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Critical properties of metallic and deconfined quantum phase transitions in Dirac systems
Physical Review B ( IF 3.2 ) Pub Date : 2024-09-11 , DOI: 10.1103/physrevb.110.125123 Zi Hong Liu 1 , Matthias Vojta 1 , Fakher F. Assaad 2 , Lukas Janssen 1
Physical Review B ( IF 3.2 ) Pub Date : 2024-09-11 , DOI: 10.1103/physrevb.110.125123 Zi Hong Liu 1 , Matthias Vojta 1 , Fakher F. Assaad 2 , Lukas Janssen 1
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We characterize, by means of large-scale fermion quantum Monte Carlo simulations, metallic and deconfined quantum phase transitions in a bilayer honeycomb model in terms of their quantum critical and finite-temperature properties. The model features three distinct phases at zero temperature as a function of interaction strength. At weak interaction, a fully symmetric Dirac semimetal state is realized. At intermediate and strong interaction, respectively, two long-range-ordered phases, each breaking different symmetries are stabilized. The ordered phases feature partial and full gap openings in the fermion spectrum, respectively. We clarify the symmetries of the different zero-temperature phases and the symmetry-breaking patterns across the two quantum phase transitions between them. The first transition between the disordered and long-range-ordered semimetallic phases has previously been argued to be described by the -dimensional Gross-Neveu-SO(3) field theory. By performing simulations with an improved symmetric Trotter decomposition, we further substantiate this claim by computing the critical exponents , , and , which turn out to be consistent with the field-theoretical expectation within numerical and analytical uncertainties. The second transition between the two long-range-ordered phases has previously been proposed as a possible instance of a metallic deconfined quantum critical point. We further develop this scenario by analyzing the spectral functions in the single-particle, particle-hole, and particle-particle channels. Our results indicate gapless excitations with a unique velocity, supporting the emergence of Lorentz symmetry at criticality. We also compute the finite-temperature phase boundaries of the ordered states above the fully gapped state at large interaction. The phase boundary vanishes smoothly in the vicinity of the putative metallic deconfined quantum critical point, in agreement with the expectation for a continuous or weakly first-order transition.
中文翻译：
狄拉克系统中金属和解禁量子相变的关键性质
我们通过大规模费米子量子蒙特卡罗模拟，描述了双层蜂窝模型中金属和解禁量子相变的量子临界和有限温度特性。该模型在零温度下具有三个不同的相，作为相互作用强度的函数。在弱相互作用下，实现了完全对称的狄拉克半金属态。分别在中间和强相互作用下，两个长程有序相（各自打破不同的对称性）得到稳定。有序相分别在费米子谱中具有部分和全部能隙开口。我们阐明了不同零温相的对称性以及它们之间两个量子相变的对称破缺模式。无序和长程有序半金属相之间的第一次转变以前被认为是由 维 Gross-Neveu-SO(3) 场论。通过使用改进的对称 Trotter 分解进行模拟，我们通过计算临界指数进一步证实了这一说法 , ， 和 ，结果与数值和分析不确定性范围内的场论期望一致。两个长程有序相之间的第二次转变先前已被提出作为金属解禁量子临界点的可能实例。我们通过分析单粒子、粒子-孔和粒子-粒子通道中的谱函数进一步发展了这种情况。我们的结果表明具有独特速度的无间隙激发，支持了临界点洛伦兹对称性的出现。 我们还计算了大相互作用下完全带隙态之上的有序态的有限温度相边界。相界在假定的金属解禁量子临界点附近平滑消失，与连续或弱一阶跃迁的预期一致。
更新日期：2024-09-11
中文翻译：
狄拉克系统中金属和解禁量子相变的关键性质
我们通过大规模费米子量子蒙特卡罗模拟，描述了双层蜂窝模型中金属和解禁量子相变的量子临界和有限温度特性。该模型在零温度下具有三个不同的相，作为相互作用强度的函数。在弱相互作用下，实现了完全对称的狄拉克半金属态。分别在中间和强相互作用下，两个长程有序相（各自打破不同的对称性）得到稳定。有序相分别在费米子谱中具有部分和全部能隙开口。我们阐明了不同零温相的对称性以及它们之间两个量子相变的对称破缺模式。无序和长程有序半金属相之间的第一次转变以前被认为是由 维 Gross-Neveu-SO(3) 场论。通过使用改进的对称 Trotter 分解进行模拟，我们通过计算临界指数进一步证实了这一说法 , ， 和 ，结果与数值和分析不确定性范围内的场论期望一致。两个长程有序相之间的第二次转变先前已被提出作为金属解禁量子临界点的可能实例。我们通过分析单粒子、粒子-孔和粒子-粒子通道中的谱函数进一步发展了这种情况。我们的结果表明具有独特速度的无间隙激发，支持了临界点洛伦兹对称性的出现。 我们还计算了大相互作用下完全带隙态之上的有序态的有限温度相边界。相界在假定的金属解禁量子临界点附近平滑消失，与连续或弱一阶跃迁的预期一致。
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