带规范固定的量子模拟：从伊辛格点规范理论到动力学通量模型
Quantum Simulation with Gauge Fixing: from Ising Lattice Gauge Theory to Dynamical Flux Model
AI总结：
本文提出基于规范固定的第三种格点规范理论量子模拟方法，以伊辛规范场与费米子耦合模型为例，经规范固定简化为动力学通量模型，并通过Floquet工程实现，预言了禁闭-退禁闭相变。
摘要：
近年来，合成动态规范场的量子模拟引起了广泛关注。传统上模拟规范理论有两种方式：一种是直接模拟具有局域规范对称性的规范理论的完整哈密顿量；另一种是在某个规范子扇区中构造投影哈密顿量。在本工作中，我们提供了基于规范固定的第三种模拟规范理论的途径。为演示这一概念，我们固定了一个与梯子几何结构上无自旋费米子耦合的伊辛格点规范场的规范。规范固定后，该规范理论简化为一个更简单的模型，其中费米子在具有涨落动力学$\mathbb{Z}_{2}$通量的梯子上跳跃。随后我们证明该模型可通过超冷原子气体中的Floquet工程实现。通过对该动力学通量模型的解析和数值研究，我们推断出在原始未固定规范理论中存在从禁闭到退禁闭的相变。本工作为利用规范固定概念量子模拟格点规范理论铺平了道路，这对凝聚态物理和高能物理均具有相关性。
英文摘要：
Quantum simulation of synthetic dynamic gauge field has attracted much attentions in recent years. There are two traditional ways to simulate gauge theories. One is to directly simulate the full Hamiltonian of gauge theories with local gauge symmetries. And the other is to engineer the projected Hamiltonian in one gauge subsector. In this work, we provide the third way towards the simulation of gauge theories based on gauge fixing. To demonstrate this concept, we fix the gauge of an Ising lattice gauge field coupled with spinless fermions on a ladder geometry. After the gauge fixing, this gauge theory is reduced to a simpler model, in which fermions hop on a ladder with a fluctuating dynamical $\mathbb{Z}_{2}$ flux. Then we shows that this model can be realized via Floquet engineering in ultracold atomic gases. By analytical and numerical studies of this dynamical flux model, we deduce that there is confinement to deconfinement phase transition in the original unfixed gauge theory. This work paves the way to quantum simulate lattice gauge theory using the concept of gauge fixing, relevant both for condensed matter and high energy physics.
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