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

Abstract

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 CaV 4 O 9 (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.

High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J_{1}-J_{2} model

“…On the other hand, by tracking the usual ('Néel-type') solution it is found (see [85]) that M changes continuously with J 2 and it is larger than for the dimerized solution for…”

“…Thus, there are two distinct types of twospin nearest-neighbor ket-state correlation coefficients, namely, those connecting the sites inside the unit cell and those connecting different unit cells. These coefficients are denoted as S It is straightforward to prove [85] that the ground state at J 2 /J 1 = …”

“…The ground-state properties of this system have been studied using methods such as exact diagonalizations [2,7], DMRG [3][4][5]55], CCM [8,52,54,78,85], and field-theoretical approaches [5] (see [5,6] for a general review). Note that previous CCM studies of the model considering only independent-spin product model states that conserve the lattice symmetry are reported in [52,79].…”

High-order coupled cluster method study of frustrated and unfrustrated quantum magnets in external magnetic fields

“…However, each method has its own specific limitations; for instance, the QMC is restricted (essentially) to unfrustrated systems because of the infamous 'sign problem. ' In this article we focus on the behaviour of quantum antiferromagnets as they react to externally imposed magnetic fields by a method of quantum many-body theory called the coupled cluster method (CCM) [23,24,25,26,27,28,29,30,31,32]. The CCM has been used previously in order to treat a wide range of strongly interacting quantum systems.…”

Ground-state phases of the frustrated spin-12J1–J2–Li1, Bishop2, Farnell3 et al. 2012Phys. Rev. BSelf Cite

“…It has been used to study various quantum magnets (see, e.g., Refs. [11][12][13][14][61][62][63][64][65][66][67][68][69][70][71] and references cited therein) very successfully. The method is particularly suitable for investigating frustrated systems, due to the fact that some of the main alternative methods are restricted by certain problems that arise in such cases.…”