Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics
Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics
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DOI：
10.1103/physrevd.101.094505
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发表时间：
2020-03
影响因子：
5
通讯作者：
N. Zerf;R. Boyack;P. Marquard;J. Gracey;J. Maciejko
中科院分区：
文献类型：
--
作者：
N. Zerf;R. Boyack;P. Marquard;J. Gracey;J. Maciejko
近年来，从高能物理中的手征对称性破缺到凝聚态物理中强关联物质的分馏相等物理问题，阐明了2+1维费米子物质格点规范理论的相图已成为一个相当感兴趣的问题。对于数量足够多的四组分Dirac费米子，最近在正方形晶格上对晶格量子电动力学({\mathm{qed}}_{3}$)进行的无符号问题量子蒙特卡罗研究发现，在幂相关的共形{{mathm{qed}}_{3}$相和具有自发破缺点群对称性的限制价键固相之间存在连续的量子相变的证据。这一转变的临界连续介质理论是与规范的Nambu-Jona-Lasinio模型等价的$O(2)$\mathm{qed}_{3}$-Gross-neveu模型，并且临界指数在大-N展开和$-确保数学展开中被计算到一阶。我们通过在大的-N}{f}$展开中计算临界指数到二阶和在四个时空维下计算临界指数到四圈阶来扩展这些研究。在后一种情况下，我们还显式地证明了价键固体序参数的离散的${\mathbb{Z}}_{4}$对称性在临界点被动态地扩大到连续的$O(2)$对称性，对于所有的${N}_{f}$。
Elucidating the phase diagram of lattice gauge theories with fermionic matter in $2+1$ dimensions has become a problem of considerable interest in recent years, motivated by physical problems ranging from chiral symmetry breaking in high-energy physics to fractionalized phases of strongly correlated materials in condensed matter physics. For a sufficiently large number ${N}_{f}$ of flavors of four-component Dirac fermions, recent sign-problem-free quantum Monte Carlo studies of lattice quantum electrodynamics (${\mathrm{QED}}_{3}$) on the square lattice have found evidence for a continuous quantum phase transition between a power-law correlated conformal ${\mathrm{QED}}_{3}$ phase and a confining valence-bond-solid phase with spontaneously broken point-group symmetries. The critical continuum theory of this transition was shown to be the $O(2)$ ${\mathrm{QED}}_{3}$-Gross-Neveu model, equivalent to the gauged Nambu--Jona-Lasinio model, and critical exponents were computed to first order in the large-${N}_{f}$ expansion and the $\ensuremath{\epsilon}$ expansion. We extend these studies by computing critical exponents to second order in the large-${N}_{f}$ expansion and to four-loop order in the $\ensuremath{\epsilon}$ expansion below four spacetime dimensions. In the latter context, we also explicitly demonstrate that the discrete ${\mathbb{Z}}_{4}$ symmetry of the valence-bond-solid order parameter is dynamically enlarged to a continuous $O(2)$ symmetry at criticality for all values of ${N}_{f}$.