[论文解读] Gapless Bosonic Excitation without symmetry breaking: Novel Algebraic Spin liquid with soft Gravitons

Cenke Xu|arXiv (Cornell University)|Sep 22, 2006

Cold Atom Physics and Bose-Einstein Condensates被引用 5

一句话总结

该论文提出了一种在fcc晶格上存在的新型三维玻色子量子自旋液体相，该相具有稳定、无能隙的玻色子激发态，其行为类似于软引力子，具有二次色散关系（$\omega \sim k^2$），并由自对偶性和大规范对称性保护。该相表现出代数密度关联，并由一组新的涌现麦克斯韦型方程描述，包含三种不同的无能隙模式，包括一个标量迹模式和两个具有引力子样规范结构的横向模式。

ABSTRACT

A novel quantum ground state of matter is realized in a bosonic model on three dimensional fcc lattice with emergent low energy excitations. The novel phase obtained is a stable gapless boson liquid phase, with algebraic boson density correlations. The stability of this phase is protected against the instanton effect and superfluidity by self-duality and large gauge symmetries on both sides of the duality. The gapless collective excitations of this phase closely resemble the graviton, although they have a soft $ω\sim k^2$ dispersion relation. There are three branches of gapless excitations in this phase, one of which is gapless scalar trace mode, the other two have the same polarization and gauge symmetries as the gravitons. The dynamics of this novel phase is described by a new set of Maxwell's equations. The defects carrying gauge charges can drive the system into the superfluid order when the defects are condensed; also the topological defects are coupled to the dual gauge field in the same manner as the charge defects couple to the original gauge field, after the condensation of the topological defects, the system is driven into the Mott Insulator phase. In the 2 dimensional case, the gapless soft graviton as well as the algebraic liquid phase are destroyed by the vertex operators in the dual theory, and the stripe order is most likely to take place close to the 2 dimensional quantum critical point at which the vertex operators are tuned to zero.

研究动机与目标

• 在无对称性破缺的三维玻色子系统中识别一种稳定且无能隙的量子液体相。
• 在晶格模型中展示具有$\omega \sim k^2$色散关系的类引力子集体模式的涌现。
• 确立代数自旋液体相的稳定性由自对偶性和大规范对称性保护。
• 表明低能动力学由一组新的涌现麦克斯韦型方程 governing。
• 探索由规范荷和拓扑缺陷凝聚引发的相变。

提出的方法

• 在三维fcc晶格上构建U(1)规范理论，通过环交换项生成涌现规范场。
• 利用自对偶性保护无能隙相，防止单极子凝聚和超流不稳定性。
• 引入一个秩-2张量规范场$A_{ij}$以描述涌现的类引力子模式。
• 推导一组新的有效麦克斯韦型方程，用于描述涌现规范场的动力学。
• 分析缺陷凝聚：电荷缺陷凝聚进入超流相，而涡旋凝聚进入莫特绝缘体相。
• 利用对偶理论表明，在二维情况下，顶点算符会破坏代数相，使条纹序在临界点附近占优。

实验结果

研究问题

• RQ1 在无对称性破缺的三维系统中，是否可能存在一种稳定且无能隙的玻色子激发态相？
• RQ2 何种机制可保护无能隙模式免受量子涨落和单极子凝聚的影响？
• RQ3 这些涌现激发态为何类似于引力子，且为何表现出$\omega \sim k^2$色散关系？
• RQ4 自对偶性和大规范对称性在稳定代数自旋液体相中起什么作用？
• RQ5 缺陷凝聚如何驱动系统向超流相和莫特绝缘体相转变？

主要发现

• 在三维fcc晶格上实现了一种稳定且无能隙的玻色子液体相，具有代数密度关联且无对称性破缺。
• 该相包含三种无能隙模式：一个标量迹模式和两个具有类引力子规范结构、且色散关系为$\omega \sim k^2$的横向模式。
• 该相的稳定性由自对偶性和大规范对称性保护，这些对称性抑制了单极子效应和超流性。
• 低能动力学由一组新的涌现麦克斯韦型方程描述，与标准电磁学不同。
• 规范荷的凝聚使系统进入超流相，而拓扑缺陷的凝聚则导致形成莫特绝缘体相。
• 在二维情况下，由于顶点算符的作用，代数相不稳定，临界点附近可能形成条纹序。