Quantum Heisenberg Research Articles

Split-and-Merge in Stationary Random Stirring on Lattice Torus

We show that in any dimension dge 1, the cycle-length process of stationary random stirring (or, random interchange) on the lattice torus converges to the canonical Markovian split-and-merge process with the invariant (and reversible) measure given by the Poisson–Dirichlet law mathsf {PD(1)}, as the size of the system grows to infinity. In the case of transient dimensions, dge 3, the problem is motivated by attempts to understand the onset of long range order in quantum Heisenberg models via random loop representations of the latter.

Non-linear Dynamics of a Double-Well Bose–Einstein Condensate–Reservoirs System

We investigate the dynamics of a Bose–Einstein condensate (BEC) confined within a symmetric double-well trap out-coupled to reservoirs. Our model is based on the quantum Heisenberg–Langevin approach. Dissipation in the system is induced by the interaction of condensate bosons with the reservoir which determines the Markovian and non-Markovian operational dynamics. These distinct dynamics correspond directly to the choice of function used in the dissipation kernel of the quantum Langevin equation. The main focus of this work is to study non-Markovian dynamics of the system proliferated by the use of Ornstein–Uhlenbeck (OU) memory function. Comparison is made with the Markovian dynamics induced by the use of δ-memory-less function. We have calculated numerically the time evolution of population imbalance and tunneling current of the system and found dissipation destroys the regular pattern of the two-mode BEC phases. Comparison between dissipative models shows significant differences in their dynamics, particularly in the strongly interacting case.

Magnetocaloric Effect in Cu5-NIPA Molecular Magnet: A Theoretical Study.

We calculated the magnetocaloric properties of the molecular nanomagnet Cu5-NIPA, consisting of five spins arranged in two corner-sharing triangles (hourglass-like structure without magnetic frustration). The thermodynamics of the system in question was described using the quantum Heisenberg model solved within the field ensemble (canonical ensemble) using exact numerical diagonalization. The dependence of the magnetic entropy and magnetic specific heat on the temperature and the external magnetic field was investigated. The isothermal entropy change for a wide range of initial and final magnetic fields was discussed. Due to plateau-like behavior of the isothermal entropy change as a function of the temperature, a high degree of tunability of magnetocaloric effect with the initial and final magnetic field was demonstrated.

Quantum Spins and Random Loops on the Complete Graph

We present a systematic analysis of quantum Heisenberg-, xy- and interchange models on the complete graph. These models exhibit phase transitions accompanied by spontaneous symmetry breaking, which we study by calculating the generating function of expectations of powers of the averaged spin density. Various critical exponents are determined. Certain objects of the associated loop models are shown to have properties of Poisson–Dirichlet distributions.

Spin functional renormalization group for quantum Heisenberg ferromagnets: Magnetization and magnon damping in two dimensions

We use the spin functional renormalization group recently developed by two of us [J. Krieg and P. Kopietz, Phys. Rev. B $\bf{99}$, 060403(R) (2019)] to calculate the magnetization $M ( H , T )$ and the damping of magnons due to classical longitudinal fluctuations of quantum Heisenberg ferromagnets. In order to guarantee that for vanishing magnetic field $H \rightarrow 0$ the magnon spectrum is gapless when the spin rotational invariance is spontaneously broken, we use a Ward identity to express the magnon self-energy in terms of the magnetization. In two dimensions our approach correctly predicts the absence of long-range magnetic order for $H=0$ at finite temperature $T$. The magnon spectrum then exhibits a gap from which we obtain the transverse correlation length. We also calculate the wave-function renormalization factor of the magnons. As a mathematical by-product, we derive a recursive form of the generalized Wick theorem for spin operators in frequency space which facilitates the calculation of arbitrary time-ordered connected correlation functions of an isolated spin in a magnetic field.

Levi-Civita connections for a class of spectral triples

We give a new definition of Levi-Civita connection for a noncommutative pseudo-Riemannian metric on a noncommutative manifold given by a spectral triple. We prove the existence-uniqueness result for a class of modules of one forms over a large class of noncommutative manifolds, including the matrix geometry of the fuzzy 3-sphere, the quantum Heisenberg manifolds and Connes-Landi deformations of spectral triples on the Connes-Dubois Violette-Rieffel-deformation of a compact manifold equipped with a free toral action. It is interesting to note that in the example of the quantum Heisenberg manifold, the definition of metric compatibility given in the paper by Frolich et al failed to ensure the existence of a unique Levi-Civita connection. In the case of the matrix geometry, the Levi-Civita connection that we get coincides with the unique real torsion-less unitary connection obtained by Frolich et al.

Heat capacity of anisotropic Heisenberg antiferromagnet within the spin Hartree-Fock approach in quasi-1D regime

We study the anisotropic quantum Heisenberg antiferromagnet for spin-1/2 that interpolates smoothly between the one-dimensional (1D) and the two-dimensional (2D) limits. Using the spin Hartree-Fock approach we construct a quantitative theory of heat capacity in the quasi-1D regime with a finite coupling between spin chains. This theory reproduces closely the exact result of Bethe Ansatz in the 1D limit and does not produces any spurious phase transitions for any anisotropy in the quasi-1D regime at finite temperatures in agreement with the Mermin-Wagner theorem. We study the static spin-spin correlation function in order to analyse the interplay of lattice geometry and anisotropy in these systems. We compare the square and triangular lattice. For the latter we find that there is a quantum transition point at an intermediate anisotropy of $\sim0.6$. This quantum phase transition establishes that the quasi-1D regime extends upto a particular point in this geometry. For the square lattice the change from the 1D to 2D occurs smoothly as a function of anisotropy, i.e. it is of the crossover type. Comparing the newly developed theory to the available experimental data on the heat capacity of $\rm{Cs}_2\rm{CuBr}_4$ and $\rm{Cs}_2\rm{CuCl}_4$ we extract the microscopic constants of the exchange interaction that previously could only be measured using inelastic neutron scattering in high magnetic fields.

Breakdown of intermediate one-half magnetization plateau of spin-1/2 Ising-Heisenberg and Heisenberg branched chains at triple and Kosterlitz-Thouless critical points.

The spin-1/2 Ising-Heisenberg branched chain composed of regularly alternating Ising spins and Heisenberg dimers involving an additional side branching is rigorously solved in a magnetic field by the transfer-matrix approach. The ground-state phase diagram, the magnetization process and the concurrence measuring a degree of bipartite entanglement within the Heisenberg dimers are examined in detail. Three different ground states were found depending on a mutual interplay between the magnetic field and two different coupling constants: the modulated quantum antiferromagnetic phase, the quantum ferrimagnetic phase, and the classical ferromagnetic phase. Two former quantum ground states are manifested in zero-temperature magnetization curves as intermediate plateaus at zero and one-half of the saturation magnetization, whereas the one-half plateau disappears at a triple point induced by a strong-enough ferromagnetic Ising coupling. The ground-state phase diagram and zero-temperature magnetization curves of the analogous spin-1/2 Heisenberg branched chain were investigated using density-matrix renormalization group calculations. The latter fully quantum Heisenberg model involves, besides two gapful phases manifested as zero and one-half magnetization plateaus, gapless quantum spin-liquid phase. The intermediate one-half plateau of the spin-1/2 Heisenberg branched chain vanishes at Kosterlitz-Thouless quantum critical point between gapful and gapless quantum ground states unlike the triple point of the spin-1/2 Ising-Heisenberg branched chain.

Yang-Mills connections on quantum Heisenberg manifolds

We investigate critical points and minimizers of the Yang-Mills functional YM on quantum Heisenberg manifolds Dμνc, where the Yang-Mills functional is defined on the set of all compatible linear connections on finitely generated projective modules over Dμνc. A compatible linear connection which is both a critical point and minimizer of YM is called a Yang-Mills connection. In this paper, we investigate Yang-Mills connections with constant curvature. We are interested in Yang-Mills connections on the following classes of modules over Dμνc: (i) Abadie's module Ξ of trace 2μ and its submodules; (ii) modules Ξ′ of trace 2ν; (iii) tensor product modules of the form PEμνc⊗Ξ, where Eμνc is Morita equivalent to Dμνc and P is a projection in Eμνc. We present a characterization of critical points and minimizers of YM, and provide a class of new Yang-Mills connections with constant curvature on Ξ over Dμνc via concrete examples. In particular, we show that every Yang-Mills connection ∇ on Ξ over Dμνc with constant curvature should have a certain form of the curvature such as Θ∇(X,Y)=Θ∇(X,Z)=0 and Θ∇(Y,Z)=πiμIdE. Also we show that these Yang-Mills connections with constant curvature do not provide global minima but only local minima. We do this by constructing a set of compatible connections that are not critical points but their values are smaller than those of Yang-Mills connections with constant curvature. Our other results include: (i) an example of a compatible linear connection with constant curvature on Dμνc such that the corresponding connection on an isomorphic projective module does not have constant curvature, and (ii) the construction of a compatible linear connection with constant curvature which neither attains its minimum nor is a critical point of YM on Dμνc. Consequently the critical points and minimizers of YM depend crucially on the geometric structure of Dμνc and of the projective modules over Dμνc. Furthermore, we construct the Grassmannian connection on the projective modules Ξ′ with trace 2ν over Dμνc and compute its corresponding curvature. Finally, we construct tensor product connections on PEμνc⊗Ξ whose coupling constant is 2ν and characterize the critical points of YM for this projective module.

Magnetocaloric properties of V6 molecular magnet

The paper presents a theoretical study of magnetocaloric properties of polyoxovanadate molecular magnet V6 containing 6 vanadium ions carrying quantum spins S=1/2. The characteristic property of such structure is the presence of two weakly interacting spin triangles with all-antiferromagnetic couplings. The properties of the system are described using the exact numerical diagonalization approach applied to the quantum Heisenberg model and utilizing a field ensemble formalism. The dependence of the magnetic entropy and magnetic specific heat on the temperature and external magnetic field is calculated and extensively discussed. The magnetocaloric properties are quantified by isothermal entropy change and entropy derivative over the magnetic field. An interesting behaviour of isothermal entropy change is found, with high degree of tunability of the magnetocaloric effect with the initial and final magnetic field values.

Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice

We consider a family of SU(2)-symmetric Projected Entangled Paired States (PEPS) on the square lattice, defining colored-Resonating Valence Bond (RVB) states, to describe the quantum disordered phase of the J_1-J_2J1−J2 frustrated Heisenberg model. For J_2/J_1\sim 0.55J2/J1∼0.55 we show the emergence of critical (algebraic) dimer-dimer correlations – typical of Rokhsar-Kivelson (RK) points of quantum dimer models on bipartite lattices – while, simultaneously, the spin-spin correlation length remains short. Our findings are consistent with a spin liquid or a weak Valence Bond Crystal in the neighborhood of an RK point.

Continuous-variable Quantum Phase Estimation based on Machine Learning

Making use of the general physical model of the Mach-Zehnder interferometer with photon loss which is a fundamental physical issue, we investigate the continuous-variable quantum phase estimation based on machine learning approach, and an efficient recursive Bayesian estimation algorithm for Gaussian states phase estimation has been proposed. With the proposed algorithm, the performance of the phase estimation may be improved distinguishably. For example, the physical limits (i.e., the standard quantum limit and Heisenberg limit) for the phase estimation precision may be reached in more efficient ways especially in the situation of the prior information being employed, the range for the estimated phase parameter can be extended from [0, π/2] to [0, 2π] compared with the conventional approach, and influences of the photon losses on the output parameter estimation precision may be suppressed dramatically in terms of saturating the lossy bound. In addition, the proposed algorithm can be extended to the time-variable or multi-parameter estimation framework.

Universal critical behavior in the ferromagnetic superconductor Eu(Fe0.75Ru0.25)2As2

The study of universal critical behavior is a crucial issue in a continuous phase transition, which groups various critical phenomena into universality classes for revealing microscopic electronic behaviors. The understanding of the nature of magnetism in Eu-based ferromagnetic superconductors is largely impeded by the infeasibility of performing inelastic neutron scattering measurements to deduce the microscopic magnetic behaviors and the effects on the superconductivity, due to the significant neutron absorption effect of natural $^{152}$Eu and unavailability of large single crystals. However, by systematically combining the neutron diffraction experiment, the first-principles calculations, and the quantum Monte Carlo simulations, we have obtained a perfectly consistent universal critical exponent value of $\beta=0.385(13)$ experimentally and theoretically for Eu(Fe$_{0.75}$Ru$_{0.25}$)$_{2}$As$_{2}$, from which the magnetism in the Eu-based ferromagnetic superconductors is identified as the universal class of a three-dimensional anisotropic quantum Heisenberg model with long-range magnetic exchange coupling. This study not only clarifies the nature of microscopic magnetic behaviors in the Eu-based ferromagnetic superconductors, but also opens a new avenue of systemic methodology for studying the universal critical behaviors associated with magnetic phase transitions in the area of magnetism and the spin fluctuations effects on the unconventional superconductivity.

Coupled oscillators in non-commutative phase space: Path integral approach

We present the path integral techniques in a non-commutative phase space and illustrate the calculation in the case of an exact problem of the coupled oscillator in two dimensions. The non-commutativity, with respect to Poisson (classical) and Heisenberg (quantum) brackets, in this phase space, is governed by two small constant parameters. They characterize the geometric deformation of this space. The path integral is formulated in a mixed representation due to the non-commutativity of the coordinates on one hand and those of the momentum on the other hand. Using a canonical linear transformation in this non-commutative phase space, we retrieve the commutative phase space properties by which the study becomes more suitable. The case of the non-commutative coupled harmonic oscillator in two dimensions is treated and the thermodynamics properties of the assembly of such oscillators are derived too.

Quantum reciprocity relations for fluctuations of position and momentum

We propose a trade-off between the Lipschitz constants of the position and momentum probability distributions for arbitrary quantum states. We refer to the trade-off as a quantum reciprocity relation. The Lipschitz constant of a function may be considered to quantify the extent of fluctuations of that function, and is, in general, independent of its spread. The spreads of the position and momentum distributions are used to obtain the celebrated Heisenberg quantum uncertainty relations. We find that the product of the Lipschitz constants of position and momentum probability distributions is bounded below by a number that is of the order of the inverse square of the Planck's constant.

Self-Trapping of Exciton-Polariton Condensates in GaAs Microcavities.

The self-trapping of exciton-polariton condensates is demonstrated and explained by the formation of a new polaronlike state. Above the polariton lasing threshold, local variation of the lattice temperature provides the mechanism for an attractive interaction between polaritons. Because of this attraction, the condensate collapses into a small bright spot. Its position and momentum variances approach the Heisenberg quantum limit. The self-trapping does not require either a resonant driving force or a presence of defects. The trapped state is stabilized by the phonon-assisted stimulated scattering of excitons into the polariton condensate. While the formation mechanism of the observed self-trapped state is similar to the Landau-Pekar polaron model, this state is populated by several thousands of quasiparticles, in a striking contrast to the conventional single-particle polaron state.

Population imbalance, macroscopic tunneling and intermodal entanglement of two-mode Bose–Einstein condensate under the influence of dissipation process

In this paper, we study the dissipative dynamics of a system which is composed of two atomic Bose–Einstein condensates (BECs) interacting through the Josephson-like coupling. To model a more realistic physical system, the inevitable dissipation effect is considered via the interaction between the system and its environment, in particular, a thermal reservoir. In this respect, after introducing a proper Hamiltonian for the model, we analytically solve the corresponding quantum Heisenberg–Langevin equations and then obtain explicit analytical expressions for population imbalance, macroscopic tunneling current and intermodal entanglement. Generally, the dynamics of the system is very sensitive to the chosen values of tunneling coupling strength, initial population as well as the characteristics of interaction between the system and its reservoirs. Also, the time evolution of the above-mentioned physical quantities shows oscillatory decaying behavior where the frequency of oscillations depends on the strength of tunneling interaction between the two subsystems. The oscillatory pattern of population imbalance and tunneling current is more regular in comparison with the intermodal entanglement. Although the system is always separable for low initial population, we show that it tends to an entangled state as its initial population is increased. In particular, the amount and the time interval of the entanglement can be effectively controlled via the dissipation parameter. Also, to get an insight into the effect of nonlinear interaction on the behavior of dynamical evolution of the considered system, we numerically investigate the population imbalance in the absence and presence of such interactions. A qualitative comparison shows that the previous theoretical works and numerical simulations confirm our obtained results.

Thermal tensor renormalization group simulations of square-lattice quantum spin models

In this work, we benchmark the well-controlled and numerically accurate exponential thermal tensor renormalization group (XTRG) in the simulation of interacting spin models in two dimensions. Finite temperature introduces a thermal correlation length, which justifies the analysis of finite system size for the sake of numerical efficiency. In this paper we focus on the square lattice Heisenberg antiferromagnet (SLH) and quantum Ising models (QIM) on open and cylindrical geometries up to width $W=10$. We explore various one-dimensional mapping paths in the matrix product operator (MPO) representation, whose performance is clearly shown to be geometry dependent. We benchmark against quantum Monte Carlo (QMC) data, yet also the series-expansion thermal tensor network results. Thermal properties including the internal energy, specific heat, and spin structure factors, etc., are computed with high precision, obtaining excellent agreement with QMC results. XTRG also allows us to reach remarkably low temperatures. For SLH we obtain at low temperature an energy per site $u_g^*\simeq -0.6694(4)$ and a spontaneous magnetization $m_S^*\simeq0.30(1)$, which is already consistent with the ground state properties. We extract an exponential divergence vs. $T$ of the structure factor $S(M)$, as well as the correlation length $\xi$, at the ordering wave vector $M=(\pi,\pi)$, which represents the renormalized classical behavior and can be observed over a narrow but appreciable temperature window, by analysing the finite-size data by XTRG simulations. For the QIM with a finite-temperature phase transition, we employ several thermal quantities, including the specific heat, Binder ratio, as well as the MPO entanglement to determine the critical temperature $T_c$.

Quantum linear Galois orders

We define a class of quantum linear Galois algebras which include the universal enveloping algebra the quantum Heisenberg Lie algebra and other quantum orthogonal Gelfand–Zetlin algebras of type A, the subalgebras of G-invariants of the quantum affine space, quantum torus for and of the quantum Weyl algebra for G = Sn. We show that all quantum linear Galois algebras satisfy the quantum Gelfand-Kirillov conjecture. Moreover, it is shown that the subalgebras of invariants of the quantum affine space and of quantum torus for the reflection groups and of the quantum Weyl algebra for symmetric groups are, in fact, Galois orders over an adequate commutative subalgebras and free as right (left) modules over these subalgebras. In the rank 1 cases the results hold for an arbitrary finite group of automorphisms when the field is

The Kahn degenerate frustration points and the Lieb-Mattis level order in heterometallic wheel molecules with competing interactions

Abstract The energy structure of heterometallic molecules with wheel topology is considered within the quantum Heisenberg spin model, using mostly the algebraic methods. In our approach, the central spin is coupled to the peripheral ones by the interaction parameter J ′ , whereas the latter located at the perimeter are subjects to the nearest-neighbour interaction J. The systems are frustrated in the regime J > 0 irrespective of the sign of J ′ and the ground state total spin quantum numbers form a universal sequence consisting of a definite number of steps as a function of the ratio α = J ′ / J . The Kahn degenerate frustration points occur at the discontinuous jumps or special symmetry junctures. In addition, the Lieb-Mattis level order is revealed despite the lack of bipartiteness, and existence of broad plateaus in the magnetisation profiles is also indicated.