Two-dimensional O(3) model at nonzero density: From dual lattice simulations to repulsive bosons
Two-dimensional O(3) model at nonzero density: From dual lattice simulations to repulsive bosons
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DOI：
10.1103/physrevd.94.114503
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发表时间：
2016-07
影响因子：
5
通讯作者：
F. Bruckmann;C. Gattringer;T. Kloiber;T. Sulejmanpasic
中科院分区：
文献类型：
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作者：
F. Bruckmann;C. Gattringer;T. Kloiber;T. Sulejmanpasic
讨论了在非零化学势(相当于磁场)下，O(3)非线性西格玛模型在$1+1$维上的热力学。在其传统的场论表述中，该模型存在符号问题。通过对偶化模型，我们能够在任意化学势值下完全进入具有动力学质量隙的渐近自由理论的非零密度区。我们发现了零温度下的量子相变，其中密度作为化学势的函数呈现非零值。通过测量自旋刚度，我们得到了相应的动力学临界指数接近2的证据。低能O(3)模型被推测为具有排斥相互作用的大质量玻色子三重态。我们确认了这种系统在低密度(和温度)下的普适平方根行为，并将我们的数据与相对论和非相对论一维玻色气体的Bethe Anatz解的结果进行了比较。我们还评论了在非零密度下潜在的Berezinskii-Kosterlitz-Thouless相变。
We discuss the thermodynamics of the O(3) nonlinear sigma model in $1+1$ dimensions at nonzero chemical potential (equivalent to a magnetic field). In its conventional field theory representation the model suffers from a sign problem. By dualizing the model, we are able to fully access the nonzero density regime of an asymptotically free theory with dynamical mass gap at arbitrary chemical potential values. We find a quantum phase transition at zero temperature where as a function of the chemical potential the density assumes a nonzero value. Measuring the spin stiffness we present evidence for a corresponding dynamical critical exponent $z$ close to 2. The low energy O(3) model is conjectured to be described by a massive boson triplet with repulsive interactions. We confirm the universal square-root behavior expected for such a system at low density (and temperature) and compare our data to the results of Bethe Ansatz solutions of the relativistic and nonrelativistic one-dimensional Bose gas. We also comment on a potential Berezinskii-Kosterlitz-Thouless transition at nonzero density.