趣，特别是由于其复杂交互性质导致的基本概念如任何子气体状态方程尚未得到深入理解。作者们引入了全息原理这一新颖的视角，旨在发展一种系统的方法，用于量子化引力对偶中的电磁自由度。他们的目标是为强相关非离子系统提供一个有效的物理描述，这是解决长期以来理论挑战的一个关键步骤。通过这种方法，他们能够处理任何子在强耦合条件下的行为，即使是在有限电荷密度和磁场环境中。具体来说，他们展示了如何将全息术应用于对偶声子流体（dual phonon fluid）的玩具模型，这是一种简化的理论模型，它与AdS 4中的强耦合黑洞对偶相联系。通过这种方法，他们成功地计算出了状态方程，这是理解和预测任何子系统热力学性质的基础。此外，他们还分析了各种传输系数，这些系数对于理解系统的动力学行为至关重要。这篇论文的重要性在于，它不仅扩展了我们对强耦合量子系统的理解，而且还提供了一个通用框架，使得科学家们能够在处理复杂相互作用时更加高效。全息异化方法的应用可能会推动未来的研究，特别是在量子信息科学、凝聚态物理以及高能物理等领域，尤其是在探索新型材料和量子计算模型方面有着潜在的应用前景。总体而言，这篇文章对于推动理论物理和实验物理之间的交叉研究具有深远的意义。"

JHEP06(2016)076

consistency check of all transformation laws for our anyonization procedure. We also derive

the equation of state and expand it at high temperatures, where the analogy with the virial

expansion is most transparent. In the ﬁnal section 4, we summarize the results and discuss

possible future directions and open problems. Appendix A provides more details on the

variation of the boundary action.

2 Holographic anyons

In this section we will outline a general method for anyonizing holographic matter. Firstly,

a few introductory comments are provided on previous work including a discussion of some

shortcomings related to ambiguities associated with gauge freedom. We then proceed to

propose a diﬀerent prescription which will ultimately manage to circumvent such ambigu-

ities and describe how the two prescriptions are connected. To demonstrate the versatility

of this novel method, the transformed Green’s functions are obtained and computed, along

with further thermodynamic quantities and transport properties.

2.1 Alternative quantization

The procedure of alternative quantization

transforms a (2+1)-dimensional conformal ﬁeld

theory (CFT) into another by changing the boundary conditions on the bulk gauge ﬁeld. In

modern language, this procedure is an SL(2, Z) electromagnetic transformation. Therefore,

as the name suggests, the manner in which boundary degrees of freedom are separated into

source and response is changed, while the bulk description and equations of motion remain

untouched. It is important to note that the bulk action does not need to be invariant under

SL(2, Z), we only demand the bulk gauge equations of motion reduce to free ones close to

the boundary where Robin, i.e., combined Dirichlet/Neumann, boundary conditions are

imposed.

In fact, one could allow for a larger group of transformations, but keeping

in mind a possible, and desirable, embedding into string theory, where both the electric

charges and magnetic ﬁelds are integer-quantized, one restricts to SL(2, Z).

To be more speciﬁc, an anyon can be viewed as a quasiparticle consisting of a boson

or fermion with some additional ﬁxed amount of magnetic ﬂux attached per fundamental

unit of charge. In a conformal ﬁeld theory with a global U(1) one can perform the pro-

cess of adding magnetic ﬂuxes using an SL(2, Z) electromagnetic transformation [12, 13].

Under this transformation, the original CFT maps into another one with mixed charges

and magnetic ﬁelds and thus the charge carriers have been transformed into anyonic de-

grees of freedom. From the bulk gravitational point of view, one is choosing an alternative

quantization scheme for the gauge ﬁelds, i.e., the boundary values on the gauge ﬁelds

have combined Dirichlet/Neumann conditions. This was ﬁrst implemented holographically

in [14] by showing that the SL(2, Z) transformation on a fractional quantum Hall state [19]

leads to a soft mode which is a prerequisite of an anyonic superﬂuid. Successful exten-

sions to ﬂowing superﬂuids [20], to other D-brane models [21–23], and even extensions to

backgrounds not dual to CFTs [24, 25] have been constructed subsequently.

For a self-contained review in the present context, see [14].

This should be contrasted with [15–18], where the SL(2,

)-symmetry was imposed in the bulk as well.

– 3 –

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