Heisenberg Interaction Research Articles

Classical and Quantum Magnetic Ground States on an Icosahedral Cluster

Recent discovery of various magnetism in Tsai-type quasicrystalline approximants, in whose alloys rare-earth ions located on icosahedral apices are coupled with each other via the Ruderman--Kittel--Kasuya--Yosida interaction, opens an avenue to find novel magnetism originating from the icosahedral symmetry. Here we investigate classical and quantum magnetic states on an icosahedral cluster within the Heisenberg interactions of all bonds. Simulated annealing and numerical diagonalization are performed to obtain the classical and quantum ground states. We obtain qualitative correspondence of classical and quantum phase diagrams. Our study gives a good starting point to understand the various magnetism in not only quasicrystalline approximants but also quasicrystals.

Universal Qudit Hamiltonians

A family of quantum Hamiltonians is said to be universal if any other finite-dimensional Hamiltonian can be approximately encoded within the low-energy space of a Hamiltonian from that family. If the encoding is efficient, universal families of Hamiltonians can be used as universal analogue quantum simulators and universal quantum computers, and the problem of approximately determining the ground-state energy of a Hamiltonian from a universal family is QMA-complete. One natural way to categorise Hamiltonians into families is in terms of the interactions they are built from. Here we prove universality of some important classes of interactions on qudits (d-level systems):We completely characterise the k-qudit interactions which are universal, if augmented with arbitrary Hermitian 1-local terms.We find that, for all k geqslant 2 and all local dimensions d geqslant 2, almost all such interactions are universal aside from a simple stoquastic class.We prove universality of generalisations of the Heisenberg model that are ubiquitous in condensed-matter physics, even if free 1-local terms are not provided. We show that the SU(d) and SU(2) Heisenberg interactions are universal for all local dimensions d geqslant 2 (spin geqslant 1/2), implying that a quantum variant of the Max-d-Cut problem is QMA-complete. We also show that for d=3 all bilinear-biquadratic Heisenberg interactions are universal. One example is the general AKLT model.We prove universality of any interaction proportional to the projector onto a pure entangled state.

Faster Digital Quantum Simulation by Symmetry Protection

Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations generated by the symmetries of the system, one can induce destructive interference between the errors from different steps of the simulation, effectively giving faster quantum simulation by symmetry protection. We derive rigorous bounds on the error of a symmetry-protected simulation algorithm and identify conditions for optimal symmetry protection. In particular, when the symmetry transformations are chosen as powers of a unitary, the error of the algorithm is approximately projected to the so-called quantum Zeno subspaces. We prove a bound on this approximation error, exponentially improving a recent result of Burgarth, Facchi, Gramegna, and Pascazio. We apply the symmetry protection technique to the simulations of the XXZ Heisenberg interactions with local disorder and the Schwinger model in quantum field theory. For both systems, the technique can reduce the simulation error by several orders of magnitude over the unprotected simulation. Finally, we provide numerical evidence suggesting that the technique can also protect simulation against other types of coherent, temporally correlated errors, such as the $1/f$ noise commonly found in solid-state experiments.

Entanglement dynamics and fractional quantum state transport in the spin-[formula omitted] triangular plaquette

The dramatic growth of research areas within the province of quantum state transmission (QST) is rapidly accelerating. An important insight to understand the process of QST can be fulfilled by considering the dynamical behavior of its entanglement content. One well-established approach to continuously transfer quantum states is utilizing spin structures. Here, from the view of entanglement propagation, we disclose the signature of fractional QST possibilities. In the present work, we proposed a form of spin-12 triangular plaquette whose Hamiltonian entails Heisenberg interaction on the legs and Dzyaloshinskii–Moriya type of coupling over the rungs. The feature of such a system is that the time instants of QST emerge in a discrete fashion, thereby the values of exchange interactions associated with these moments behave fractionally. Importantly, it is found that for special values of magnetic interaction, QST has singularity i.e., the entanglement propagation is forbidden for such values. In addition, the finite-size nature of this system makes it possible for us to read the nexus between time crystallinity and symmetry breaking. The development of our knowledge about time crystalline symmetry and its breaking helps us to understand the defined concept and fundamental physics of this phenomenon.

Van Hove singularity in the magnon spectrum of the antiferromagnetic quantum honeycomb lattice

In quantum magnets, magnetic moments fluctuate heavily and are strongly entangled with each other, a fundamental distinction from classical magnetism. Here, with inelastic neutron scattering measurements, we probe the spin correlations of the honeycomb lattice quantum magnet YbCl3. A linear spin wave theory with a single Heisenberg interaction on the honeycomb lattice, including both transverse and longitudinal channels of the neutron response, reproduces all of the key features in the spectrum. In particular, we identify a Van Hove singularity, a clearly observable sharp feature within a continuum response. The demonstration of such a Van Hove singularity in a two-magnon continuum is important as a confirmation of broadly held notions of continua in quantum magnetism and additionally because analogous features in two-spinon continua could be used to distinguish quantum spin liquids from merely disordered systems. These results establish YbCl3 as a benchmark material for quantum magnetism on the honeycomb lattice.

Kitaev interactions in the Co honeycomb antiferromagnets Na3Co2SbO6 and Na2Co2TeO6

${\mathrm{Co}}^{2+}$ ions in an octahedral crystal field stabilize a ${j}_{\mathrm{eff}}=1/2$ ground state with an orbital degree of freedom and have been recently put forward for realizing Kitaev interactions, a prediction we have tested by investigating spin dynamics in two cobalt honeycomb lattice compounds, ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}$ and ${\mathrm{Na}}_{3}{\mathrm{Co}}_{2}{\mathrm{SbO}}_{6}$, using inelastic neutron scattering. We used linear spin wave theory to show that the magnetic spectra can be reproduced with a spin Hamiltonian including a dominant Kitaev nearest-neighbor interaction, weaker Heisenberg interactions up to the third neighbor, and bond-dependent off-diagonal exchange interactions. Beyond the Kitaev interaction that alone would induce a quantum spin liquid state, the presence of these additional couplings is responsible for the zigzag-type long-range magnetic ordering observed at low temperature in both compounds. These results provide evidence for the realization of Kitaev-type coupling in cobalt-based materials, despite hosting a weaker spin-orbit coupling than their $4d$ and $5d$ counterparts.

Thermal Hall effect from a two-dimensional Schwinger boson gas with Rashba spin-orbit interaction: Application to ferromagnets with in-plane Dzyaloshinskii-Moriya interaction

Recently, uncovering the sources of thermal Hall effect in insulators has become an important issue. In the case of ferromagnetic insulators, it is well known that Dzyaloshinskii-Moriya (DM) interaction can induce magnon thermal Hall effect. Specifically, the DM vector parallel to the magnetization direction induces complex magnon hopping amplitudes, so that magnons act as if they feel Lorentz force. However, the DM vector which is orthogonal to the magnetization direction has hitherto been neglected as a possible source of magnon thermal Hall effect. This is because they play no role in the linear spin wave theory, an often invoked approximation when computing the magnon thermal Hall effect. Here, we challenge this expectation by presenting the self-consistent Schwinger-boson mean field study of two-dimensional magnets with ferromagnetic Heisenberg interaction and in-plane DM interaction. We find that the relevant Schwinger-boson mean field Hamiltonian takes the form of two-dimensional electron gas with Rashba spin-orbit interaction, which is known to show anomalous Hall effect, spin Hall effect, and Rashba-Edelstein effect, whose thermal counterparts also appear in our system. Importantly, the thermal Hall effect can be induced when out-of-plane magnetic field is applied, and persists even when the magnetic field is large, so that the spins are significantly polarized, and the linear spin wave theory is expected to be a reasonable approximation. Since the linear spin wave theory predicts vanishing thermal Hall effect, our result implies that linear spin wave is not a sufficient approximation, and that magnon-magnon interaction must be taken into account to predict the correct thermal Hall conductivity.

Phases and quantum phase transitions in an anisotropic ferromagnetic Kitaev-Heisenberg- Γ magnet

We study the spin-$1/2$ ferromagnetic Heisenberg-Kitaev-$\Gamma$ model in the anisotropic (Toric code) limit to reveal the nature of the quantum phase transition between the gapped $Z_2$ quantum spin liquid and a spin ordered phase (driven by Heisenberg interactions) as well as a trivial paramagnet (driven by pseudo-dipolar interactions, $\Gamma$). The transitions are obtained by a simultaneous condensation of the Ising electric and magnetic charges-- the fractionalized excitations of the $Z_2$ quantum spin liquid. Both these transitions can be continuous and are examples of deconfined quantum critical points. Crucial to our calculations are the symmetry implementations on the soft electric and magnetic modes that become critical. In particular, we find strong constraints on the structure of the critical theory arising from time reversal and lattice translation symmetries with the latter acting as an anyon permutation symmetry that endows the critical theory with a manifestly self-dual structure. We find that the transition between the quantum spin liquid and the spin-ordered phase belongs to a self-dual modified Abelian Higgs field theory while that between the spin liquid and the trivial paramagnet belongs to a self-dual $Z_2$ gauge theory. We also study the effect of an external Zeeman field to show an interesting similarity between the polarised paramagnet obtained due to the Zeeman field and the trivial paramagnet driven the pseudo-dipolar interactions. Interestingly, both the spin liquid and the spin ordered phases have easily identifiable counterparts in the isotropic limit and the present calculations may shed insights into the corresponding transitions in the material relevant isotropic limit.

Competing interactions and spin-vector chirality in spin chains

Studies of competing orders in 1D magnetic chains have attracted considerable attention in recent years, as the presence of long-range Heisenberg interactions is found to allow interesting quantum phase transitions. We investigate here the role of spin-orbit effects by considering spin-1/2 chains in the presence of both collinear and non-collinear long-range interactions. By employing exact diagonalization and density matrix renormalization group calculations we investigate the rich phase diagram of this system. We find transitions from collinear to transverse magnetic correlated order as the strength of the non-collinear coupling increases, accompanied by a jump in the vector spin chirality order parameter of the system. This shows that tuning long-range interactions allows control of the onset of sizable vector spin chirality in a system, which may be used to transmit information down the chain. We investigate the characteristic structure of the distinct phases and explore their possible physical implementation in different materials systems.

Topological phase transition to Abelian anyon phases due to off-diagonal exchange interaction in the Kitaev spin liquid state

We investigate how the Kitaev spin liquid state described by Majorana fermions coupled with $Z_2$ gauge fields is affected by non-Kitaev interactions which exist in real candidate materials of the Kitaev magnet. It is found that the off-diagonal exchange interaction referred to as the $\Gamma'$ term dramatically changes the Majorana band structure in the case of the antiferromagnetic Kitaev interaction, and gives rise to a topological phase transition from a non-Abelian topological phase with the Chern number equal to $\pm 1$ to an Abelian phase with the Chern number equal to $\pm 2$, in which the $Z_{2}$ vortices behave as Abelian anyons. On the other hand, other non-Kitaev interactions such as the Heisenberg interaction and the $\Gamma$ term, only affect the bandwidth of the Majorana band as long as the spin liquid state is not destabilized.

مطالعۀ ترابرد درهمتنیدگی گرمایی از طریق دو کیوبیت با برهمکنش هایزنبرگ در مدل جینز کامینگز

In this paper, we study a system consisting of two two-level atoms under XXX and XYZ Heisenberg interaction coupled with optical cavity. Calculating Hamiltonian of two-qubit Heisenberg interaction in the presence of electromagnetic field in Jaynes-Cummings model, we obtain the density matrix of the system by Gibbs equation in the thermal equilibrium. Assuming an arbitrary pure state as input state in the quantum channel, we obtain the output state for the system under the thermal equilibrium. The result of our study shows, as the temperature increases as the entanglement decreases until it reaches to zero and the fidelity decreases until it reaches to a steady amount. Also, we have found that the assumed model is a suitable system for transmitting quantum information with high efficiency..

Proximate Kitaev system for an intermediate magnetic phase in in-plane magnetic fields

Motivated by the magnetic phase transition of a proximate Kitaev system $\alpha$-RuCl$_3$ in the presence of a magnetic field, we study the simplest but essential quantum spin model with the ferromagnetic nearest neighboring (NN) Kitaev interaction and additional antiferromagnetic third NN Heisenberg interaction. Employing both exact diagonalization and density matrix renormalization group methods, we demonstrate that the model shows the magnetic phase transition from the zigzag order phase to the spin polarized phase through an intermediate phase in both cases when an in-plane magnetic field is applied perpendicular to the NN bond direction and when an out-of-plane field is applied, in good agreement with experimental observations. Furthermore, we verify that additional symmetric off-diagonal $\Gamma$ interaction and ferromagnetic Heisenberg interaction between NN spins can both suppress the intermediate phase with the in-plane field. Our result gives important clues on determining relevant interactions in the field-induced magnetic phase transition of proximate Kiteav systems.

Thermal entanglement in a spin-1/2 Ising–Heisenberg butterfly-shaped chain with impurities**Project supported by the National Natural Science Foundation of China (Grant No. 12074101), the Science Fund for the New Century Excellent Talents in University of the Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20134208110001).

We investigate the effect of impurities on the thermal entanglement in a spin-1/2 Ising–Heisenberg butterfly-shaped chain, where four interstitial Heisenberg spins are localized on the vertices of a rectangular plaquette in a unit block. By using the transfer-matrix approach, we numerically calculate the partition function and the reduced density matrix of this model. The bipartite thermal entanglement between different Heisenberg spin pairs is quantified by the concurrence. We also discuss the fluctuations caused by the impurities through the uniform distribution and the Gaussian distribution. Considering the effects of the external magnetic field, temperature, Heisenberg and Ising interactions as well as the parameter of anisotropy on the thermal entanglement, our results show that comparing with the case of the clean model, in both the two-impurity model and the impurity fluctuation model the entanglement is more robust within a certain range of anisotropic parameters and the region of the magnetic field where the entanglement occurred is also larger.

Spin-1 Kitaev-Heisenberg model on a honeycomb lattice

We study the Kitaev-Heisenberg model with spin-1 local degree of freedom on a two-dimensional honeycomb lattice numerically by density matrix renormalization group method. By tuning the relative value of the Kitaev and Heisenberg exchange couplings, we obtain the whole phase diagram with two spin liquid phases and four symmetry broken phases. We identify that the spin liquid phases are gapless by calculating the central charge at the pure Kitaev points without Heisenberg interaction. Comparing to its spin-1/2 counterpart, the position and number of gapless modes of the spin-1 case are quite different. Due to the approximate $Z_2$ local conservations, the expectation value of Wilson loop operator measuring the flux of each plaquette stays near to 1, and the static spin-spin correlations remain short-range in the entire spin liquid phases.

Kitaev quasiparticles in a proximate spin liquid: A many-body localization perspective

We study the stability of Kitaev quasiparticles in the presence of a perturbing Heisenberg interaction as a Fock space localization phenomenon. We identify parameter regimes where Kitaev states are localized, fractal or delocalized in the Fock space of exact eigenstates, with the first two implying quasiparticle stability. Finite temperature calculations show that a vison gap, and a nonzero plaquette Wilson loop at low temperatures, both characteristic of the deconfined Kitaev spin liquid phase, persist far into the neighboring phase that has a concomitant stripy spin-density wave (SDW) order. The key experimental implication for Kitaev materials is that below a characteristic energy scale, unrelated to the SDW ordering, Kitaev quasiparticles are stable.

Integrability and dark states in an anisotropic central spin model

Central spin models describe a variety of quantum systems in which a spin-1/2 qubit interacts with a bath of surrounding spins, as realized in quantum dots and defect centers in diamond. We show that the fully anisotropic central spin Hamiltonian with (XX) Heisenberg interactions is integrable. Building on the class of integrable Richardson-Gaudin models, we derive an extensive set of conserved quantities and obtain the exact eigenstates using the Bethe ansatz. These states divide into two exponentially large classes: bright states, where the qubit is entangled with the bath, and dark states, where it is not. We discuss how dark states limit qubit-assisted spin bath polarization and provide a robust long-lived quantum memory for qubit states.

Featureless quantum paramagnet with frustrated criticality and competing spiral magnetism on spin-1 honeycomb lattice magnet

We study the spin-1 honeycomb lattice magnets with frustrated exchange interactions. The proposed microscopic spin model contains first and second neighbor Heisenberg interactions as well as the single-ion anisotropy. We establish a rich phase diagram that includes a featureless quantum paramagnet and various spin spiral states induced by the mechanism of order by quantum disorder. Although the quantum paramagnet is dubbed featureless, it is shown that, the magnetic excitations develop a contour degeneracy in the reciprocal space at the band minima. These contour degenerate excitations are responsible for the frustrated criticality from the quantum paramagnet to the ordered phases. This work illustrates the effects of magnetic frustration on both magnetic orderings and the magnetic excitations. We discuss the experimental relevance to various Ni-based honeycomb lattice magnets.

Study of quantum state transmission across a spin chain and two-leg ladder

In this work we investigate the influence of three-spin interaction (TSI) on quantum state transmission (QST) at T = 0K and in the absence of an external field in a lightly modified 1D spin-1/2 chain and a slightly modified spin-1/2 two-leg ladder with different lengths. To reach this goal, we study the time evolution of concurrence for our models. Our results show that the TSI in the presence of isotropic Heisenberg interaction (XX interaction) within a 1D chain promotes the occurrence of QST and enhances the frequency of such events, as well. Moreover, when only TSI is considered within a spin ladder, QST occurs faster and in comparison to the case where both interactions are present, the XX interaction has more contribution in the occurrence of QST.

Effective low-energy RKKY interaction in doped topological crystalline insulators

We study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities resided on the (001) plane of topological crystalline insulator (TCI) SnTe associated with four anisotropic Dirac cones protected by the mirror symmetry. The lattice Green's functions governing the correlation of both the sublattices and spins are deduced by developing a two-band effective model. We explore the RKKY Heisenberg interaction of the system established by the interference between four Dirac cones. Our key finding is that, independent of the position of magnetic impurities on the same sublattices or different ones, multiple wave vectors with different orders describe the RKKY coupling physics in TCIs. Further, both the undoped and doped spin susceptibility give rise to the same decay rates like graphene. Magnetic impurities on the same and different sublattices propose the ferromagnetic and antiferromagnetic base phase of the undoped system, respectively. Here we demonstrate that RKKY exchange in TCIs, undergoes a ferromagnetic-to-antiferromagnetic transition and vice versa in response to switching on/off the electron and hole doping. Analytic expressions of doped TCIs are obtained to draw the magnetic phase diagram of the distance between two magnetic impurities and the doping concentration, clarifying the contributions of short and long distances as well as low and high concentrations to the RKKY coupling. Our results may tailor the magnetic features of TCIs for further research and application.

Magnetic field induced topological nodal-lines in triplet excitations of frustrated antiferromagnet CaV4O9

Magnetic field induced multiple non-Dirac nodal-lines are found to emerge in the triplet dispersion bands of a frustrated spin-1/2 antiferromagnetic model on the CaVO lattice. Plaquette and bond operator formalisms have been employed to obtain the triplet plaquette and bond excitations for two different parameter regimes in the presence of nearest and next-nearest-neighbor Heisenberg interactions based on the plaquette-resonating-valence-bond and dimerized ground states, respectively. In the absence of magnetic field a pair of six-fold degenerate nodal-loops with distinct topological feature is noted in the plaquette excitations. They are found to split into three pairs of two-fold degenerate nodal-loops in the presence of magnetic field. In the other parameter regime, system hosts two-fold degenerate multiple nodal-lines with a variety of shapes in the triplon dispersion bands in the presence of magnetic field. Ground state energy and spin gap have been determined additionally for the two regimes. Those nodal-lines are expected to be detectable in neutron scattering experiment on the frustrated antiferromagnet, CaV$_4$O$_9$.