Two-dimensional Heisenberg Research Articles

Estimating correlations and entanglement in the two-dimensional Heisenberg model in the strong-rung-coupling limit

Estimating correlations and entanglement in the two-dimensional Heisenberg model in the strong-rung-coupling limit

Deep neural networks as variational solutions for correlated open quantum systems

In this work we apply deep neural networks to find the non-equilibrium steady state solution to correlated open quantum many-body systems. Motivated by the ongoing search to find more powerful representations of (mixed) quantum states, we design a simple prototypical convolutional neural network and show that parametrizing the density matrix directly with more powerful models can yield better variational ansatz functions and improve upon results reached by neural density operator based on the restricted Boltzmann machine. Hereby we give up the explicit restriction to positive semi-definite density matrices. However, this is fulfilled again to good approximation by optimizing the parameters. The great advantage of this approach is that it opens up the possibility of exploring more complex network architectures that can be tailored to specific physical properties. We show how translation invariance can be enforced effortlessly and reach better results with fewer parameters. We present results for the dissipative one-dimensional transverse-field Ising model and a two-dimensional dissipative Heisenberg model compared to exact values.

Applicability of measurement-based quantum computation towards physically-driven variational quantum eigensolver

Variational quantum algorithms are considered one of the most promising methods for obtaining near-term quantum advantages; however, most of these algorithms are only expressed in the conventional quantum circuit scheme. The roadblock to developing quantum algorithms with the measurement-based quantum computation (MBQC) scheme is resource cost. Recently, we discovered that the realization of multi-qubit rotation operations only requires a constant number of single-qubit measurements with the MBQC scheme, providing a potential advantage in terms of resource cost. The structure of the Hamiltonian variational ansatz aligns well with this characteristic. Thus, we propose an efficient measurement-based quantum algorithm for quantum many-body system simulation tasks, called measurement-based Hamiltonian variational ansatz (MBHVA). We then demonstrate its effectiveness, efficiency, and advantages with the two-dimensional Heisenberg model and the Fermi–Hubbard chain. Numerical experiments show that MBHVA can have similar performance as circuit-based ansatz, and is expected to reduce operation counts during execution compared to quantum circuits, bringing the advantage of running time. We conclude that the MBQC scheme is potentially feasible for achieving near-term quantum advantages in the noisy intermediate-scale quantum era, especially in the presence of large multi-qubit rotation operations.

Existence of long-range magnetic order in Heisenberg spin nanoribbons with edge modification

Long-range magnetic order appears on a side decorated Heisenberg spin nanoribbon at nonzero temperature, although no spontaneous magnetization exists in a one- or two-dimensional isotropic Heisenberg model at any nonzero temperature according to the Mermin–Wagner theorem. By use of the spin Green’s function method, we calculated the magnetizations of Heisenberg nanoribbons decorated by side spins with single-ion anisotropy and found that the system exhibits a nonzero transition temperature, whether the decorated edge spins of the system link together or separate from each other. When the width of the nanoribbon achieves infinite limit, the transition temperatures of the system tend to the same finite constant eventually whether one edge or both edges are decorated by side spins in the nanoribbon. The results reveal that the magnetism of a low-dimensional spin system is different from that of a three-dimensional spin system. When the single-ion anisotropy of edge spins in a Heisenberg spin nanoribbon can be modulated by an electric field experimentally, various useful long-range magnetic orders of the system can be obtained. This work can provide a detailed theoretical basis for designing and fabricating next-generation low-dimensional magnetic random-access memory.

Measuring the Boundary Gapless State and Criticality via Disorder Operator.

The disorder operator is often designed to reveal the conformal field theory (CFT) information in quantum many-body systems. By using large-scale quantum MonteCarlo simulation, we study the scaling behavior of disorder operators on the boundary in the two-dimensional Heisenberg model on the square-octagon lattice with gapless topological edge state. In the Affleck-Kennedy-Lieb-Tasaki phase, the disorder operator is shown to hold the perimeter scaling with a logarithmic term associated with the Luttinger liquid parameter K. This effective Luttinger liquid parameter K reflects the low-energy physics and CFT for (1+1)D boundary. At bulk critical point, the effective K is suppressed but it keeps finite value, indicating the coupling between the gapless edge state and bulk fluctuation. The logarithmic term numerically captures this coupling picture, which reveals the (1+1)D SU(2)_{1} CFT and (2+1)D O(3) CFT at boundary criticality. Our Letter paves a new way to study the exotic boundary state and boundary criticality.

Imaginary-time relaxation quantum critical dynamics in the two-dimensional dimerized Heisenberg model

Imaginary-time relaxation quantum critical dynamics in the two-dimensional dimerized Heisenberg model

Topological Kolmogorov complexity and the Berezinskii-Kosterlitz-Thouless mechanism.

Topology plays a fundamental role in our understanding of many-body physics, from vortices and solitons in classical field theory to phases and excitations in quantum matter. Topological phenomena are intimately connected to the distribution of information content that, differently from ordinary matter, is now governed by nonlocal degrees of freedom. However, a precise characterization of how topological effects govern the complexity of a many-body state, i.e., its partition function, is presently unclear. In this paper, we show how topology and complexity are directly intertwined concepts in the context of classical statistical mechanics. We concretely present a theory that shows how the Kolmogorov complexity of a classical partition function sampling carries unique, distinctive features depending on the presence of topological excitations in the system. We confront two-dimensional Ising, Heisenberg, and XY models on several topologies and study the corresponding samplings as high-dimensional manifolds in configuration space, quantifying their complexity via the intrinsic dimension. While for the Ising and Heisenberg models the intrinsic dimension is independent of the real-space topology, for the XY model it depends crucially on temperature: across the Berezkinskii-Kosterlitz-Thouless (BKT) transition, complexity becomes topology dependent. In the BKT phase, it displays a characteristic dependence on the homology of the real-space manifold, and, for g-torii, it follows a scaling that is solely genus dependent. We argue that this behavior is intimately connected to the emergence of an order parameter in data space, the conditional connectivity, which displays scaling behavior. Our approach paves the way for an understanding of topological phenomena emergent from many-body interactions from the perspective of Kolmogorov complexity.

CrO<sub>2</sub> monolayer: a two-dimensional ferromagnet with high Curie temperature and half-metallicity

Owing to the complete spin-polarization of electronic states near Fermi energy, half-metallic ferromagnets, especially two-dimensional half-metallic ferromagnets, have garnered significant attention in the field of spintronics. However, the practical applications of these materials are greatly hindered by their low Curie temperatures. Therefore, the exploration of high Curie temperature half-metallic ferromagnets poses a necessary and challenging task. In this study, we predict a two-dimensional transition metal oxide, CrO<sub>2</sub> monolayer, and employ first-principles calculations to investigate the crystal structure, electronic properties, magnetic ground state, and ferromagnetic phase transition. The calculations of phonon spectrum, elastic constant, and molecular dynamics simulations indicate that CrO<sub>2</sub> monolayer is dynamically, mechanically, and thermally stable. The convex hull diagram of Cr-O systems shows that the hull energy of the predicted CrO<sub>2</sub> layer is only 0.18 eV, further confirming the structural stability and large possibility for experimental fabrication. More importantly, the electronic and magnetic properties of CrO<sub>2</sub> monolayer demonstrate that it is a two-dimensional ferromagnetic half-metal with wide band gap. Five d suborbitals are divided into E<sub>g</sub> and T<sub>2g</sub> orbitals because of the crystal field of Cr atom in the center of O tetrahedron, and the spin-polarizations of E<sub>g</sub> orbitals make a major contribution to the moment around Cr atom. The ferromagnetic coupling along Cr-O-Cr chain is dominated by the superexchange interaction bridged by O 2p orbitals, similar to the typical Mn-O-Mn superexchange model. The magnetic behavior of the Cr spin lattice in a CrO<sub>2</sub> monolayer is described by a two-dimensional Heisenberg model, in which the exchange coupling anisotropy is ignored and the single ion anisotropy is the main consideration. By solving the Heisenberg model through using the Monte Carlo simulation method, the Curie temperature is determined to be over 400 K. The high Curie temperature ferromagnetism is rare in two-dimensional ferromagnetic materials and even rarer in semi-metallic materials, which makes it an ideal material for fabricating spintronic devices and studying spin quantum effects.

Topological magnons on triangular antiferromagnetic lattices in an external field

The influence of topological magnons of the antiferromagnet in triangular lattice on Hall spin conductivity and thermodynamics is investigated. The magnons splitting due to the triangular lattice geometry leads to a complex and interesting behavior in all quantities analyzed of the system. We get the behavior of the Hall spin conductivity as a function of T as well as the specific heat, magnetization and magnetic susceptibility, where the behavior of the Hall spin conductivity decreases at low-temperature limit, dropping to zero at T→0 as expected for all bosonic system. Moreover, we get the behavior of the magnetization as a function of field h presenting problems of convergence at h→0 which is expected for the two-dimensional like Heisenberg model.

Integration of the two-dimensional Heisenberg model by methods of differential geometry

Integration of the two-dimensional Heisenberg model by methods of differential geometry

Integration of the two-dimensional Heisenberg model by methods of differential geometry

Для интегрирования двумерной модели Гейзенберга использованы методы классической дифференциальной геометрии. Уравнения модели после преобразования годографа были записаны в терминах метрического тензора, связанного с криволинейной системой координат, и его производных. Показано, что их общее решение описывает все известные ранее точные решения, кроме плоского вихря. Предсказан и проанализирован новый тип вихревой структуры - "вихревая полоса" в двумерном ферромагнетике. Ее отличительные свойства - конечные размеры области определения, конечность полной энергии и отсутствие ядра вихря при наличии вихревой структуры.

Special transition and extraordinary phase on the surface of a two-dimensional quantum Heisenberg antiferromagnet

Continuous phase transitions exhibit richer critical phenomena on the surface than in the bulk, because distinct surface universality classes can be realized at the same bulk critical point by tuning the surface interactions. The exploration of surface critical behavior provides a window looking into higher-dimensional boundary conformal field theories. In this work, we study the surface critical behavior of a two-dimensional (2D) quantum critical Heisenberg model by tuning the surface coupling strength, and discover a direct special transition on the surface from the ordinary phase into an extraordinary phase. The extraordinary phase has a long-range antiferromagnetic order on the surface, in sharp contrast to the logarithmic decaying spin correlations in the 3D classical O(3) model. The special transition point has a new set of critical exponents, y_{s}=0.86(4)ys=0.86(4) and \eta_{\parallel}=-0.33(1)η∥=−0.33(1), which are distinct from the special transition of the classical O(3) model and indicate a new surface universality class of the 3D O(3) Wilson-Fisher theory.

Two-dimensional Heisenberg model with material-dependent superexchange interactions

The two-dimensional (2D) van der Waals ferromagnetic semiconductors, such as CrI$_3$ and Cr$_2$Ge$_2$Te$_6$, and the 2D ferromagnetic metals, such as Fe$_3$GeTe$_2$ and MnSe$_2$, have been obtained in recent experiments and attracted a lot of attentions. The superexchange interaction has been suggested to dominate the magnetic interactions in these 2D magnetic systems. In the usual theoretical studies, the expression of the 2D Heisenberg models were fixed by hand due to experiences. Here, we propose a method to determine the expression of the 2D Heisenberg models by counting the possible superexchange paths with the density functional theory (DFT) and Wannier function calculations. With this method, we obtain a 2D Heisenberg model with six different nearest-neighbor exchange coupling constants for the 2D ferromagnetic metal Cr$_3$Te$_6$, which is very different for the crystal structure of Cr atoms in Cr$_3$Te$_6$. The calculated Curie temperature Tc = 328 K is close to the Tc = 344 K of 2D Cr$_3$Te$_6$ reported in recent experiment. In addition, we predict two stable 2D ferromagnetic semiconductors Cr$_3$O$_6$ and Mn$_3$O$_6$ sharing the same crystal structure of Cr$_3$Te$_6$. The similar Heisenberg models are obtained for 2D Cr$_3$O$_6$ and Mn$_3$O$_6$, where the calculated Tc is 218 K and 208 K, respectively. Our method offers a general approach to determine the expression of Heisenberg models for these 2D magnetic semiconductors and metals, and builds up a solid basis for further studies.

Weak trimerization in the frustrated two-dimensional triangular Heisenberg antiferromagnet LuyY1−yMnO3

To understand the 2D triangular Heisenberg antiferromagnetic system, we investigated the magnetic structures and the dynamics of ${\mathrm{Lu}}_{y}{\mathrm{Y}}_{1\ensuremath{-}y}{\mathrm{MnO}}_{3}$ in detail. The substitutions are adjusted to the Mn atomic position close to ${x}_{\text{Mn}}=\frac{1}{3}$. The neutron powder diffraction data claims that the magnetic structure of ${\mathrm{Lu}}_{y}{\mathrm{Y}}_{1\ensuremath{-}y}{\mathrm{MnO}}_{3}$ is described as a mixture of ${\mathrm{\ensuremath{\Gamma}}}_{3}$ ($P{6}_{3}^{\ensuremath{'}}c{m}^{\ensuremath{'}}$) and ${\mathrm{\ensuremath{\Gamma}}}_{4}$ ($P{6}_{3}^{\ensuremath{'}}{c}^{\ensuremath{'}}m$) at the ${x}_{\text{Mn}}$ position for $y=0.15$, 0.30, and 0.45. The ratio of ${\mathrm{\ensuremath{\Gamma}}}_{3}$ and ${\mathrm{\ensuremath{\Gamma}}}_{4}$ depends on temperature and composition and the fraction of ${\mathrm{\ensuremath{\Gamma}}}_{3}$ increases upon cooling, while no clear trimerization was observed at the ${x}_{\text{Mn}}$ position. We estimated exchange parameters from the analysis of the low-energy part of the spin waves. The results showed a weak trimerization effect on cooling because the nearest-neighbor exchange interaction is slightly enhanced. The temperature dependence of the spin-wave dispersion around the $\mathrm{\ensuremath{\Gamma}}$ point shows that the spin gap closes with increasing temperature because the exchange interactions in the nearest Mn-Mn neighbor become smaller. Gapless diffusive magnetic excitation from a Mn triangular lattice has been observed in a wide range in $Q$ and $E$ space of ${\mathrm{Lu}}_{y}{\mathrm{Y}}_{1\ensuremath{-}y}{\mathrm{MnO}}_{3}$. We found that ${\mathrm{Lu}}_{0.7}{\mathrm{Y}}_{0.3}{\mathrm{MnO}}_{3}$ could be an ideal case to investigate the trimerization, frustrated magnetism, and magnetoelastic coupling often observed in two-dimensional triangular lattice Heisenberg antiferromagnet systems.

Sizable suppression of magnon Hall effect by magnon damping in Cr2Ge2Te6

Two-dimensional (2D) Heisenberg honeycomb ferromagnets are expected to have interesting topological magnon effects as their magnon dispersion can have Dirac points. The Dirac points are gapped with finite second nearest neighbor Dzyaloshinskii-Moriya interaction, providing nontrivial Berry curvature with finite magnon Hall effect. Yet, it is unknown how the topological properties are affected by magnon damping. We report the thermal Hall effect in Cr$_2$Ge$_2$Te$_6$, an insulating 2D honeycomb ferromagnet with a large Dirac magnon gap and significant magnon damping. Interestingly, the thermal Hall conductivity in Cr$_2$Ge$_2$Te$_6$ shows the coexisting phonon and magnon contributions. Using an empirical two-component model, we successfully estimate the magnon contribution separate from the phonon part, revealing that the magnon Hall conductivity was 20 times smaller than the theoretical calculation. Finally, we suggest that such considerable suppression in the magnon Hall conductivity is due to the magnon damping effect in Cr$_2$Ge$_2$Te$_6$.

Augmenting Density Matrix Renormalization Group with Disentanglers

Density matrix renormalization group (DMRG) and its extensions in the form of matrix product states are arguably the choice for the study of one-dimensional quantum systems in the last three decades. However, due to the limited entanglement encoded in the wave-function ansatz, to maintain the accuracy of DMRG with the increase of the system size in the study of two-dimensional systems, exponentially increased resources are required, which limits the applicability of DMRG to only narrow systems. We introduce a new ansatz in which DMRG is augmented with disentanglers to encode area-law-like entanglement entropy (entanglement entropy supported in the new ansatz scales as l for an l × l system). In the new method, the O(D 3) low computational cost of DMRG is kept (with an overhead of O(d 4) and d the dimension of the physical degrees of freedom). We perform benchmark calculations with this approach on the two-dimensional transverse Ising and Heisenberg models. This new ansatz extends the power of DMRG in the study of two-dimensional quantum systems.

Impact of organic amine cations on photoluminescence and magnetic properties in Dion-Jacobson hybrid manganese halide perovskites

A strenuous effort has been made to design multifunctional lead-free organic–inorganic hybrid (OIH) halide compounds, which are envisioned as next generation solar cell materials. However, it is challenging to design OIH halides that can exhibit both long-range magnetic ordering and high photoluminescence quantum yield (PLQY) since the dimensionality of the compounds has a contrasting effect on them. In this article, we have shown an approach to enhance PLQY in two-dimensional (2D) Heisenberg antiferromagnets by increasing the alkylene chain length of [H3N–(CH2)m–NH3]MnCl4 (m = 2, 3, and 4) compounds. All these compounds exhibit 2D layers of corner-sharing MnCl6 octahedra where the organic cations are intercalated between them. These compounds exhibit long-range antiferromagnetic ordering confirmed by the DC magnetic susceptibility and heat capacity measurements. The Néel temperature (TN) decreases with increasing the length of spacer cations due to a decrease in interlayer exchange interactions; however, interestingly, the lifetime of photoexcited electrons and PLQY enhances from 24 to 56 µs and 8% to 23%, respectively. Furthermore, the temperature-dependent photoluminescence measurements provide insight into thermal quenching and exciton binding energy. We believe this study can help to design new OIH halides with long-range magnetic ordering and high PLQY.

Contrasting pseudocriticality in the classical two-dimensional Heisenberg and RP^{2} models: Zero-temperature phase transition versus finite-temperature crossover.

Tensor-network methods are used to perform a comparative study of the two-dimensional classical Heisenberg and RP^{2} models. We demonstrate that uniform matrix product states (MPSs) with explicit SO(3) symmetry can probe correlation lengths up to O(10^{3}) sites accurately, and we study the scaling of entanglement entropy and universal features of MPS entanglement spectra. For the Heisenberg model, we find no signs of a finite-temperature phase transition, supporting the scenario of asymptotic freedom. For the RP^{2} model we observe an abrupt onset of scaling behavior, consistent with hints of a finite-temperature phase transition reported in previous studies. A careful analysis of the softening of the correlation length divergence, the scaling of the entanglement entropy, and the MPS entanglement spectra shows that our results are inconsistent with true criticality, but are rather in agreement with the scenario of a crossover to a pseudocritical region which exhibits strong signatures of nematic quasi-long-range order at length scales below the true correlation length. Our results reveal a fundamental difference in scaling behavior between the Heisenberg and RP^{2} models: Whereas the emergence of scaling in the former shifts to zero temperature if the bond dimension is increased, it occurs at a finite bond-dimension independent crossover temperature in the latter.

Thermodynamic properties of the two-dimensional Heisenberg antiferromagnetic model on kagome lattice

Thermodynamic quantities as entropy and specific heat that are of evident interest, are obtained for the nearest-neighbor antiferromagnetic Heisenberg model on kagome lattice using the linear spin-wave approach. The results are obtained for different extensions of the model with single-ion anisotropy and out-of-plane Dzyaloshinskii–Moriya (DMI) interaction. We obtain the entropy as a function of the DMI interaction, single-ion anisotropy strength and anisotropy with aim to verify the effect of these corrections that occurs in real magnetic materials on entropy and specific heat. Furthermore, we obtain the specific heat as a function of temperature T and found a discontinuity in the range of large T indicating so, a phase transition in this range of temperature.

Provably efficient machine learning for quantum many-body problems.

Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground-state properties of gapped Hamiltonians after learning from other Hamiltonians in the same quantum phase of matter. By contrast, under a widely accepted conjecture, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, two-dimensional random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.