The S=1/2 Heisenberg bilayer spin model at zero temperature is studied in the dimerized phase using analytic triplet-wave expansions and dimer series expansions. The occurrence of two-triplon bound states in the S=0 and S=1 channels, and antibound states in the S=2 channel, is predicted by the triplet-wave theory, and confirmed by series expansions. All bound states are found to vanish at or before the critical coupling separating the dimerized phase from the Neel phase. The critical behaviour of the total and single-particle static transverse structure factors is also studied by series, and found to conform with theoretical expectations. The single-particle state dominates the structure factor at all couplings.
Low-temperature magnetization curves and thermodynamics of a frustrated spin-1/2 Heisenberg triangular bilayer with the antiferromagnetic intradimer interaction and either ferromagnetic or antiferromagnetic interdimer interaction are investigated in a highly frustrated parameter region, where localized many-magnon eigenstates provide the most dominant contribution to magnetothermodynamics. Low-energy states of the highly frustrated spin-1/2 Heisenberg triangular bilayer can be accordingly found from a mapping correspondence with an effective triangular-lattice spin-1/2 Ising model in a field. …
We study the spectrum of a bilayer of Kitaev magnets on the honeycomb lattice, coupled by Heisenberg exchange in the quantum-dimer phase at strong interlayer coupling. Using the perturbative Continuous Unitary transformation (pCUT) we perform series expansion starting from the fully dimerized limit, to evaluate the elementary excitations, reaching up to and focusing on the two-triplon sector. In stark contrast to conventional bilayer quantum magnets, and because of the broken $SU(2)$-invariance, encoded in the intralayer directional compass-exchange, the bilayer Kitaev magnet is shown to exhib…
We consider the finite-temperature phase diagram of the $S = 1/2$ frustrated Heisenberg bilayer. Although this two-dimensional system may show magnetic order only at zero temperature, we demonstrate the presence of a line of finite-temperature critical points related to the line of first-order transitions between the dimer-singlet and -triplet regimes. We show by high-precision quantum Monte Carlo simulations, which are sign-free in the fully frustrated limit, that this critical point is in the Ising universality class. At zero temperature, the continuous transition between the ordered bilayer…
The criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model was investigated numerically. The dynamical conductivity (associated with the O$(3)$ symmetry) displays the inductor $σ(ω) =(iωL)^{-1}$ and capacitor $i ωC$ behaviors for the ordered and disordered phases, respectively. Both constants, $C$ and $L$, have the same scaling dimension as that of the reciprocal paramagnetic gap $Δ^{-1}$. Then, there arose a question to fix the set of critical amplitude ratios among them. So far, the O$(2)$ case has been investigated in the context of the boson-vortex duality. …
We study the spin dynamics of classical Heisenberg antiferromagnet with nearest neighbor interactions on a quasi-two-dimensional kagome bilayer. This geometrically frustrated lattice consists of two kagome layers connected by a triangular-lattice linking layer. By combining Monte Carlo with precessional spin dynamics simulations, we compute the dynamical structure factor of the classical spin liquid in kagome bilayer and investigate the thermal and dilution effects. While the low frequency and long wavelength dynamics of the cooperative paramagnetic phase is dominated by spin diffusion, weak m…
We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this quantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo si…
We study the phase diagram of an effective model of competing nematic and antiferromagnetic orders of interacting electrons on the Bernal-stacked honeycomb bilayer, as relevant for bilayer graphene. In the noninteracting limit, the model features a semimetallic ground state with quadratic band touching points at the Fermi level. Taking the effects of short-range interactions into account, we demonstrate the existence of an extended region in the mean-field phase diagram characterized by coexisting nematic and antiferromagnetic orders. By means of a renormalization group approach, we reveal tha…
We study a bilayer of the frustrated $J_1$-$J_2$ Heisenberg-model on the square lattice. Starting from the dimer limit at strong interlayer coupling, we perform series expansions using the perturbative Continuous Unitary Transformation, based on the flow equation method, in order to determine the spectrum up to the two-triplon sector. From the one-triplon dispersion we obtain quantum critical lines for transitions from the dimer phase into either Néel or collinear magnetic order. For low to intermediate frustration these transitions are consistent with existing findings, based on the magnetic …
We investigate the influence of quenched disorder on the dynamic structure factor of Heisenberg bilayers on the square, triangular, and kagome lattice in the quantum paramagnetic phase. Perturbative continuous unitary transformations and white graphs are employed to calculate the one-triplon contribution up to high orders in perturbation about the dimer limit for bimodal and continuous disorder. For the square lattice we find that the lifetime of the gap mode is increased by stronger quantum correlations while stronger disorder effects are observed for the triangular lattice due to geometric f…
We explore several classes of quadrupolar ordering in a system of antiferromagnetically coupled quantum spin-1 dimers, which are stacked in the triangular lattice geometry forming a bilayer. Low-energy properties of this model is described by an $\mathcal{S}=1$ hard-core bosonic degrees of freedom defined on each dimer-bond, where the singlet and triplet states of the dimerized spins are interpreted as the vacuum and the occupancy of boson, respectively. The number of bosons per dimer and the magnetic and density fluctuations of bosons are controlled by the inter-dimer Heisenberg interactions.…
Ground state properties, excitation spectra and phase transitions in the $S=1/2$ and $S=3/2$ bilayer Heisenberg models on the honeycomb Lattice
受$S=3/2$材料Bi $_3$ Mn $_4$ O $_{12}$ NO $_3$中无序自旋基态观察的启发，我们研究了蜂窝晶格上的$S=3/2$（和作为比较的$S=1/2$）双层海森堡模型的基态性质和激发光谱，有和没有进一步的邻居相互作用。我们使用Néel态附近的级数展开来计算磁有序相的性质。此外，在$1/λ=J_1/J_{\perp}$，其中$J_1$是一个平面内的交换常数和$J_\perp$是层之间的交换常数的级数展开被用来研究自旋单线态相的性质。对于未受挫折的情况下，我们的相变的结果是在最近的量子蒙特卡罗研究非常好的协议。我们还获得了在无序相的激发光谱和研究的变化时，令人沮丧的交换相互作用添加到$S=3/2$系统中的关键$λ$，并找到一个快速抑制的有序相挫折。讨论了材料Bi $_3$ Mn $_4$ O $_{12}$ NO $_3$的含义。
We use the coupled cluster method (CCM) to study a frustrated spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ Heisenberg antiferromagnet on a bilayer honeycomb lattice with $AA$ stacking. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor antiferromagnetic (AFM) exchange interactions are present in each layer, with respective exchange coupling constants $J_{1}>0$ and $J_{2} \equiv κJ_{1} > 0$. The two layers are coupled with NN AFM exchanges with coupling strength $J_{1}^{\perp}\equiv δJ_{1}>0$. We calculate to high orders of approximation within the CCM the zero-field trans…
We present a theoretical study of single-particle and many-body properties of twisted bilayer WSe$_2$. For single-particle physics, we calculate the band topological phase diagram and electron local density of states (LDOS), which are found to be correlated. By comparing our theoretical LDOS with those measured by scanning tunneling microscopy, we comment on the possible topological nature of the first moiré valence band. For many-body physics, we construct a generalized Hubbard model on a triangular lattice based on the calculated single-particle moiré bands. We show that a layer potential di…
Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on an $AA$-stacked honeycomb bilayer: High-order study of the collinear magnetic phases of the $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model
The zero-temperature quantum phase diagram of the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model on an $AA$-stacked bilayer honeycomb lattice is investigated using the coupled cluster method (CCM). The model comprises two monolayers in each of which the spins, residing on honeycomb-lattice sites, interact via both nearest-neighbor (NN) and frustrating next-nearest-neighbor isotropic antiferromagnetic (AFM) Heisenberg exchange iteractions, with respective strengths $J_{1} > 0$ and $J_{2} \equiv κJ_{1}>0$. The two layers are coupled via a comparable Heisenberg exchange interaction be…
The zero-temperature phase diagram of the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model on an $AA$-stacked square-lattice bilayer is studied using the coupled cluster method implemented to very high orders. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor Heisenberg exchange interactions, of strengths $J_{1}>0$ and $J_{2} \equiv κJ_{1}>0$, respectively, are included in each layer. The two layers are coupled via a NN interlayer Heisenberg exchange interaction with a strength $J_{1}^{\perp} \equiv δJ_{1}$. The magnetic order parameter $M$ (viz., the sublattice magnet…
We use the coupled cluster method to study the zero-temperature quantum phase diagram of the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model on the honeycomb bilayer lattice. In each layer we include both nearest-neighbor and frustrating next-nearest-neighbor antiferromagnetic exchange couplings, of strength $J_{1}>0$ and $J_{2} \equiv κJ_{1} > 0$, respectively. The two layers are coupled by an interlayer nearest-neighbor exchange, with coupling constant $J_{1}^{\perp} \equiv δJ_{1}>0$. We calculate directly in the infinite-lattice limit both the ground-state energy per spin and the…
We study the spin-1/2 Heisenberg antiferromagnet on a bilayer honeycomb lattice including interlayer frustration. Using a set of complementary approaches, namely Schwinger bosons, dimer series expansion, bond operators, and exact diagonalization, we map out the quantum phase diagram. Analyzing ground state energies and elementary excitation spectra, we find four distinct phases, corresponding to three collinear magnetic long range ordered states, and one quantum disordered interlayer dimer phase. We detail, that the latter phase is adiabatically connected to an "exact" singlet product ground s…
The spin$-1/2$ Heisenberg antiferromagnet on the honeycomb bilayer lattice is shown to display a rich variety of semiclassical and genuinely quantum phases, controlled by the interplay between intralayer frustration and interlayer exchange. Employing a complementary set of techniques, comprising spin rotationally invariant Schwinger boson mean field theory, bond operators, and series expansions we unveil the quantum phase diagram, analyzing low-energy excitations and order parameters. By virtue of Schwinger bosons we scan the complete range of exchange parameters, covering both long range orde…
The spin-3/2 Heisenberg antiferromagnet on the bilayer honeycomb lattice is a minimal model to describe the magnetic behavior of Bi$_3$Mn$_4$O$_{12}$(NO$_3$). We study this model with frustrating inter-layer second-neighbor couplings, taking into account quantum and thermal fluctuations. We use a path integral formulation in terms of coherent states to describe the low energy physics of the model. We show that for a particular point in the parameter space, close to the experimental estimated couplings, a continuum classical degeneracy is lifted by both quantum and thermal fluctuations, and a c…
Phase diagrams of S=1/2 bilayer Models of SU(2) symmetric antiferromagnets
School of Physics and Astronomy, Beijing Normal University（北京师范大学物理学院）；Tata Institute for Fundamental Research（塔塔基础研究所）；Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University（北京师范大学多尺度自旋物理教育部重点实验室）；Department of Physics, The Pennsylvania State University（宾夕法尼亚州立大学物理系）
Employing the recently developed momentum-space quantum Monte Carlo scheme, we study the dynamic response of single-particle and collective excitations in realistic continuum models of twisted bilayer graphene. At charge neutrality, this unbiased numerical method reveals strong competition between different symmetry breaking channels with a leading instability towards the intervalley coherent state. Single-particle spectra indicate that repulsive interactions push the fermion spectral weight away from the Fermi energy and open up an insulating gap. The spectra of collective excitations suggest…
We examine the ground-state phase diagram and thermal phase transitions in a plaquettized fully frustrated bilayer spin-1/2 Heisenberg model. Based on a combined analysis from sign-problem free quantum Monte Carlo simulations, perturbation theory and free-energy arguments, we identify a first-order quantum phase transition line that separates two competing quantum-disordered ground states with dominant singlet formations on inter-layer dimers and plaquettes, respectively. At finite temperatures, this line extends to form a wall of first-order thermal transitions, which terminates in a line of …
