We investigate dimerized quantum spin systems using the spin functional renormalization group approach proposed by Krieg and Kopietz [Phys. Rev. B 99, 060403(R) (2019)] which directly focuses on the physical spin correlation functions and avoids the representation of the spins in terms of fermionic or bosonic auxiliary operators. Starting from decoupled dimers as initial condition for the renormalization group flow equations, we obtain the spectrum of the triplet excitations as well as the magnetization in the quantum paramagnetic, ferromagnetic, and thermally disordered phases at all temperatures. Moreover, we compute the full phase diagram of a weakly coupled dimerized spin system in three dimensions, including the correct mean field critical exponents at the two quantum critical points.
We study the low-lying spectrum of the bilinear-biquadratic Heisenberg model in the dimerized and Haldane phases using a tensor renormalization method. At the (Takhtajan-Babujian) critical point the finite size spectrum predicted by the Wess-Zumino-Witten (WZW) model can only partly be confirmed. We find a singlet-singlet gap which does not fit into the WZW systematics. The results obtained are compared to Bethe Ansatz, exact diagonalization, and density matrix renormalization group (DMRG) calculations for specific parameters.
We use the density matrix renormalization group method (DMRG) to compute the frequency and momentum resolved spin-spin correlation functions of a dimerized spin-1/2 chain under a magnetic field at finite temperature. The spectral features strongly depend on the regime of the magnetic field. For increasing magnetic fields, the transitions from a gapped spin liquid phase to a Tomonaga-Luttinger liquid, and then to a totally polarized phase, can be identified in the spectra. Compared to the zero temperature case, the finite temperature excitations give rise to additional spectral features that we…
Cross-over from an incommensurate singlet spiral state with a vanishingly small spin-gap to a valence bond solid state in dimerized frustrated ferromagnetic spin-chains
受自旋链化合物LiCuSbO $_4$ $\equiv$ LiSbCuO $_4$和Rb $_2$ Cu $_2$ Mo $_3$ O $_{12}$的磁性的启发，我们研究了具有二聚最近邻铁磁（FM）（$J_1, J_1^\prime<0$）和次最近邻反铁磁（$J_2>0$）耦合的海森堡链的基态.利用密度矩阵重整化群技术和自旋波理论，我们发现了一个在全极化FM和无公度螺旋态之间的一阶跃迁，其中$α$是阻挫比$J_2/|J_1|$，$β$是二聚化度$J_1^\prime/J_1$ .在单重螺旋态中，在FM跃迁附近自旋能隙非常小，对应于LiCuSbO $_4$的情况.对于较大的$α$，对应于Rb $_2$ Cu $_2$ Mo $_3$ O $_{12}$，和较小的$β$，存在从该阻挫诱导的无公度态到具有实质性自旋带隙的Affleck-Lieb-Paddy-Tasaki型价键固态的交叉。
We present an unbiased numerical density-matrix renormalization group study of the one-dimensional Bose-Hubbard model supplemented by nearest-neighbor Coulomb interaction and bond dimerization. It places the emphasis on the determination of the ground-state phase diagram and shows that, besides dimerized Mott and density-wave insulating phases, an intermediate symmetry-protected topological Haldane insulator emerges at weak Coulomb interactions for filling factor one, which disappears, however, when the dimerization becomes too large. Analyzing the critical behavior of the model, we prove that…
Using {\it ab initio} density functional theory, here we systematically study the monolayer MoOCl$_2$ with a $4d^2$ electronic configuration. Our main results is that an orbital-selective Peierls phase (OSPP) develops in MoOCl$_2$, resulting in the dimerization of the Mo chain along the $b$-axis. Specifically, the Mo-$d_{xy}$ orbitals form robust molecular-orbital states inducing localized $d_{xy}$ singlet dimers, while the Mo-$d_{xz/yz}$ orbitals remain delocalized and itinerant. Our study shows that MoOCl$_2$ is globally metallic, with the Mo-$d_{xy}$ orbital bonding-antibonding splittings o…
Topological phases of bosons with local parity coupling on a dimerized lattice
Univ. Toulouse, CNRS, Laboratoire de Physique Théorique（图卢兹大学，法国国家科学研究中心，理论物理实验室）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（国际理论科学中心，塔塔基础研究所）
We investigate the ground state properties of the spin-$1/2$ pyrochlore Heisenberg antiferromagnet using pseudofermion functional renormalization group techniques. The first part of our analysis is based on an enhanced parton mean-field approach which takes into account fluctuation effects from renormalized vertex functions. Our implementation of this technique extends earlier approaches and resolves technical difficulties associated with a diagrammatic overcounting. Using various parton ansätze for quantum spin liquids, dimerized and nematic states our results indicate a tendency for lattice …
Confinement, deconfinement, and bound states in the spin-$1$ and spin-$3/2$ generalizations of the Majumdar--Ghosh chain
Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；Department of Physics, University of Fribourg（弗里堡大学物理系）；Department of Physics and Astronomy, The University of Tennessee（田纳西大学物理与天文学系）；Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学开普勒纳米科学研究所）
The ground state phase diagram of the dimerized spin-1/2 XX honeycomb model in presence of a transverse magnetic field (TF) is known. With the absence of the magnetic field, two quantum phases, namely, the Néel and the dimerized phases have been identified. Moreover, canted Néel and the paramagnetic (PM) phases also emerge by applying the magnetic field. In this paper, using two complementary numerical exact techniques, Lanczos exact diagonalization, and Density matrix renormalization group (DMRG) methods, we study this model by focusing on the quantum correlations, the concurrence, and the qu…
We investigate the properties of a frustrated spin-5/2 chain with next-nearest neighbor two and three-site interactions, with two questions in mind: the nature of the transition into the dimerized phase induced by the three-site interaction, and the possible presence of a critical floating phase at intermediate values of the next-nearest neighbor interaction. We provide strong evidence that the continuous transition into the dimerized phase, which has been found to be generically in the Wess-Zumino-Witten SU(2)$_{2S}$ universality class up to spin $S=2$, is SU(2)$_5$ only at two isolated point…
We show that the N-patch functional renormalization group (pFRG), a theoretical method commonly applied for correlated electron systems, is unable to implement consistently the matrix element interference arising from strong momentum dependence in the Bloch state contents or the interaction vertices. We show that such a deficit could lead to results incompatible with checkable limits of weak and strong coupling. We propose that the pFRG could be improved by a better account of momentum conservation.
Although the functional renormalization group (fRG) is by now a well-established method for investigating correlated electron systems, it is still undergoing significant technical and conceptual improvements. In particular, the motivation to optimally exploit the parallelism of modern computing platforms has recently led to the development of the "truncated-unity" functional renormalization group (TU-fRG). Here, we review this fRG variant, and we provide its extension to multiband systems with spin-orbit coupling. Furthermore, we discuss some aspects of the implementation and outline opportuni…
We present a multiloop flow equation for the four-point vertex in the functional renormalization group (fRG) framework. The multiloop flow consists of successive one-loop calculations and sums up all parquet diagrams to arbitrary order. This provides substantial improvement of fRG computations for the four-point vertex and, consequently, the self-energy. Using the X-ray-edge singularity as an example, we show that solving the multiloop fRG flow is equivalent to solving the (first-order) parquet equations and illustrate this with numerical results.
We present here a study of the magnetic properties of the antiferromagnetic dimer material CuVOF$_4$(H$_2$O)$_6\cdot$H$_2$O, in which the dimer unit is composed of two different $S = 1/2$ species, Cu(II) and V(IV). An applied magnetic field of $μ_0H_{\rm c1} = 13.1(1)~\rm T$ is found to close the singlet-triplet energy gap, the magnitude of which is governed by the antiferromagnetic intradimer, $J_0 \approx 21~\rm K$, and interdimer, $J' \approx 1~\rm K$, exchange energies, determined from magnetometry and electron-spin resonance measurements. The results of density functional theory (DFT) cal…
We analyze a variety of integration schemes for the momentum space functional renormalization group calculation with the goal of finding an optimized scheme. Using the square lattice $t-t'$ Hubbard model as a testbed we define and benchmark the quality. Most notably we define an error estimate of the solution for the ordinary differential equation circumventing the issues introduced by the divergences at the end of the FRG flow. Using this measure to control for accuracy we find a threefold reduction in number of required integration steps achievable by choice of integrator. We herewith publis…
What is so unique in TlCuCl3 which drives so many unique magnetic features in this compound? To study these properties, here we employ a combination of ab-initio band structure, tight-binding model, and an effective quantum field theory. Within a density-functional theory (DFT) calculation, we find an unexpected bulk Dirac cone without spin-orbit coupling (SOC). Tracing back to its origin, we identify, for the first time, the presence of a Su-Schrieffer-Heeger (SSH) like dimerized Cu chain lying in the 3D crystal structure. The SSH chain, combined with SOC, stipulates an anisotropic 3D Dirac c…
Quantum Spin Singlet Ground State with Large Excitation Gap in the S = 3/2 quasi-1D van der Waals materials MoX3 (X = I, Br)
University of California, Los Angeles（加州大学洛杉矶分校）；California NanoSystems Institute, University of California, Los Angeles（加州纳米系统研究所，加州大学洛杉矶分校）；University of California, Riverside（加州大学河滨分校）；Auburn University（奥本大学）；University of Georgia（佐治亚大学）；Oak Ridge National Laboratory（橡树岭国家实验室）
本研究发现 MoX3 (X = I, Br) 晶体同时具有量子自旋单态基态和经典 Néel 有序，通过实验与理论计算证实了其一维链内与三维链间耦合的相互作用，为探索原子链极限下的量子磁性提供了独特平台。
