We derive an extended lattice gauge theory type action for quantum dimermodels and relate it to the height representations of these systems. We examinethe system in two and three dimensions and analyze the phase structure in termsof effective theories and duality arguments. For the two-dimensional case wederive the effective potential both at zero and finite temperature. Thezero-temperature theory at the Rokhsar-Kivelson (RK) point has a critical pointrelated to the self-dual point of a class of $Z_N$ models in the $N\to\infty$limit. Two phase transitions featuring a fixed line are shown to appear in thephase diagram, one at zero temperature and at the RK point and another one atfinite temperature above the RK point. The latter will be shown to correspondto a Kosterlitz-Thouless (KT) phase transition, while the former will begoverned by a KT-like universality class, i.e., sharing many features with a KTtransition but actually corresponding to a different universality class. On theother hand, we show that at the RK point no phase transition happens at finitetemperature. For the three-dimensional case we derive the corresponding dualgauge theory model at the RK point. We show in this case that at zerotemperature a first-order phase transition occurs, while at finite temperaturesboth first- and second-order phase transitions are possible, depending on therelative values of the couplings involved.
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机译：我们为量子二聚体模型推导了扩展的晶格规理论类型作用，并将其与这些系统的高度表示联系起来。我们从两个维度和三个维度检查系统，并根据有效的理论和对偶论点分析相结构。对于二维情况，在零温度和有限温度下都推导有效电势。 Rokhsar-Kivelson（RK）点处的零温度理论具有与$ N \ to \ infty $极限内的一类$ Z_N $模型的自对偶点有关的临界点。在相图中显示了以固定线为特征的两个相变，一个在零温度和RK点处，另一个在RK点以上的无限温度处。后者将显示为与Kosterlitz-Thouless（KT）相变相对应，而前者将由类似KT的通用性类别所控制，即与KTtransition共享许多功能，但实际上对应于不同的通用性类别。另一方面，我们表明在RK点在有限温度下没有相变发生。对于三维情况，我们在RK点导出了相应的对偶理论模型。我们在这种情况下表明，在零温度下会发生一阶相变，而在有限的温度下，一阶和二阶相变都是可能的，这取决于所涉及的耦合的相对值。
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