Exact renormalization group for quantum spin systems and strongly correlated electrons

量子自旋系统和强相关电子的精确重整化群

• 批准号: 431190042
• 负责人: Professor Dr. Peter Kopietz
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/431190042?language=en
• 关键词: Exact; renormalization; group; quantum; spin

In this renewal proposal we will extend the applicability of the functional renormalization group (FRG) method to general quantum systems with projected Hilbert spaces. An important example is the quantum spin systems which we have studied during the first funding period of this proposal; in this case the charge degrees of freedom of an underlying electronic lattice model are projected out, so that the effective spin Hamiltonian acts only on the spin sector of the electronic Hilbert space. Another example is the so-called $t-J$-model which retains not only the spin sector of the Hilbert space, but also the part of the charge sector involving states without doubly occupied lattice sites. Up until now a direct application of the FRG to the $t-J$-model is not possible because the projected Hilbert space does not allow a representation of its correlation functions in terms of unconstrained functional integrals over bosonic or fermionic coherent states. However, the crucial insight in our initial work on the application of the FRG to quantum spin systems is that the FRG can also be used to study quantum systems which do not have a functional integral representation. Apparently, a large part of the FRG community is not aware of this fact. The purpose of this proposal is to further develop this strategy and apply it to fermionic lattice models with projected Hilbert spaces, thus opening a new way to study strongly correlated fermionic lattice models non-perturbatively.

在这个更新提案中，我们将把函数重正化群（FRG）方法的适用性扩展到具有投影希尔伯特空间的一般量子系统。一个重要的例子是我们在本提案的第一个资助期间研究的量子自旋系统；在这种情况下，底层电子晶格模型的电荷自由度被投影出来，因此有效自旋哈密顿量仅作用于电子希尔伯特空间的自旋扇区。另一个例子是所谓的$t-J$模型，它不仅保留了希尔伯特空间的自旋扇区，而且还保留了涉及没有双占据晶格位点的状态的电荷扇区部分。到目前为止，将 FRG 直接应用于 $t-J$ 模型是不可能的，因为投影希尔伯特空间不允许用玻色子或费米子相干态上的无约束函数积分来表示其相关函数。然而，我们最初将 FRG 应用到量子自旋系统的工作中的关键见解是，FRG 也可以用于研究没有函数积分表示的量子系统。显然，FRG 社区的很大一部分人并没有意识到这一事实。该提案的目的是进一步发展这一策略并将其应用于具有投影希尔伯特空间的费米子晶格模型，从而开辟一种非扰动研究强相关费米子晶格模型的新方法。