اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدExact enumeration of Hamiltonian circuits, walks, and chains in two and three dimensions
119
0
0.0
(
0
)
تأليف
Jesper Lykke Jacobsen
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We present an algorithm for enumerating exactly the number of Hamiltonian chains on regular lattices in low dimensions. By definition, these are sets of k disjoint paths whose union visits each lattice vertex exactly once. The well-known Hamiltonian circuits and walks appear as the special cases k=0 and k=1 respectively. In two dimensions, we enumerate chains on L x L square lattices up to L=12, walks up to L=17, and circuits up to L=20. Some results for three dimensions are also given. Using our data we extract several quantities of physical interest.
قيم البحث
اقرأ أيضاً
Sharp two- and three-dimensional phase transitional magnetization curves are obtained by an iterative renormalization-group coupling of Ising chains, which are solved exactly. The chains by themselves do not have a phase transition or non-zero magnet
ization, but the method reflects crossover from temperature-like to field-like renormalization-group flows as the mechanism for the higher-dimensional phase transitions. The magnetization of each chain acts, via the interaction constant, as a magnetic field on its neighboring chains, thus entering its renormalization-group calculation. The method is highly flexible for wide application.
Exact analyses are given for two three-dimensional lattice systems: A system of close-packed dimers placed in layers of honeycomb lattices and a layered triangular-lattice interacting domain wall model, both with nontrivial interlayer interactions. W
e show that both models are equivalent to a 5-vertex model on the square lattice with interlayer vertex-vertex interactions. Using the method of Bethe ansatz, a closed-form expression for the free energy is obtained and analyzed. We deduce the exact phase diagram and determine the nature of the phase transitions as a function of the strength of the interlayer interaction.
We consider a lattice version of the Bisognano-Wichmann (BW) modular Hamiltonian as an ansatz for the bipartite entanglement Hamiltonian of the quantum critical chains. Using numerically unbiased methods, we check the accuracy of the BW-ansatz by bot
h comparing the BW Renyi entropy to the exact results, and by investigating the size scaling of the norm distance between the exact reduced density matrix and the BW one. Our study encompasses a variety of models, scanning different universality classes, including transverse field Ising, Potts and XXZ chains. We show that the Renyi entropies obtained via the BW ansatz properly describe the scaling properties predicted by conformal field theory. Remarkably, the BW Renyi entropies faithfully capture also the corrections to the conformal field theory scaling associated to the energy density operator. In addition, we show that the norm distance between the discretized BW density matrix and the exact one asymptotically goes to zero with the system size: this indicates that the BW-ansatz can be also employed to predict properties of the eigenvectors of the reduced density matrices, and is thus potentially applicable to other entanglement-related quantities such as negativity.
We construct a class of lattices in three and higher dimensions for which the number of dimer coverings can be determined exactly using elementary arguments. These lattices are a generalization of the two-dimensional kagome lattice, and the method al
so works for graphs without translational symmetry. The partition function for dimer coverings on these lattices can be determined also for a class of assignments of different activities to different edges.
We derive exact analytic results for several four-point correlation functions for statistical models exhibiting phase separation in two-dimensions. Our theoretical results are then specialized to the Ising model on the two-dimensional strip and found
to be in excellent agreement with high-precision Monte Carlo simulations.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
