We employ a plaquette basis---generated by coupling the four spins in a $2\ifmmode\times\else\texttimes\fi{}2$ lattice to a well-defined total angular momentum---for the study of Heisenberg ladders with antiferromagnetic coupling. Matrix elements of the Hamiltonian in this basis are evaluated using standard techniques in angular-momentum (Racah) algebra. We show by exact diagonalization of small $(2\ifmmode\times\else\texttimes\fi{}4$ and $2\ifmmode\times\else\texttimes\fi{}6)$ systems that in excess of 90% of the ground-state probability is contained in a very small number of basis states. These few basis states can be used to define a severely truncated basis which we use to approximate low-lying exact eigenstates. We show how, in this low-energy basis, the isotropic spin- $1/2$ Heisenberg ladder can be mapped onto an anisotropic spin- $1$ ladder for which the coupling along the rungs is much stronger than the coupling between the rungs. The mapping thereby generates two distinct energy scales which greatly facilitates understanding the dynamics of the original spin- $1/2$ ladder. Moreover, we use these insights to define an effective low-energy Hamiltonian in accordance to the contractor renormalization group (CORE) method. We show how a simple range-2 CORE approximation to the effective Hamiltonian to be used with our truncated basis reproduces the low-energy spectrum of the exact $2\ifmmode\times\else\texttimes\fi{}6$ theory at the $\ensuremath{\lesssim}1%$ level.We employ a plaquette basis---generated by coupling the four spins in a $2\ifmmode\times\else\texttimes\fi{}2$ lattice to a well-defined total angular momentum---for the study of Heisenberg ladders with antiferromagnetic coupling. Matrix elements of the Hamiltonian in this basis are evaluated using standard techniques in angular-momentum (Racah) algebra. We show by exact diagonalization of small $(2\ifmmode\times\else\texttimes\fi{}4$ and $2\ifmmode\times\else\texttimes\fi{}6)$ systems that in excess of 90% of the ground-state probability is contained in a very small number of basis states. These few basis states can be used to define a severely truncated basis which we use to approximate low-lying exact eigenstates. We show how, in this low-energy basis, the isotropic spin-$1/2$ Heisenberg ladder can be mapped onto an anisotropic spin-$1$ ladder for which the coupling along the rungs is much stronger than the coupling between the rungs. The mapping thereby generates two distinct energy scales which greatly facilitates understanding the dynamics of the original spin-$1/2$ ladder. Moreover, we use these insights to define an effective low-energy Hamiltonian in accordance to the contractor renormalization group (CORE) method. We show how a simple range-2 CORE approximation to the effective Hamiltonian to be used with our truncated basis reproduces the low-energy spectrum of the exact $2\ifmmode\times\else\texttimes\fi{}6$ theory at the $\ensuremath{\lesssim}1%$ level.

arXiv:cond-mat/9612139Physical review. B, Condensed matterSep 1, 199723 citations

Quantum Monte Carlo Calculation for Spin Systems in Two-Leg Ladders with Alternating Heisenberg-Bond Chains

Takafumi Momose, Toshihiko Suzuki, Yuhei Natsume

Thermodynamic properties of spin=1/2 two-leg ladders with alternating chains including ferromagnetic and antiferromagnetic interactions are discussed on the basis of the numerical results obtained by quantum Monte Carlo simulations. As well as the role of exchange interaction of rungs, the essential role of the bond alternation in the chain on ladder systems is investigated in connection with the appearance of characteristic properties in magnetic susceptibilities and heat capacities. Furthermore, quantum effects on the ground-state energy are obtained. On the basis of calculated results, the relationship between singlet dimer phases and Haldane states is discussed.Thermodynamic properties of spin=1/2 two-leg ladders with alternating chains including ferromagnetic and antiferromagnetic interactions are discussed on the basis of the numerical results obtained by quantum Monte Carlo simulations. As well as the role of exchange interaction of rungs, the essential role of the bond alternation in the chain on ladder systems is investigated in connection with the appearance of characteristic properties in magnetic susceptibilities and heat capacities. Furthermore, quantum effects on the ground-state energy are obtained. On the basis of calculated results, the relationship between singlet dimer phases and Haldane states is discussed.

Journal of the Physical Society of JapanJun 15, 19970 citations

Magnetic phase transitions in Heisenberg ladders

Dirk K. Morr

APSMar 1, 19970 citations

1/2

Heisenberg ladder can be mapped onto an anisotropic spin-

1

ladder for which the coupling along the rungs is much stronger than the coupling between the rungs. The mapping thereby generates two distinct energy scales which greatly facilitates understanding the dynamics of the original spin-

1/2

ladder. Moreover, we use these insights to define an effective low-energy Hamiltonian in accordance to the contractor renormalization group (CORE) method. We show how a simple range-2 CORE approximation to the effective Hamiltonian to be used with our truncated basis reproduces the low-energy spectrum of the exact $2\ifmmode\times\else\texttimes\fi{}6$ theory at the $\ensuremath{\lesssim}1%$ level.