Pinwheel valence bond crystal ground state of the spin- 12 Heisenberg antiferromagnet on the shuriken lattice

Abstract

We investigate the nature of the ground state of the spin-12 Heisenberg antiferromagnet on the shuriken lattice by complementary state-of-the-art numerical techniques, such as variational Monte Carlo (VMC) with versatile Gutzwiller-projected Jastrow wave functions, unconstrained multivariable variational Monte Carlo (mVMC), and pseudofermion/pseudo-Majorana functional renormalization group (PFFRG/PMFRG) methods. We establish the presence of a quantum paramagnetic ground state and investigate its nature, by classifying symmetric and chiral quantum spin liquids, and inspecting their instabilities towards competing valence bond crystal (VBC) orders. Our VMC analysis reveals that a VBC with a pinwheel structure emerges as the lowest-energy variational ground state, and it is obtained as an instability of the U(1) Dirac spin liquid. Analogous conclusions are drawn from mVMC calculations employing accurate BCS pairing states supplemented by symmetry projectors, which confirm the presence of pinwheel VBC order by a thorough analysis of dimer-dimer correlation functions. Our work highlights the nontrivial role of quantum fluctuations via the Gutzwiller projector in resolving the subtle interplay between competing orders.

Low-temperature specific-heat studies on two square-kagome antiferromagnets

“…On the contrary, there is only one J 2 between Cu1 and Cu2 in NaCu7 as shown in Fig. 1(b), which probably makes the spin system of NaCu7 more close to the proposed SKL model [18][19][20][21][22][23][24][25]. These differences make it necessary to compare the properties of KCu6 and NaCu7.…”

“…Experimentally, herbertsmithite and its related compounds with the kagome structure show strong signatures for the existence of QSLs although there are still debates on the exact nature of their ground states [7][8][9][10][11][12][13][14][15][16][17]. Starting from the kagome lattice, it has been proposed that the shuriken or square-kagome lattice (SKL) may also host exotic ground states including QSLs [18][19][20][21][22][23][24][25][26]. The triangles are also corner-sharing as those in the kagome lattice, but the SKL has smallest loops with four and eight sites.…”

“…Moreover, the square loops of the SKL endure stronger quantum fluctuations and thus the system exhibits long-range correlations of virtual singlets [22]. The ground states of the SKL could be incommensurate orders, pinwheel valence bond crystal (VBC), U (1) and topological QSLs [24,25].…”

Thermodynamics of the spin-half square-kagome lattice antiferromagnet

“…While it is not questioned that the strong frustration prevents groundstate magnetic ordering, the specific nature of the quantum ground state is under debate. Thus, a recent Schwinger-boson approach leads to a topological spinliquid ground state with weak nematicity and a small gap [22], whereas a variational Monte-Carlo study is in favor of a gapped pinwheel valence-bond crystal state [25]. Previous exact-diagonalization studies seem to also suggest a finite singlet-triplet gap (spin gap) [12,13], though this issue seems as yet unresolved.…”

“…Over the last decade, the interest in the spin-1/2 SKHAF has been growing as a model system of quantum magnetism with a quantum paramagnetic ground state as well as flat-band physics near the saturation field and quantum scars [13][14][15][16][17][18][19][20][21][22][23][24][25]. It is expected that the low-energy physics of the SKHAF is just as fascinating as for the related kagome HAF.…”