An Efficient Implementation of High-Order Coupled-Cluster Techniques Applied to Quantum Magnets

We illustrate how the systematic inclusion of multi-spin correlations of the quantum spin–lattice systems can be efficiently implemented within the framework of the coupled-cluster method by examining the ground-state properties of both the square-lattice and the frustrated triangular-lattice quantum antiferromagnets. The ground-state energy and the sublattice magnetization are calculated for the square-lattice and triangular-lattice Heisenberg antiferromagnets, and our best estimates give values for the sublattice magnetization which are 62% and 51% of the classical results for the square and triangular lattices, respectively. We furthermore make a conjecture as to why previous series expansion calculations have not indicated Néel-like long-range order for the triangular-lattice Heisenberg antiferromagnet. We investigate the critical behavior of the anisotropic systems by obtaining approximate values for the positions of phase transition points.     

The ground states of the classical heisenberg and planar models on the triangular and plane hexagonal lattices

The energies and the spin configurations of the ground states of the classical Heisenberg and classical planar (XY) models with first- and second-neighbor interactions on the triangular and plane hexagonal lattices are obtained. The phase diagrams in theJ ₁–J ₂ plane are determined, whereJ ₁ andJ ₂ are the coefficients of the first- and second-neighbor interactions, respectively. It is noted for the system on the plane hexagonal lattice, that an infinite degeneracy of the ground states occurs in some region of theJ ₁–J ₂ plane and then the study is made under an introduction of an infinitesimal third-neighbor interaction, removing the degeneracy.     

Effects of biquadratic-exchange in antiferromagnets

The effects of the biquadratic-exchange interaction on magnetic specific heat and sublattice magnetization are studied for antiferromagnets. At the critical ratio of the biquadratic-exchange to the Heisenberg interaction, the spin structure changes abruptly and magnetic properties are affected significantly.     

Symmetry breaking and finite-size effects in quantum many-body systems

We consider a quantum many-body system on a lattice which exhibits a spontaneous symmetry breaking in its infinite-volume ground states, but in which the corresponding order operator does not commute with the Hamiltonian. Typical examples are the Heisenberg antiferromagnet with a Néel order and the Hubbard model with a (superconducting) off-diagonal long-range order. In the corresponding finite system, the symmetry breaking is usually obscured by quantum fluctuation and one gets a symmetric ground state with a long-range order. In such a situation, Horsch and von der Linden proved that the finite system has a low-lying eigenstate whose excitation energy is not more than of orderN ^–1, whereN denotes the number of sites in the lattice. Here we study the situation where the broken symmetry is a continuous one. For a particular set of states (which are orthogonal to the ground state and with each other), we prove bounds for their energy expectation values. The bounds establish that there exist ever-increasing numbers of low-lying eigenstates whose excitation energies are bounded by a constant timesN ^–1. A crucial feature of the particular low-lying states we consider is that they can be regarded as finite-volume counterparts of the infinite-volume ground states. By forming linear combinations of these low-lying states and the (finite-volume) ground state and by taking infinite-volume limits, we construct infinite-volume ground states with explicit symmetry breaking. We conjecture that these infinite-volume ground states are ergodic, i.e., physically natural. Our general theorems not only shed light on the nature of symmetry breaking in quantum many-body systems, but also provide indispensable information for numerical approaches to these systems. We also discuss applications of our general results to a variety of interesting examples. The present paper is intended to be accessible to readers without background in mathematical approaches to quantum many-body systems.     

High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States

In this article, we prove that exact representations of dimer and plaquette valence-bond ket ground states for quantum Heisenberg antiferromagnets may be formed via the usual coupled cluster method (CCM) from independent-spin product (e.g. Néel) model states. We show that we are able to provide good results for both the ground-state energy and the sublattice magnetization for dimer and plaquette valence-bond phases within the CCM. As a first example, we investigate the spin-half J ₁–J ₂ model for the linear chain, and we show that we are able to reproduce exactly the dimerized ground (ket) state at J ₂/J ₁=0.5. The dimerized phase is stable over a range of values for J ₂/J ₁ around 0.5, and results for the ground-state energies are in good agreement with the results of exact diagonalizations of finite-length chains in this regime. We present evidence of symmetry breaking by considering the ket- and bra-state correlation coefficients as a function of J ₂/J ₁. A radical change is also observed in the behavior of the CCM sublattice magnetization as we enter the dimerized phase. We then consider the Shastry-Sutherland model and demonstrate that the CCM can span the correct ground states in both the Néel and the dimerized phases. Once again, very good results for the ground-state energies are obtained. We find CCM critical points of the bra-state equations that are in agreement with the known phase transition point for this model. The results for the sublattice magnetization remain near to the “true” value of zero over much of the dimerized regime, although they diverge exactly at the critical point. Finally, we consider a spin-half system with nearest-neighbor bonds for an underlying lattice corresponding to the magnetic material CaV₄O₉ (CAVO). We show that we are able to provide excellent results for the ground-state energy in each of the plaquette-ordered, Néel-ordered, and dimerized regimes of this model. The exact plaquette and dimer ground states are reproduced by the CCM ket state in their relevant limits. Furthermore, we estimate the range over which the Néel order is stable, and we find the CCM result is in reasonable agreement with the results obtained by other methods. Our new approach has the dual advantages that it is simple to implement and that existing CCM codes for independent-spin product model states may be used from the outset. Furthermore, it also greatly extends the range of applicability to which the CCM may be applied. We believe that the CCM now provides an excellent choice of method for the study of systems with valence-bond quantum ground states.     

Magnetization plateaus and sublattice ordering in easy-axis kagome lattice antiferromagnets

We study kagome lattice antiferromagnets where the effects of easy-axis single-ion anisotropy (D) dominates over the Heisenberg exchange J. For S> or =3/2, virtual quantum fluctuations help lift the extensive classical degeneracy. We demonstrate the presence of a one-third magnetization plateau for a broad range of magnetic fields J3/D2 < or = B < or = JS along the easy axis. The fully equilibrated system at low temperature on this plateau develops an unusual nematic order that breaks sublattice rotation symmetry but not translation symmetry; however, extremely slow dynamics associated with this ordering is expected to lead to glassy freezing of the system on intermediate time scales.     

Symmetry breaking in Heisenberg antiferromagnets

We extend Griffith's theorem on symmetry breaking in quantum spin systems to the situation where the order operator and the Hamiltonian do not commute with each other. The theorem establishes that the existence of a long range order in a symmetric (non-pure) infinite-volume state implies the existence of a symmetry breaking in the state obtained by applying an infinitesimal symmetry-breaking field. The theorem is most meaningful when applied to a class of quantum antiferromagnets where the existence of a long range order has been proved by the Dyson-Lieb-Simon method. We also present a related theorem for the ground states. It is an improvement of the theorem by Kaplan, Horsch and von der Linden. Our lower bounds on the spontaneous staggered magnetization in terms of the long range order parameter take into account the symmetry of the system properly, and are likely to be saturated in general models.     

Spin configurations in hexagonal antiferromagnets with competing interactions

The ordered phase of the most part of ABX₃ antiferromagnets appears as a stacking of 120°-three sublattice spin layers with alternate spin direction along thec-axis. This configuration is easy to be explained because it is the minimum energy configuration of the Heisenberg hexagonal model with nearest neighbour antiferromagnetic interaction. However we show that moderate competitive interactions between in plane next nearest and third nearest neighbours stabilize incommensurate spin configurations. This gives some insight into the unexplained spin configuration observed in RbMnBr₃ by elastic neutron scattering experiment.     

Thin spectrum states in bulk superconductors and superconducting grains

We show how a local pairing model for superconductivity can be used to describe the symmetry breaking mechanism in exact analogy to the cases of quantum crystals and antiferromagnets. We find that there are low energy states associated with the symmetry breaking process which are not influenced by the Anderson-Higgs mechanism. The presence of these ‘thin spectrum’ states in qubits based on superconducting material leads to a maximum time for which such qubits can remain quantum coherent. We also show how the charging energy of superconducting quantum dots may give the thin spectrum states a finite energy gap, impeding the spontaneous breaking of phase symmetry.     

Thermodynamic study of 3D XY model and Heisenberg model by analytical method

With Variational-Cumulant Expansion method, the specific heat and spontaneous magnetization of 3D classical XY model and Heisenberg model are calculated respectively up to the 5th and 4th order. The variational parameter is determined both by the Main Value method and by the accumulation point method. It is shown that the specific heat curve and the magnetization curve obtained by the accumulation point method are in better agreement with the MC results. The critical point T _c and critical exponent β* are also calculated for the XY model.     

On a quantum theory of superconducting glasses and other impure superconducting phases

We review and extend a previous electronic mean field theory of superconducting glass phases. These phases are defined by vanishing ensemble averaged BCS-order parameter and non-vanishing Edwards-Anderson type averages of the inhomogeneous superconducting order parameter. Solutions are worked out for the replica symmetric case, but the possibility of replica symmetry breaking and hence ergodicity breaking is also discussed in the field theory. The order parameter for Ising-like, anisotropic and isotropicXY-like superconducting glass phases are identified by their spontaneous symmetry breaking effect in the action of the discorder ensemble. The isotropicXY-like phase is found to allow superconductivity in arbitrary strong magnetic fields. Generally the results show that: the occurrence of superconducting glass phases is supported by strong local attractive electron-electron coupling together with a high probability of nonsuper-conducting areas, the vicinity of a metal-insulator transition or the presence of a magnetic field. We suggest that for strong coupling the theory is applicable to HighT _c superconductors like Ba–La–Cu–O.A first result beyond mean field approximation displays at one loop order quantum fluctuation contributions to the density of states in the superconducting glass phases. We suggest that these phases may show an infinite nonlinear dc conductivity in higher order response.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

One-dimensionalXY model: Ergodic properties and hydrodynamic limit

We prove theorems on convergence to a stationary state in the course of time for the one-dimensionalXY model and its generalizations. The key point is the well-known Jordan-Wigner transformation, which maps theXY dynamics onto a group of Bogoliubov transformations on the CARC ^*-algebra overZ ¹. The role of stationary states for Bogoliubov transformations is played by quasifree states and for theXY model by their inverse images with respect to the Jordan-Wigner transformation. The hydrodynamic limit for the one-dimensionalXY model is also considered. By using the Jordan-Wigner transformation one reduces the problem to that of constructing the hydrodynamic limit for the group of Bogoliubov transformations. As a result, we obtain an independent motion of normal modes, which is described by a hyperbolic linear differential equation of second order. For theXX model this equation reduces to a first-order transfer equation.     

Comments on nonlinear excitations in the anisotropic Heisenberg chain

It is suggested that pulse soliton solutions for the classical, continuum, isotropic, ferromagnetic Heisenberg chain in a magnetic field continuously deform to sine Gordon breather solutions as anisotropy is increased to an extremeXY limit (theXY plane containing the applied field). The relevance of this observation for applications to magnetic chains such as CsNiF₃ is emphasized, and comparisons with the zero-field limit are noted.     

On the critical dynamics of disordered spin systems

The dynamic critical behaviour of spin systems with quenched impurities, and of amorphous spin systems as characterized by the additional presence of random anisotropy directions, is studied by renormalization group methods to second order in=4–d. For the Halperin-Hohenberg-Ma model with purely relaxational dynamics it is concluded that in three dimensions (d=3) the critical slowing down should be enhanced by impurities for systems with Ising type statics, whereas there is no change forXY- and Heisenberg systems. For amorphous systems, however, the critical dynamics should change also in theXY- and Heisenberg cases. Furthermore, it is concluded that additional conserved, but noncritical modes become always statically decoupled from the order parameter for systems with impurities, but not for amorphous systems. Thus, for the impure system, the energy density mode and the asymmetric models of Halperin, Hohenberg and Siggia are ruled out. But the effects of dynamic coupling remain: Especially, the relationz=d/2 for the dynamic exponent of planar and isotropic antiferromagnets is modified for impure or amorphous systems.     

On the dynamics and ergodic properties of theXY model

The return to equilibrium is investigated for one-dimensional (one-sided) chain of theXY model. The initial state is taken to be the Gibbs state for the sum of the Hamiltonian for theXY model of lengthN and a perturbation by a uniform magnetic field acting on the firstn sites. The time evolution under the unperturbedXY model Hamiltonian is studied for the expectation value of the average magnetization of the same firstn sites in the infinitely extended system (i.e., after taking the limitN). It is found that the return to equilibrium occurs for a finite-size perturbation (i.e., for a fixedn), while it does not occur for an infinite-size perturbation (i.e., the limit n is taken simultaneously as N). A certain twisted asymptotic Abelian property of theXY model is shown and used as a technical tool.     

Magnetic-breakdown oscillations of the thermoelectric field in layered conductors

We consider the quasi-two-dimensional pseudo-spin-1/2 Kitaev–Heisenberg model proposed for A₂IrO₃ (A = Li, Na) compounds. The spin-wave excitation spectrum, the sublattice magnetization, and the transition temperatures are calculated in the random phase approximation for four different ordered phases observed in the parameter space of the model: antiferromagnetic, stripe, ferromagnetic, and zigzag phases. The Néel temperature and temperature dependence of the sublattice magnetization are compared with the experimental data on Na₂IrO₃.     

Spin-correlations and low lying excited states of the spin-1/2 Heisenberg antiferromagnet on a square lattice

The ground state and the lowest excited states of the spin 1/2-Heisenberg model are investigated by exact diagonalization and variational Monte Carlo techniques. Our trial state represents a generalization of a wave function introduced by Hulthen, Kasteleijn and Marshall. The long range character of the spin-correlation function is in excellent agreement with exact diagonalization and also with recent neutron scattering results for La₂CuO₄. The asymptotic behavior of the spin-correlation function is found to differ from spin-wave theory. From the exact (N<=20 spins) and variational (N<=400) ground state energies we determine as asymptotic values 1.3025 and 1.288, respectively. We calculate the dispersion for the spin-wave excitations and identify an excited triplet which becomes degenerate with the ground state in the thermodynamic limit. This triplet state allows spontaneous symmetry breaking to occur atT=0 K. Quantum fluctuations reduce the sublattice magnetization to an effective value of 0.195 (3) as compared to the Néel-state value of 1/2.     

Spin quantum number in the ground state of the Mattis-Heisenberg model

Total spin quantum number is rigorously calculated for a quantum version of the Mattis model of random spin systems. Crossover between three universality classes of the Ising model, theXY model, and the Heisenberg model is explicitly worked out in the presence of randomness. The randomness of the type of the Mattis model is shown to have no thermodynamic effects even in quantum systems.     

Real-space renormalization group for two-dimensional quantum spin systems

A generalization of the Niemeijer and Van Leeuwen real-space renormalization group method for quantum lattice spin systems is presented. A proposed rotationally invariant transformation which preserves the symmetry of the spin space is applied to several quantum systems on a triangular lattice. For the spin-1/2XY-model in both first- and second-order cumulant expansions a nontrivial fixed point exists, giving in the best approximation a critical interactionK _XY ^c =0.453 and critical exponent =1.65. A method of the reduction of the generalized arbitrary spin anisotropic Heisenberg model to the spin-half model is presented.     

Axial-vector symmetry breaking and the mass generation of the singlet pseudoscalar meson

The Fabri-Picasso formulation of the spontancous breaking of theSU _A (3) symmetry is applied to theU _A (1) symmetry. It is argued that the notion of the spontaneous breaking of theU _A (1) symmetry is different from that of theSU _A (3) symmetry. In contrast to the octet sector, absence of the massless Goldstone mode amounts to the existence of an exotic vacuum-like degenerated state.