Quasi-one-dimensional (Q1D) systems, i.e., three- and two-dimensional (3D/2D) arrays composed of weakly coupled one-dimensional lattices of interacting quantum particles, exhibit rich and fascinating physics. They are studied across various areas of condensed matter and ultracold atomic lattice-gas physics, and are often marked by dimensional crossover as the coupling between one-dimensional systems is increased or temperature decreased, i.e., the Q1D system goes from appearing largely 1D to largely 3D. Phase transitions occurring along the crossover can strongly enhance this effect. Understanding these crossovers and associated phase transitions can be challenging due to the very different elementary excitations of 1D systems compared to higher-dimensional ones. In the present work, we combine numerical matrix product state (MPS) methods with mean-field (MF) theory to study paradigmatic cases of dimensional crossovers and the associated phase transitions in systems of both hard-core and soft-core lattice bosons, with relevance to both condensed matter physics and ultracold atomic gases. We show that the superfluid-to-insulator transition is a first order one, as opposed to the isotropic cases, and calculate transition temperatures for the superfluid states, finding excellent agreement with analytical theory. At the same time, our $\mathrm{MPS}+\mathrm{MF}$ approach keeps functioning well where the current analytical framework cannot be applied. We further confirm the qualitative and quantitative reliability of our approach by comparison to exact quantum Monte Carlo calculations for the full 3D arrays.

中文翻译：

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耦合链中的尺寸交叉和相变：密度矩阵重归一化组结果

准一维（Q1D）系统，即由相互作用的量子粒子的弱耦合一维晶格组成的三维和二维（3D / 2D）阵列，展现出丰富而引人入胜的物理学。他们在冷凝物和超冷原子晶格气体物理学的各个领域进行了研究，并且通常随着一维系统之间的耦合增加或温度降低而出现尺寸交叉现象，即Q1D系统从出现的一维大体变为了一维的大体。 3D 沿着分频器发生的相变可以大大增强这种效果。由于与一维系统相比，一维系统的基本激励非常不同，因此了解这些交叉点和相关的相变可能具有挑战性。在目前的工作中，我们将数值矩阵乘积状态（MPS）方法与均值场（MF）理论相结合，研究硬核和软核晶格玻色子系统中尺寸交叉和相关相变的范式案例，并与凝结物质相关物理和超冷原子气体。我们证明，与各向同性情况相反，超流体到绝缘体的转变是一阶的，并计算了超流体状态的转变温度，与分析理论非常吻合。同时，我们的 我们证明，与各向同性情况相反，超流体到绝缘体的转变是一阶的，并计算了超流体状态的转变温度，与分析理论非常吻合。同时，我们的 我们表明，与各向同性情况相反，超流体到绝缘体的转变是一阶的，并且计算出了超流体状态的转变温度，与分析理论非常吻合。同时，我们的$\mathrm{MPS}+\mathrm{中频}$该方法在无法应用当前分析框架的地方保持良好的功能。通过与完整3D阵列的精确量子蒙特卡洛计算进行比较，我们进一步确定了我们方法的定性和定量可靠性。