The square-kagome quantum Heisenberg antiferromagnet at high magnetic fields: The localized-magnon paradigm and beyond

We consider the spin-1/2 antiferromagnetic Heisenberg model on the two-dimensional square-kagome lattice with almost dispersionless lowest magnon band. For a general exchange coupling geometry we elaborate low-energy effective Hamiltonians which emerge at high magnetic fields. The effective model to describe the low-energy degrees of freedom of the initial frustrated quantum spin model is the (unfrustrated) square-lattice spin-1/2 $XXZ$ model in a $z$-aligned magnetic field. For the effective model we perform quantum Monte Carlo simulations to discuss the low-temperature properties of the square-kagome quantum Heisenberg antiferromagnet at high magnetic fields. We pay special attention to a magnetic-field driven Berezinskii-Kosterlitz-Thouless phase transition which occurs at low temperatures.Comment: 6 figure

Atomic Fermi gas in the trimerized Kagom\'e lattice at the filling 2/3

We study low temperature properties of an atomic spinless interacting Fermi gas in the trimerized Kagom\'e lattice for the case of two fermions per trimer. The system is described by a quantum spin 1/2 model on the triangular lattice with couplings depending on bonds directions. Using exact diagonalizations we show that the system exhibits non-standard properties of a {\it quantum spin-liquid crystal}, combining a planar antiferromagnetic order with an exceptionally large number of low energy excitations.Comment: 4 pages & 4 figures + 2 tables, better version of Fig.

A Class of W-Algebras with Infinitely Generated Classical Limit

There is a relatively well understood class of deformable W-algebras, resulting from Drinfeld-Sokolov (DS) type reductions of Kac-Moody algebras, which are Poisson bracket algebras based on finitely, freely generated rings of differential polynomials in the classical limit. The purpose of this paper is to point out the existence of a second class of deformable W-algebras, which in the classical limit are Poisson bracket algebras carried by infinitely, nonfreely generated rings of differential polynomials. We present illustrative examples of coset constructions, orbifold projections, as well as first class Hamiltonian reductions of DS type W-algebras leading to reduced algebras with such infinitely generated classical limit. We also show in examples that the reduced quantum algebras are finitely generated due to quantum corrections arising upon normal ordering the relations obeyed by the classical generators. We apply invariant theory to describe the relations and to argue that classical cosets are infinitely, nonfreely generated in general. As a by-product, we also explain the origin of the previously constructed and so far unexplained deformable quantum W(2,4,6) and W(2,3,4,5) algebras.Comment: 39 pages (plain TeX), ITP-SB-93-84, BONN-HE-93-4

Magnetization Process of the Classical Heisenberg Model on the Shastry-Sutherland Lattice

We investigate classical Heisenberg spins on the Shastry-Sutherland lattice and under an external magnetic field. A detailed study is carried out both analytically and numerically by means of classical Monte-Carlo simulations. Magnetization pseudo-plateaux are observed around 1/3 of the saturation magnetization for a range of values of the magnetic couplings. We show that the existence of the pseudo-plateau is due to an entropic selection of a particular collinear state. A phase diagram that shows the domains of existence of those pseudo-plateaux in the $(h, T)$ plane is obtained.Comment: 9 pages, 11 figure

High-Order Coupled Cluster Method Study of Frustrated and Unfrustrated Quantum Magnets in External Magnetic Fields

We apply the coupled cluster method (CCM) in order to study the ground-state properties of the (unfrustrated) square-lattice and (frustrated) triangular-lattice spin-half Heisenberg antiferromagnets in the presence of external magnetic fields. Here we determine and solve the basic CCM equations by using the localised approximation scheme commonly referred to as the `LSUB$m$' approximation scheme and we carry out high-order calculations by using intensive computational methods. We calculate the ground-state energy, the uniform susceptibility, the total (lattice) magnetisation and the local (sublattice) magnetisations as a function of the magnetic field strength. Our results for the lattice magnetisation of the square-lattice case compare well to those results of QMC for all values of the applied external magnetic field. We find a value for magnetic susceptibility of $\chi=0.070$ for the square-lattice antiferromagnet, which is also in agreement with the results of other approximate methods (e.g., $\chi=0.0669$ via QMC). Our estimate for the range of the extent of the ($M/M_s=$)$\frac 13$ magnetisation plateau for the triangular-lattice antiferromagnet is $1.37< \lambda < 2.15$, which is in good agreement with results of spin-wave theory ($1.248 < \lambda < 2.145$) and exact diagonalisations ($1.38 < \lambda < 2.16$). The CCM value for the in-plane magnetic susceptibility per site is $\chi=0.065$, which is below the result of the spin-wave theory (evaluated to order 1/S) of $\chi_{SWT}=0.0794$.Comment: 30 pages, 13 figures, 1 Tabl

Quantum Monte Carlo simulations in the trimer basis:First-order transitions and thermal critical points in frustrated trilayer magnets

The phase diagrams of highly frustrated quantum spin systems can exhibit first-order quantum phase transitions and thermal critical points even in the absence of any long-ranged magnetic order. However, all unbiased numerical techniques for investigating frustrated quantum magnets face significant challenges, and for generic quantum Monte Carlo methods the challenge is the sign problem. Here we report on a general quantum Monte Carlo approach with a loop-update scheme that operates in any basis, and we show that, with an appropriate choice of basis, it allows us to study a frustrated model of coupled spin-1/2 trimers: simulations of the trilayer Heisenberg antiferromagnet in the spin-trimer basis are sign-problem-free when the intertrimer couplings are fully frustrated. This model features a first-order quantum phase transition, from which a line of first-order transitions emerges at finite temperatures and terminates in a thermal critical point. The trimer unit cell hosts an internal degree of freedom that can be controlled to induce an extensive entropy jump at the quantum transition, which alters the shape of the first-order line. We explore the consequences for the thermal properties in the vicinity of the critical point, which include profound changes in the lines of maxima defined by the specific heat. Our findings reveal trimer quantum magnets as fundamental systems capturing in full the complex thermal physics of the strongly frustrated regime.Comment: 27 pages, 10 figures, Resubmission to SciPos

Ghost Systems: A Vertex Algebra Point of View

Fermionic and bosonic ghost systems are defined each in terms of a single vertex algebra which admits a one-parameter family of conformal structures. The observation that these structures are related to each other provides a simple way to obtain character formulae for a general twisted module of a ghost system. The U(1) symmetry and its subgroups that underly the twisted modules also define an infinite set of invariant vertex subalgebras. Their structure is studied in detail from a W-algebra point of view with particular emphasis on Z_N-invariant subalgebras of the fermionic ghost system.Comment: 20 pages, plain Te

Topological energy barrier for skyrmion lattice formation in MnSi

We report the direct measurement of the topological skyrmion energy barrier through a hysteresis of the skyrmion lattice in the chiral magnet MnSi. Measurements were made using small-angle neutron scattering with a custom-built resistive coil to allow for high-precision minor hysteresis loops. The experimental data was analyzed using an adapted Preisach model to quantify the energy barrier for skyrmion formation and corroborated by the minimum-energy path analysis based on atomistic spin simulations. We reveal that the skyrmion lattice in MnSi forms from the conical phase progressively in small domains, each of which consisting of hundreds of skyrmions, and with an activation barrier of several eV.Comment: Final accepted versio

Strong disorder fixed points in the two-dimensional random-bond Ising model

The random-bond Ising model on the square lattice has several disordered critical points, depending on the probability distribution of the bonds. There are a finite-temperature multicritical point, called Nishimori point, and a zero-temperature fixed point, for both a binary distribution where the coupling constants take the values +/- J and a Gaussian disorder distribution. Inclusion of dilution in the +/- J distribution (J=0 for some bonds) gives rise to another zero-temperature fixed point which can be identified with percolation in the non-frustrated case (J >= 0). We study these fixed points using numerical (transfer matrix) methods. We determine the location, critical exponents, and central charge of the different fixed points and study the spin-spin correlation functions. Our main findings are the following: (1) We confirm that the Nishimori point is universal with respect to the type of disorder, i.e. we obtain the same central charge and critical exponents for the +/- J and Gaussian distributions of disorder. (2) The Nishimori point, the zero-temperature fixed point for the +/- J and Gaussian distributions of disorder, and the percolation point in the diluted case all belong to mutually distinct universality classes. (3) The paramagnetic phase is re-entrant below the Nishimori point, i.e. the zero-temperature fixed points are not located exactly below the Nishimori point, neither for the +/- J distribution, nor for the Gaussian distribution.Comment: final version to appear in JSTAT; minor change