Journal of Physics Condensed Matter

The phase diagram of the XXZ model for slab and layered geometries

Dirk Jan Bukman, J. M. J. van Leeuwen

Published Dec 16, 1991• 0 citations

Abstract

The phase diagram of the spin 1/2 XXZ model is examined for two different geometries, which can be changed from two- to three-dimensional. The first of these consists of an infinite stack of simple quadratic layers with a variable inter-layer coupling, where the ratio of the inter-layer and intra-layer couplings varies between zero and one. Second, the authors consider a slab geometry consisting of n such layers, with equal couplings in all directions. For both geometries they use the cluster variation method for two-spin clusters to construct the phase diagram of the model, and they examine the changes that take place as the system changes from two- to three-dimensional. For the slab geometry they also calculate the order parameter profile near T c . It turns out that Dirichlet boundary conditions for the related superfluid wavefunction are most realistic.

DOI: 10.1088/0953-8984/3/50/006

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Journal of Physics Condensed Matter

The phase diagram of the XXZ model for slab and layered geometries

Dirk Jan Bukman, J. M. J. van Leeuwen

Published Dec 16, 1991• 0 citations

Publisher

Abstract

DOI: 10.1088/0953-8984/3/50/006

Related papers

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{\mathit{J}}_{\mathit{z}}

/J and for arbitrary external magnetic fields. Lattices with different values of the coordination number z are considered. Analytic expressions are found for nearly all phase boundaries; the remaining phase boundary is located numerically. Despite some problems at low temperature, the results based on this approach are in quite good agreement with the results from series-expansion methods. A connection is made with the Hubbard model, which can be mapped onto the XXZ Hamiltonian in the limit of strong on-site attraction.

Quantum phase diagram of a frustrated spin-

\frac{1}{2}

J_{1}

J_{2}

J_{1}^{\perp}

Heisenberg model on an

AA

-stacked bilayer honeycomb lattice

The zero-temperature quantum phase diagram of the spin-

\frac{1}{2}

J_{1}

J_{2}

J_{1}^{\perp}

model on an

AA

-stacked bilayer honeycomb lattice is investigated using the coupled cluster method (CCM). The model comprises two monolayers in each of which the spins, residing on honeycomb-lattice sites, interact via both nearest-neighbor (NN) and frustrating next-nearest-neighbor isotropic antiferromagnetic (AFM) Heisenberg exchange iteractions, with respective strengths

J_{1} > 0

and

J_{2} \equiv \kappa J_{1}>0

. The two layers are coupled via a comparable Heisenberg exchange interaction between NN interlayer pairs, with a strength

J_{1}^{\perp} \equiv \delta J_{1}

. The complete phase boundaries of two quasiclassical collinear AFM phases, namely the Neel and Neel-II phases, are calculated in the

\kappa \delta

half-plane with

\kappa > 0

. Whereas on each monolayer in the Neel state all NN pairs of spins are antiparallel, in the Neel-II state NN pairs of spins on zigzag chains along one of the three equivalent honeycomb-lattice directions are antiparallel, while NN interchain spins are parallel. We calculate directly in the thermodynamic (infinite-lattice) limit both the magnetic order parameter

M

and the excitation energy

\Delta

from the

s^{z}_{T}=0

ground state to the lowest-lying

|s^{z}_{T}|=1

excited state (where

s^{z}_{T}

is the total

z

component of spin for the system as a whole, and where the collinear ordering lies along the

z

direction) for both quasiclassical states used (separately) as the CCM model state, on top of which the multispin quantum correlations are then calculated to high orders (

n \leq 10

) in a systematic series of approximations involving

n

-spin clusters. The sole approximation made is then to extrapolate the sequences of

n

th-order results for

M

and

\Delta

to the exact limit,

n \to \infty

D

phase, with a continuous change of the Hamiltonian parameters. Furthermore, we study the spin-3 XXZ chain to help explain the development of the classical phase diagram. We present details on how to use the iDMRG method to map out the phase diagram and include an extensive discussion of the numerical methods.

We study the

T=0

phase diagrams of models of bilayers of

S=1/2

square lattices antiferromagnets with SU(2) Heisenberg symmetry that have 2, 4, and 6 spin exchanges. We study two families of bilayer models with distinct internal symmetries and, hence, different phase diagram topologies. A traditional bilayer model in which the interlayer interaction is Heisenberg so that the two layers can exchange spin (and energy) with each other, making it possible to achieve a simple dimerized valence bond liquid-like state. The resulting phase diagram is rich with Néel, valence bond solid and simple dimer phases, and both first-order and continuous transitions, which we demonstrate are consistent with the conventional Landau theory of order parameters. In the second family of models in which the layers can exchange only energy but no spin (reminiscent of the Ashkin-Teller coupling), the simple dimer state cannot occur. The phase diagrams reveal a number of phase transitions that are accessed for the first time. We find that the phase transition between Néel and VBS is first order in both the spin-spin and energy-energy coupled models, although they have strikingly distinct finite-size scaling behavior and that the transition from VBS to dimer in the spin-spin coupling model deviates from the expected scenario of an XY model with dangerously irrelevant four-fold anisotropy.