اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدInterlaced coarse-graining for the dynamic cluster approximation
219
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The dynamical cluster approximation (DCA) and its DCA$^+$ extension use coarse-graining of the momentum space to reduce the complexity of quantum many-body problems, thereby mapping the bulk lattice to a cluster embedded in a dynamical mean-field host. Here, we introduce a new form of an interlaced coarse-graining and compare it with the traditional coarse-graining. While it gives a more localized self-energy for a given cluster size, we show that it leads to more controlled results with weaker cluster shape and smoother cluster size dependence, which converge to the results obtained from the standard coarse-graining with increasing cluster size. Most importantly, the new coarse-graining reduces the severity of the fermionic sign problem of the underlying quantum Monte Carlo cluster solver and thus allows for calculations on larger clusters. This enables the treatment of longer-ranged correlations than those accessible with the standard coarse-graining and thus can allow for the evaluation of the exact infinite cluster size result via finite size scaling. As a demonstration, we study the hole-doped two-dimensional Hubbard model and show that the interlaced coarse-graining in combination with the extended DCA$^+$ algorithm permits the determination of the superconducting $T_c$ on cluster sizes for which the results can be fit with a Kosterlitz-Thouless scaling law.
قيم البحث
اقرأ أيضاً
We propose a dynamic coarse-graining (CG) scheme for mapping heterogeneous polymer fluids onto extremely CG models in a dynamically consistent manner. The idea is to use as target function for the mapping a wave-vector dependent mobility function der
ived from the single-chain dynamic structure factor, which is calculated in the microscopic reference system. In previous work, we have shown that dynamic density functional calculations based on this mobility function can accurately reproduce the order/disorder kinetics in polymer melts, thus it is a suitable starting point for dynamic mapping. To enable the mapping over a range of relevant wave vectors, we propose to modify the CG dynamics by introducing internal friction parameters that slow down the CG monomer dynamics on local scales, without affecting the static equilibrium structure of the system. We illustrate and discuss the method using the example of infinitely long linear Rouse polymers mapped onto ultrashort CG chains. We show that our method can be used to construct dynamically consistent CG models for homopolymers with CG chain length N=4, whereas for copolymers, longer CG chain lengths are necessary
We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor renormalization group a
nd the other based on the higher-order tensor renormalization group, are introduced. In order to optimize the tensor-network model globally, a sweeping scheme is proposed to account for the renormalization effect from the environment tensors under the framework of second renormalization group. We demonstrate the algorithms by the classical Ising model on the square lattice and the Kitaev model on the honeycomb lattice, and show that the finite-size algorithms achieve substantially more accurate results than the corresponding infinite-size ones.
We consider the application of fluctuation relations to the dynamics of coarse-grained systems, as might arise in a hypothetical experiment in which a system is monitored with a low-resolution measuring apparatus. We analyze a stochastic, Markovian j
ump process with a specific structure that lends itself naturally to coarse-graining. A perturbative analysis yields a reduced stochastic jump process that approximates the coarse-grained dynamics of the original system. This leads to a non-trivial fluctuation relation that is approximately satisfied by the coarse-grained dynamics. We illustrate our results by computing the large deviations of a particular stochastic jump process. Our results highlight the possibility that observed deviations from fluctuation relations might be due to the presence of unobserved degrees of freedom.
We study the coarse-graining approach to derive a generator for the evolution of an open quantum system over a finite time interval. The approach does not require a secular approximation but nevertheless generally leads to a Lindblad-Gorini-Kossakows
ki-Sudarshan generator. By combining the formalism with Full Counting Statistics, we can demonstrate a consistent thermodynamic framework, once the switching work required for the coupling and decoupling with the reservoir is included. Particularly, we can write the second law in standard form, with the only difference that heat currents must be defined with respect to the reservoir. We exemplify our findings with simple but pedagogical examples.
We develop the Gutzwiller approximation method to obtain the renormalized Hamiltonian of the SU(4) $t$-$J$ model, with the corresponding renormalization factors. Subsequently, a mean-field theory is employed on the renormalized Hamiltonian of the mod
el on the honeycomb lattice under the scenario of a cooperative condensation of carriers moving in the resonating valence bond state of flavors. In particular, we find the extended $s$-wave superconductivity is much more favorable than the $d+id$ superconductivity in the doping range close to quarter filling. The pairing states of the SU(4) case reveal the property that the spin-singlet pairing and the spin-triplet pairing can exist simultaneously. Our results might provide new insights into the twisted bilayer graphene system.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
