A new method of determining the spectra of simple quantum-mechanical spin Hamiltonians by direct Hamiltonian-matrix diagonalization is presented. The method is illustrated by applying it to the isotropic one-dimensional Heisenberg antiferromagnet, for which calculations were performed for longer spin chains than by previous direct Hamiltonian-matrix diagonalizations. For spin s=1/2 it was possible to accurately determine the ground- and first-excited-state energies for chains of length N=32 and 64. For s=1 the longest chain for which a similar computation was performed was N=32; the singlet-triplet Haldane gap is found to be 0.421\ifmmode\pm\else\textpm\fi{}0.005 which is consistent with earlier Monte Carlo results. Long-spin-chain calculations are performed iteratively by solving smaller-chain problems, and constructing from their eigenvalues, and eigenstates, the longer-spin-chain basis and Hamiltonian matrices. The computations were performed on a small computer, which suggests that much larger problems could be handled with a parallel-processing supercomputer.A new method of determining the spectra of simple quantum-mechanical spin Hamiltonians by direct Hamiltonian-matrix diagonalization is presented. The method is illustrated by applying it to the isotropic one-dimensional Heisenberg antiferromagnet, for which calculations were performed for longer spin chains than by previous direct Hamiltonian-matrix diagonalizations. For spin s=1/2 it was possible to accurately determine the ground- and first-excited-state energies for chains of length N=32 and 64. For s=1 the longest chain for which a similar computation was performed was N=32; the singlet-triplet Haldane gap is found to be 0.421\ifmmode\pm\else\textpm\fi{}0.005 which is consistent with earlier Monte Carlo results. Long-spin-chain calculations are performed iteratively by solving smaller-chain problems, and constructing from their eigenvalues, and eigenstates, the longer-spin-chain basis and Hamiltonian matrices. The computations were performed on a small computer, which suggests that much larger problems could be handled with a parallel-processing supercomputer.

Physical review. B, Condensed matterApr 1, 199015 citations

Chemistry of the spin- 12 kagome Heisenberg antiferromagnet

Yuan Yao, Cyrus J. Umrigar, Veit Elser

We believe that a necessary first step in understanding the ground-state properties of the spin- $\frac{1}{2}$ kagome Heisenberg antiferromagnet is a better understanding of this model's very large number of low-energy singlet states. A description of the low-energy states that is both accurate and amenable for numerical work may ultimately prove to have greater value than knowing only what these properties are, in particular, when they turn on the delicate balance of many small energies. We demonstrate how this program would be implemented using the basis of spin-singlet dimerized states, though other bases that have been proposed may serve the same purpose. The quality of a basis is evaluated by its participation in all low-energy singlets, not just the ground state. From an experimental perspective, and again in light of the small energy scales involved, methods that can deliver all low-energy states promise more robust predictions than methods that only refine a fraction of these states.We believe that a necessary first step in understanding the ground-state properties of the spin-$\frac{1}{2}$ kagome Heisenberg antiferromagnet is a better understanding of this model's very large number of low-energy singlet states. A description of the low-energy states that is both accurate and amenable for numerical work may ultimately prove to have greater value than knowing only what these properties are, in particular, when they turn on the delicate balance of many small energies. We demonstrate how this program would be implemented using the basis of spin-singlet dimerized states, though other bases that have been proposed may serve the same purpose. The quality of a basis is evaluated by its participation in all low-energy singlets, not just the ground state. From an experimental perspective, and again in light of the small energy scales involved, methods that can deliver all low-energy states promise more robust predictions than methods that only refine a fraction of these states.

arXiv:2004.01107Physical review. B./Physical review. BJul 10, 20204 citations

Ground States of Quantum Antiferromagnets in Two Dimensions

Subir Sachdev A, Kwon Park

arXiv:cond-mat/0108214Annals of PhysicsMay 1, 2002102 citations

A Coherent-State Representation of the Ground State of Quantum Antiferromagnets

G. G. Cabrera

Springer eBooksJan 1, 19942 citations

Generalization of the singlet sector valence-bond loop algorithm to antiferromagnetic ground states with total spinStot= 1/2

Argha Banerjee, Kedar Damle

We develop a generalization of the singlet sector valence-bond basis projection algorithm of Sandvik, Beach, and Evertz (Sandvik 2005 Phys. Rev. Lett. 95 207203; Beach and Sandvik 2006 Nucl. Phys. B 750 142; Sandvik and Evertz 2010 Phys. Rev. B 82 024407) to cases in which the ground state of an antiferromagnetic Hamiltonian has total spin S tot = 1/2 in a finite-size system. We explain how various ground state expectation values may be calculated by using generalizations of the estimators developed in the singlet case, and illustrate the power of the method by calculating the ground state spin texture and bond energies in an L × L Heisenberg antiferromagnet with L odd and free boundaries.We develop a generalization of the singlet sector valence-bond basis projection algorithm of Sandvik, Beach, and Evertz (Sandvik 2005 Phys. Rev. Lett. 95 207203; Beach and Sandvik 2006 Nucl. Phys. B 750 142; Sandvik and Evertz 2010 Phys. Rev. B 82 024407) to cases in which the ground state of an antiferromagnetic Hamiltonian has total spin S tot = 1/2 in a finite-size system. We explain how various ground state expectation values may be calculated by using generalizations of the estimators developed in the singlet case, and illustrate the power of the method by calculating the ground state spin texture and bond energies in an L × L Heisenberg antiferromagnet with L odd and free boundaries.

arXiv:1006.2598Journal of Statistical Mechanics Theory and ExperimentAug 20, 201019 citations

We believe that a necessary first step in understanding the ground-state properties of the spin-

\frac{1}{2}

kagome Heisenberg antiferromagnet is a better understanding of this model's very large number of low-energy singlet states. A description of the low-energy states that is both accurate and amenable for numerical work may ultimately prove to have greater value than knowing only what these properties are, in particular, when they turn on the delicate balance of many small energies. We demonstrate how this program would be implemented using the basis of spin-singlet dimerized states, though other bases that have been proposed may serve the same purpose. The quality of a basis is evaluated by its participation in all low-energy singlets, not just the ground state. From an experimental perspective, and again in light of the small energy scales involved, methods that can deliver all low-energy states promise more robust predictions than methods that only refine a fraction of these states.