Quantum Heisenberg Research Articles

Emergence of quantum spin frustration in spin-1/2 Ising-Heisenberg model on a decorated honeycomb lattice.

We study the spin-1/2 Ising-XXZ model on a decorated honeycomb lattice composed of five spins per unit cell, one Ising spin, and four Heisenberg spins. This model involving the Heisenberg exchange interaction is one of the few models that can be exactly solvable through the generalized star-triangle transformation. The significance of this model is its close relationship to the fully decorated quantum Heisenberg honeycomb lattice since 4/5 of the particles are Heisenberg spins. We investigate the phase diagram at zero temperature and identify a relevant quantum spin frustrated phase resulting from the contribution of quantum Heisenberg exchange interaction. We obtain an exact residual entropy for the quantum spin frustrated phase, which coincides with the residual entropy of the antiferromagnetic spin-1/2 Ising model on a triangular lattice. We also thoroughly explore its thermodynamic properties, focusing mainly on the frustrated region such as entropy, specific heat, spontaneous magnetization, and critical temperature under several conditions.

Far-from-equilibrium universality in the two-dimensional Heisenberg model

We characterize the universal far-from-equilibrium dynamics of the two-dimensional quantum Heisenberg magnet isolated from its environment. For a broad range of initial conditions, we find a long-lived universal prethermal regime characterized by self-similar behavior of spin-spin correlations. We analytically derive the spatial-temporal scaling exponents and find excellent agreement with numerics using phase space methods. The scaling exponents are insensitive to the choice of initial conditions, which include coherent and incoherent spin states with values of total magnetization and energy in a wide range. Compared to previously studied self-similar dynamics in nonequilibrium O(n) field theories and Bose gases, we find qualitatively distinct scaling behavior originating from the presence of spin modes that remain gapless at long times and are protected by the global SU(2) symmetry. Our predictions, which suggest a distinct nonequilibrium universality class from Bose gases and O(n) theories, are readily testable in ultracold atoms simulators of Heisenberg magnets.

Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations

We develop a nonequilibrium increment method in quantum Monte Carlo simulations to obtain the Rényi entanglement entropy of various quantum many-body systems with high efficiency and precision. To demonstrate its power, we show the results on a few important yet difficult (2 + 1)d quantum lattice models, ranging from the Heisenberg quantum antiferromagnet with spontaneous symmetry breaking, the quantum critical point with O(3) conformal field theory (CFT) to the toric code {{mathbb{Z}}}_{2} topological ordered state and the Kagome {{mathbb{Z}}}_{2} quantum spin liquid model with frustration and multi-spin interactions. In all these cases, our method either reveals the precise CFT data from the logarithmic correction or extracts the quantum dimension in topological order, from the dominant area law in finite-size scaling, with very large system sizes, controlled errorbars, and minimal computational costs. Our method, therefore, establishes a controlled and practical computation paradigm to obtain the difficult yet important universal properties in highly entangled quantum matter.

Thermal Ising Transition in the Spin-1/2 J_{1}-J_{2} Heisenberg Model.

Using an SU(2) invariant finite-temperature tensor network algorithm, we provide strong numerical evidence in favor of an Ising transition in the collinear phase of the spin-1/2 J_{1}-J_{2} Heisenberg model on the square lattice. In units of J_{2}, the critical temperature reaches a maximal value of T_{c}/J_{2}≃0.18 around J_{2}/J_{1}≃1.0. It is strongly suppressed upon approaching the zero-temperature boundary of the collinear phase J_{2}/J_{1}≃0.6, and it vanishes as 1/log(J_{2}/J_{1}) in the large J_{2}/J_{1} limit, as predicted by Chandra etal., [Phys. Rev. Lett. 64, 88 (1990)PRLTAO0031-900710.1103/PhysRevLett.64.88]. Enforcing the SU(2) symmetry is crucial to avoid the artifact of finite-temperature SU(2) symmetry breaking of U(1) algorithms, opening new perspectives in the investigation of the thermal properties of quantum Heisenberg antiferromagnets.

Quantum Heisenberg model on a sawtooth-chain lattice: rotation-invariant Green’s function method

We apply the rotation-invariant Green's function method (RGM) to study the spin $S=1/2$ Heisenberg model on a one-dimensional sawtooth lattice, which has two nonequivalent sites in the unit cell. We check the RGM predictions for observable quantities by comparison with the exact-diagonalization and finite-temperature-Lanczos calculations. We discuss the thermodynamic and dynamic properties of this model in relation to the mineral atacamite Cu$_2$Cl(OH)$_3$ complementing the RGM outcomes by results of other approaches.

The Role of Magnetic Dipole—Dipole Coupling in Quantum Single-Molecule Toroics

For single-molecule toroics (SMTs) based on noncollinear Ising spins, intramolecular magnetic dipole–dipole coupling favours a head-to-tail vortex arrangement of the semi-classical magnetic moments associated with a toroidal ground state. However, to what extent does this effect survive beyond the semi-classical Ising limit? Here, we theoretically investigate the role of dipolar interactions in stabilising ground-state toroidal moments in quantum Heisenberg rings with and without on-site magnetic anisotropy. For the prototypical triangular SMT with strong on-site magnetic anisotropy, we illustrate that, together with noncollinear exchange, intramolecular magnetic dipole–dipole coupling serves to preserve ground-state toroidicity. In addition, we investigate the effect on quantum tunnelling of the toroidal moment in Kramers and non-Kramers systems. In the weak anisotropy limit, we find that, within some critical ion–ion distances, intramolecular magnetic dipole–dipole interactions, diagonalised over the entire Hilbert space of the quantum system, recover ground-state toroidicity in ferromagnetic and antiferromagnetic odd-membered rings with up to seven sites, and are further stabilised by Dzyaloshinskii–Moriya coupling.

Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion.

The Kardar-Parisi-Zhang (KPZ) universality class describes the coarse-grained behavior of a wealth of classical stochastic models. Surprisingly, KPZ universality was recently conjectured to also describe spin transport in the one-dimensional quantum Heisenberg model. We tested this conjecture by experimentally probing transport in a cold-atom quantum simulator via the relaxation of domain walls in spin chains of up to 50 spins. We found that domain-wall relaxation is indeed governed by the KPZ dynamical exponent z = 3/2 and that the occurrence of KPZ scaling requires both integrability and a nonabelian SU(2) symmetry. Finally, we leveraged the single-spin-sensitive detection enabled by the quantum gas microscope to measure an observable based on spin-transport statistics. Our results yield a clear signature of the nonlinearity that is a hallmark of KPZ universality.

Randomness and frustration in a S=12 square-lattice Heisenberg antiferromagnet

Chemical substitution in Sr${}_{2}$CuTe${}_{1\ensuremath{-}x}$W${}_{x}$O${}_{6}$ introduces a combination of randomness and frustration in the square-lattice Heisenberg quantum antiferromagnet. Neutron scattering is used to probe the ground and excited states of the mixed compounds in this series. It is demonstrated that the random network of interactions is only mildly frustrated. A semiclassical mean-field treatment of the random-bond model, which produces a ground state of small and weakly interlinked ordered patches hosting spin-wave-like excitations, agrees well with the experimental observations.

Quantitative functional renormalization for three-dimensional quantum Heisenberg models

We employ a recently developed variant of the functional renormalization group method for spin systems, the so-called pseudo Majorana functional renormalization group, to investigate three-dimensional spin-1/2 Heisenberg models at finite temperatures. We study unfrustrated and frustrated Heisenberg systems on the simple cubic and pyrochlore lattices. Comparing our results with other quantum many-body techniques, we demonstrate a high quantitative accuracy of our method. Particularly, for the unfrustrated simple cubic lattice antiferromagnet ordering temperatures obtained from finite-size scaling of one-loop data deviate from error controlled quantum Monte Carlo results by \sim5\%∼5% and we confirm consistency of our data with established critical exponents \nuν and \etaη of the three-dimensional Heisenberg universality class. As the PMFRG yields results in good agreement with QMC, but remains applicable when the system is frustrated, we next treat the pyrochlore Heisenberg antiferromagnet as a paradigmatic magnetically disordered system and find nearly perfect agreement of our two-loop static homogeneous susceptibility with other methods. We further investigate the broadening of pinch points in the spin structure factor as a result of quantum and thermal fluctuations and confirm a finite width in the extrapolated limit T\rightarrow0T→0. While extensions towards higher loop orders \ellℓ seem to systematically improve our approach for magnetically disordered systems we also discuss subtleties when increasing \ellℓ in the presence of magnetic order. Overall, the pseudo Majorana functional renormalization group is established as a powerful many-body technique in quantum magnetism with a wealth of possible future applications.

Quantum black hole–white hole entangled states

We investigate the quantum deformation of the Wheeler–DeWitt equation of a Schwarzchild black hole. Specifically, the quantum deformed black hole is a quantized model constructed from the quantum Heisenberg–Weyl Uq(h4) group. We show that the event horizon area and the mass are quantized, degenerate, and bounded. The degeneracy of states indicates entangled quantum black hole/white hole states. Accordingly, quantum deformation provides a new framework to examine Einstein–Rosen wormhole solutions. Besides, we obtain the mass, the temperature, and the entropy of the q-deformed quantum Schwarzschild black hole. We find an upper bound on the mass of a black hole/white hole pair. Also, at the quantum deformation level, the entropy of the black hole contains three parts: the usual Bekenstein–Hawking entropy, the logarithmic term, and a Cube of usual black hole entropy.

Quantum Turbulence and Planckian Dissipation

The notion of the Planckian dissipation is extended to the system of the Caroli–de Gennes–Matricon discrete energy levels in the vortex core of superconductors and fermionic superfluids. In this extension, the Planck dissipation takes place when the relaxation time τ is comparable with the quantum Heisenberg time {{t}_{H}} = hbar {text{/}}Delta E, where Delta E is the interlevel distance in the vortex core (the minigap). This type of Planck dissipation has two important physical consequences. First, it determines the regime, when the effect of the axial anomaly becomes important. The anomalous spectral flow of the energy levels along the chiral branch of the Caroli–de Gennes–Matricon states becomes important in the super-Planckian region, i.e., when tau < hbar {text{/}}Delta E. Second, the Planck dissipation separates the laminar flow of the superfluid liquid at tau < hbar {text{/}}Delta E and the vortex turbulence regime at tau > hbar {text{/}}Delta E.

Critical spin dynamics of Heisenberg ferromagnets revisited

We calculate the dynamic structure factor $S (\boldsymbol{k},\omega)$ in the paramagnetic regime of quantum Heisenberg ferromagnets for temperatures $T$ close to the critical temperature $T_c$ using our recently developed functional renormalization group approach to quantum spin systems. In $d=3$ dimensions we find that for small momenta $\boldsymbol{k}$ and frequencies $\omega$ the dynamic structure factor assumes the scaling form $S(\boldsymbol{k},\omega) = (\tau T G (\boldsymbol{k})/\pi)\Phi (k\xi, \omega\tau)$, where $ G (\boldsymbol{k})$ is the static spin-spin correlation function, $\xi$ is the correlation length, and the characteristic time-scale $\tau$ is proportional to $\xi^{5/2}$. We explicitly calculate the dynamic scaling function $\Phi (x,y)$ and find satisfactory agreement with neutron scattering experiments probing the critical spin dynamics in EuO and EuS. Precisely at the critical point where $\xi = \infty$ our result for the dynamic structure factor can be written as $S (\boldsymbol{k},\omega) = (\pi\omega_k)^{-1} T_c G (\boldsymbol{k}) \Psi_c (\omega/\omega_k)$, where $\omega_k \propto k^{5/2}$. We find that $\Psi_c(\nu)$ vanishes as $\nu^{-13/5}$ for large $\nu$, and as $\nu^{3/5}$ for small $\nu$. While the large-frequency behavior of $\Psi_c (\nu)$ is consistent with calculations based on mode-coupling theory and with perturbative renormalization group calculations to second order in $\epsilon = 6-d$, our result for small frequencies disagrees with previous calculations. We argue that up until now neither experiments nor numerical simulations are sufficiently accurate to determine the low-frequency behavior of $\Psi_c (\nu)$. We also calculate the low-temperature behavior of $S ( \boldsymbol{k},\omega)$ in one- and two dimensional ferromagnets and find that it satisfies dynamic scaling with exponent $z=2$ and exhibits a pseudogap for small frequencies.

Categorification of the elliptic Hall algebra

We show that the central charge k reduction of the universal central extension of the elliptic Hall algebra is isomorphic to the trace, or zeroth Hochschild homology, of the quantum Heisenberg category of central charge k . As an application, we construct large families of representations of the universal extension of the elliptic Hall algebra.

Fast high-fidelity geometric quantum control with quantum brachistochrones

We experimentally demonstrate fast and high-fidelity geometric control of a quantum system with the brachistochrone method on hybrid spin registers in diamond. Based on the time-optimal universal geometric control, single geometric gates with fidelities over $99.2%$ on the spin state of the nitrogen-vacancy center are realized with average durations shortened by $21.5%$ compared with the conventional geometric method. The fidelity of the fast geometric two-qubit gate exceeds $96.5%$ on the hybrid spin registers. With the fast and high-fidelity universal set of geometric gates available, we implement a quantum entanglement-enhanced phase estimation algorithm and demonstrate the Heisenberg quantum limit of phase estimation at room temperature. Hence our results show that high-fidelity quantum control based on a fast geometric route will be a versatile tool for broad applications of quantum information processing in practice.

When can localized spins interacting with conduction electrons in ferro- or antiferromagnets be described classically via the Landau-Lifshitz equation: Transition from quantum many-body entangled to quantum-classical nonequilibrium states

Experiments in spintronics and magnonics operate with macroscopically large number of localized spins within ferromagnetic (F) or antiferromagnetic (AF) materials, so that their nonequilibrium dynamics is standardly described by the Landau-Lifshitz (LL) equation treating localized spins as classical vectors of fixed length. However, spin is a genuine quantum degree of freedom, and even though quantum effects become progressively less important for spin value $S>1$, they exist for all $S < \infty$. While this has motivated exploration of limitations/breakdown of the LL equation, by using examples of F insulators, analogous comparison of fully quantum many-body vs. quantum (for electrons)-classical (for localized spins) dynamics in systems where nonequilibrium conduction electrons are present is lacking. Here we employ quantum Heisenberg F or AF chains of $N=4$ sites, whose localized spins interact with conduction electrons via $sd$ exchange interaction, to perform such comparison by starting from unentangled pure (at zero temperature) or mixed (at finite temperature) quantum state of localized spins as the initial condition. This reveals that quantum-classical dynamics can faithfully reproduce fully quantum dynamics in the F metallic case, but only when spin $S$, Heisenberg exchange between localized spins and $sd$ exchange are sufficiently small. Increasing any of these three parameters can lead to substantial deviations, which are explained by the dynamical buildup of entanglement between localized spins and/or between them and electrons. In the AF metallic case, substantial deviations appear even at early times, despite starting from unentangled N\'{e}el state, which therefore poses a challenge on how to rigorously justify wide usage of the LL equation in phenomenological modeling of antiferromagnetic spintronics experiments.

Time-Dependent Variational Principle for Open Quantum Systems with Artificial Neural Networks.

We develop a variational approach to simulating the dynamics of open quantum many-body systems using deep autoregressive neural networks. The parameters of a compressed representation of a mixed quantum state are adapted dynamically according to the Lindblad master equation by employing a time-dependent variational principle. We illustrate our approach by solving the dissipative quantum Heisenberg model in one dimension for up to 40 spins and in two dimensions for a 4×4 system and by applying it to the simulation of confinement dynamics in the presence of dissipation.

Two-spin and multi-spin quantum entanglement in V12 polyoxovanadate molecular nanomagnet

The paper reports a computational study of the quantum entanglement in V12 cluster molecular magnet. The low-temperature properties of the system are modelled with anisotropic quantum Heisenberg model on a tetramer of spins S=1/2 in the external magnetic field. The two-spin entanglement is quantified using the concurrence, whereas the fidelity serves as a measure of four-spin entanglement. The analytic and numerical results are derived and discussed, emphasizing the importance of real-space and spin-space interaction anisotropy and the role of quantum level crossings in the entanglement description in V12.

Weak three-dimensional coupling of Heisenberg quantum spin chains in SrCuTe2O6

The magnetic Hamiltonian of the Heisenberg quantum antiferromagnet SrCuTe$_{2}$O$_{6}$ is studied by inelastic neutron scattering technique on powder and single crystalline samples above and below the magnetic transition temperatures at 8 K and 2 K. The high temperature spectra reveal a characteristic diffuse scattering corresponding to a multi-spinon continuum confirming the dominant quantum spin-chain behavior due to the third neighbour interaction J$_{intra}$ = 4.22 meV (49 K). The low temperature spectra exhibits sharper excitations at energies below 1.25 meV which can be explained by considering a combination of weak antiferromagnetic first nearest neighbour interchain coupling J$_1$ = 0.17 meV (1.9 K) and even weaker ferromagnetic second nearest neighbour J$_2$ = -0.037 meV (-0.4 K) or a weak ferromagnetic J$_2$ = -0.11 meV (-1.3 K) and antiferromagnetic J$_6$ = 0.16 meV (1.85 K) giving rise to the long-range magnetic order and spin-wave excitations at low energies. These results suggest that SrCuTe$_{2}$O$_{6}$ is a highly one-dimensional Heisenberg system with three mutually perpendicular spin-chains coupled by a weak ferromagnetic J$_2$ in addition to the antiferromagnetic J$_1$ or J$_6$ presenting a contrasting scenario from the highly frustrated hyper-hyperkagome lattice (equally strong antiferromagnetic J$_1$ and J$_2$) found in the iso-structural PbCuTe$_{2}$O$_{6}$.

Noninterfering and simultaneous Stern-Gerlach and Heisenberg microscope experiments to measure the full electron coordinate in an entangled state

In two celebrated experiments of quantum mechanics, the Stern-Gerlach (SG) and Heisenberg microscope (HM) experiments, the electron spin ${s}_{z}$ and spatial $\mathbit{r}$ coordinates are measured separately. In this paper, the combined $\mathrm{SG}+\mathrm{HM}$ experiment is proposed to measure the full electron coordinate $\mathbit{x}={\mathbit{r},{s}_{z}}$. To this end, noninterfering and (virtually) simultaneous SG and HM experiments are proposed to apply to the individual fragments A and B of an entangled dissociating system $\mathrm{A}\text{\ensuremath{-}}\mathrm{B}$. The theoretical description of a spin-collapsed and partially spatially collapsed state of the $\mathrm{SG}+\mathrm{HM}$ experiment is given for the prototype ``perfectly'' entangled system, the dissociating ${\mathrm{H}}_{2}$ molecule.

Lee-Yang theory of criticality in interacting quantum many-body systems

Quantum phase transitions are a ubiquitous many-body phenomenon that occurs in a wide range of physical systems, including superconductors, quantum spin liquids, and topological materials. However, investigations of quantum critical systems also represent one of the most challenging problems in physics, since highly correlated many-body systems rarely allow for an analytic and tractable description. Here we present a Lee-Yang theory of quantum phase transitions including a method to determine quantum critical points which readily can be implemented within the tensor network formalism and even in realistic experimental setups. We apply our method to a quantum Ising chain and the anisotropic quantum Heisenberg model and show how the critical behavior can be predicted by calculating or measuring the high cumulants of properly defined operators. Our approach provides a powerful formalism to analyze quantum phase transitions using tensor networks, and it paves the way for systematic investigations of quantum criticality in two-dimensional systems.