Cluster functional renormalization group and absence of a bilinear spin liquid in the J_{1}J_{2} Heisenberg model
Abstract
The pseudofermion functional renormalization group (pfFRG) has been put forward as a semianalytical scheme that, for a given microscopic spin model, allows to discriminate whether the lowtemperature states exhibit magnetic ordering or a tendency toward the formation of quantum spin liquids. However, the precise nature of the putative spinliquid ground state has remained hard to infer from the original (singlesite) pfFRG scheme. Here, we introduce a cluster pfFRG approach, which allows for a more stringent connection between a microscopic spin model and its lowtemperature spinliquid ground states. In particular, it allows to calculate spatially structured fermion bilinear expectation values on spatial clusters, which are formed by splitting the original lattice into several sublattices, thereby allowing for the positive identification of a family of bilinear spinliquid states. As an application of this cluster pfFRG approach, we consider the J_{1}J_{2}SU (N ) Heisenberg model on a square lattice, which is a paradigmatic example for a frustrated quantum magnet exhibiting quantum spinliquid behavior for intermediate coupling strengths. In the wellestablished largeN limit of this model, we show that our approach correctly captures the emergence of the π flux spinliquid state at low temperatures. For small N , where the precise nature of the ground state remains controversial, we focus on the widely studied case of N =2 , for which we determine the lowtemperature phase diagram near the strongly frustrated regime after implementing the fermionnumber constraint by the flowing PopovFedotov method. Our results suggest that the J_{1}J_{2} Heisenberg model does not support the formation of a fermion bilinear spinliquid state.
 Publication:

Physical Review B
 Pub Date:
 September 2019
 DOI:
 10.1103/PhysRevB.100.125130
 arXiv:
 arXiv:1905.01060
 Bibcode:
 2019PhRvB.100l5130R
 Keywords:

 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 13 pages, 9 figures