论文标题
三维$ \ mathbb {z} _2 $ gauge理论中的自我划时关键
Self-dual criticality in three-dimensional $\mathbb{Z}_2$ gauge theory with matter
论文作者
论文摘要
2+1D中最简单的拓扑排序阶段是$ z_2 $量规理论的缩放阶段，例如在复式代码中实现。此阶段允许二元性交换电气和磁激发（``$ e $'''和``$ m $''粒子。凝结任何一个粒子，而另一个粒子的间隙产生了3D ISING指数的相变。然而，更神秘的是保留自偶性对称性时，从脱合阶段的过渡。如果这种过渡是连续的，到目前为止尚不清楚，那么这可能是我们仍然缺乏任何有用的连续性Lagrangian描述的最简单关键点。这种过渡也具有软物质解释，是3D经典膜的多政治点。 我们研究了$ z_2 $ gauge-higgs型号的蒙特卡洛模拟的自动偶尔过渡，这是线性尺寸的立方晶格$ l \ leq 96 $。我们的结果表明一个连续的过渡：例如，累积物显示出惊人的无参数缩放缩小。我们通过使用二重性对称性来区分领先的duality-odd/duality-even缩放运算符$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $。所有本地操作员都有较大的缩放尺寸，这是定位临界点无效的标准技术。我们使用累积剂的``重新归一化组轨迹''开发替代方案。我们检查了蒙特卡罗动态中的两个和三点功能以及尺度不变的时间相关器，并具有缩放尺寸$ x_a $和$ x_s $以及动态指数$ z $。 我们还为在相图的某些部分中，就膜/世界曲面的“修补”而言，给出了1形对称性的出现图片。我们将其与时空中任何人世界线的渗透联系起来。分析渗透会为自偶转换产生第四指数。我们提出了该模型的变化以进行进一步研究。
The simplest topologically ordered phase in 2+1D is the deconfined phase of $Z_2$ gauge theory, realized for example in the toric code. This phase permits a duality that exchanges electric and magnetic excitations (``$e$'' and ``$m$'' particles). Condensing either particle while the other remains gapped yields a phase transition with 3D Ising exponents. More mysterious, however, is the transition out of the deconfined phase when self-duality symmetry is preserved. If this transition is continuous, which has so far been unclear, then it may be the simplest critical point for which we still lack any useful continuum Lagrangian description. This transition also has a soft matter interpretation, as a multicritical point for classical membranes in 3D. We study the self-dual transition with Monte Carlo simulations of the $Z_2$ gauge-Higgs model on cubic lattices of linear size $L\leq 96$. Our results indicate a continuous transition: for example, cumulants show a striking parameter-free scaling collapse. We estimate scaling dimensions by using duality symmetry to distinguish the leading duality-odd/duality-even scaling operators $A$ and $S$. All local operators have large scaling dimensions, making standard techniques for locating the critical point ineffective. We develop an alternative using ``renormalization group trajectories'' of cumulants. We check that two- and three-point functions, and temporal correlators in the Monte-Carlo dynamics, are scale-invariant, with scaling dimensions $x_A$ and $x_S$ and dynamical exponent $z$. We also give a picture for emergence of 1-form symmetries, in some parts of the phase diagram, in terms of ``patching'' of membranes/worldsurfaces. We relate this to the percolation of anyon worldlines in spacetime. Analyzing percolation yields a fourth exponent for the self-dual transition. We propose variations of the model for further investigation.
