AI 中文总结
研究两味矩阵 QCD 在高化学势区域的量子相，通过变分技术对角化哈密顿量，发现\(\mu_{_B}\)与\(c\)或\(\mu_{_I}\)主导时调参导致 QPTs，形成复杂相网，部分相类似 LOFF，基态有特定自旋特性，结果与早期预测一致，明确夸克自旋分数占比。
AI 中文摘要
我们研究了双色两味 QCD（矩阵 - QCD₂,₂）在重子（\(\mu_{_B}\)）、同位旋（\(\mu_{_I}\)）和/或手征（\(c\)）化学势较大的区域。在这些区域，哈密顿量大幅简化，使得研究中间和强杨 - 米尔斯耦合下的基态成为可能。通过变分技术对角化哈密顿量，我们表明在\(\mu_{_B}\)和\(c\)（或\(\mu_{_B}\)和\(\mu_{_I}\)）主导的区域，调整其余参数会导致量子相变（QPTs）。这些相变形成了一个复杂的相网，每个相都有一个由重子数\(B\)和同位旋\(I\)唯一标记的基态。其中几个相类似 LOFF，其基态携带非零自旋，从而自发打破旋转对称性。这些结果与 Splittorff - Son - Stephanov 的早期有效场论预测一致。这些类似 LOFF 的基态的费米子内容由自旋为 1 的双（反）夸克组成，类似于库珀对。我们计算了夸克携带 的自旋分数，发现它在某些情况下构成了总自旋的很大一部分，甚至几乎是全部。
英文摘要
We investigate the matrix model of two-color two-flavor QCD (matrix-QCD$_{2,2}$) in regimes with large baryon ($μ_{_B}$), isospin ($μ_{_I}$), and/or chiral ($c$) chemical potentials. In these regimes, the Hamiltonian simplifies considerably, making it possible to investigate the ground state for intermediate and strong Yang-Mills coupling. By diagonalizing the Hamiltonian using the variational techniques, we show that in regimes where $μ_{_B}$ and $c$ (or $μ_{_B}$ and $μ_{_I}$) dominate, tuning the remaining parameters leads to quantum phase transitions (QPTs). These transitions form a complex web of phases, each of which has a ground state uniquely labelled by baryon number $B$ and isospin $I$. Several of these phases are LOFF-like, characterized by a ground state carrying non-zero spin and hence spontaneously breaking rotational symmetry. These results are consistent with older effective field theory predictions by Splittorff-Son-Stephanov \cite{Splittorff:2000mm}. The fermionic content of these LOFF-like ground states consists of spin-1 di-(anti-) quarks which are analogous to Cooper pairs. We compute the spin-fraction carried by the quarks and find that it constitutes a significant portion -- in some cases nearly the entirety -- of the total spin.
CommentsLaTeX2e, 23 pages, 15 figures, minor corrections
