We study the spin-1/2 quantum Heisenberg antiferromagnet on a Bethe lattice diluted to the percolation threshold. Dilution creates areas of even or odd sublattice imbalance resulting in "dangling spins" [L. Wang and A. W. Sandvik, Phys. Rev. Lett. 97, 117204 (2006); Phys. Rev. B 81, 054417 (2010)]. These collectively act as "emergent" spin-1/2 degrees of freedom and are responsible for the creation of a set of low-lying "quasidegenerate states." Using density matrix renormalization group calculations, we detect the presence and location of these emergent spins. We find an effective Hamiltonian of these emergent spins, with Heisenberg interactions that decay exponentially with the distance between them.We study the spin-1/2 quantum Heisenberg antiferromagnet on a Bethe lattice diluted to the percolation threshold. Dilution creates areas of even or odd sublattice imbalance resulting in "dangling spins" [L. Wang and A. W. Sandvik, Phys. Rev. Lett. 97, 117204 (2006); Phys. Rev. B 81, 054417 (2010)]. These collectively act as "emergent" spin-1/2 degrees of freedom and are responsible for the creation of a set of low-lying "quasidegenerate states." Using density matrix renormalization group calculations, we detect the presence and location of these emergent spins. We find an effective Hamiltonian of these emergent spins, with Heisenberg interactions that decay exponentially with the distance between them.

arXiv:1210.4621Physical Review LettersOct 7, 201319 citations

Density matrix renormalization group algorithm for Bethe lattices of spin- 12 or spin-1 sites with Heisenberg antiferromagnetic exchange

Manoranjan Kumar, S. Ramasesha, Z. G. Soos

A density matrix renormalization group (DMRG) algorithm is presented for the Bethe lattice with connectivity $Z=3$ and antiferromagnetic exchange between nearest-neighbor spins $s=1/2$ or 1 sites in successive generations $g$ . The algorithm is accurate for $s=1$ sites. The ground states are magnetic with spin $S(g)={2}^{g}s$ , staggered magnetization that persists for large $g>20$ , and short-range spin correlation functions that decrease exponentially. A finite energy gap to $S>S(g)$ leads to a magnetization plateau in the extended lattice. Closely similar DMRG results for $s$ $=$ 1/2 and 1 are interpreted in terms of an analytical three-site model.A density matrix renormalization group (DMRG) algorithm is presented for the Bethe lattice with connectivity $Z=3$ and antiferromagnetic exchange between nearest-neighbor spins $s=1/2$ or 1 sites in successive generations $g$. The algorithm is accurate for $s=1$ sites. The ground states are magnetic with spin $S(g)={2}^{g}s$, staggered magnetization that persists for large $g>20$, and short-range spin correlation functions that decrease exponentially. A finite energy gap to $S>S(g)$ leads to a magnetization plateau in the extended lattice. Closely similar DMRG results for $s$ $=$ 1/2 and 1 are interpreted in terms of an analytical three-site model.

arXiv:1111.1442Physical Review BApr 6, 201219 citations

The spin-2 antiferromagnet on the Bethe lattice

Ahmet Erdinç, Osman Canko, Erhan Albayrak

The European Physical Journal BAug 1, 200611 citations

Density-matrix renormalization study of the Hubbard model on a Bethe lattice

Marie-Bernadette Lepetit, Maixent Cousy, G. M. Pastor

The half-filled Hubbard model on the Bethe lattice with coordination number $z=3$ is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy $E$ , average local magnetization $$, its fluctuations $ - < \hat S_z>^2$ and various spin correlation functions $ - < S_z(i)> < S_z(j)>$ are determined as a function of the Coulomb interaction strength $U/t$. The calculated local magnetic moments $$ increase monotonically with increasing Coulomb repulsion $U/t$ forming an antiferromagnetic spin-density-wave state which matches the two sublattices of the bipartite Bethe lattice. At large $U/t$ , $$ is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins ($|< S_z(i)>|\simeq 0.35$ for $U/t\to +\infty$). $ - < S_z(i)>^2$ shows a maximum for $U/t=2.4$--2.9 which results from the interplay between the usual increase of $$ with increasing $U/t$ and the formation of important permanent moments $$ at large $U/t$ . NN sites show antiferromagnetic spin correlations which increase with increasing Coulomb repulsion. In contrast next NN sites are very weakly correlated over the whole range of $U/t$ . The accuracy of the DMRG results is discussed by comparison with tight-binding exact results, independent DMRG calculations for the Heisenberg model and simple first-order perturbation estimates.The half-filled Hubbard model on the Bethe lattice with coordination number $z=3$ is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy $E$, average local magnetization $$, its fluctuations $ - < \hat S_z>^2$ and various spin correlation functions $ - < S_z(i)> < S_z(j)>$ are determined as a function of the Coulomb interaction strength $U/t$. The calculated local magnetic moments $$ increase monotonically with increasing Coulomb repulsion $U/t$ forming an antiferromagnetic spin-density-wave state which matches the two sublattices of the bipartite Bethe lattice. At large $U/t$, $$ is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins ($|< S_z(i)>|\simeq 0.35$ for $U/t\to +\infty$). $ - < S_z(i)>^2$ shows a maximum for $U/t=2.4$--2.9 which results from the interplay between the usual increase of $$ with increasing $U/t$ and the formation of important permanent moments $$ at large $U/t$. NN sites show antiferromagnetic spin correlations which increase with increasing Coulomb repulsion. In contrast next NN sites are very weakly correlated over the whole range of $U/t$. The accuracy of the DMRG results is discussed by comparison with tight-binding exact results, independent DMRG calculations for the Heisenberg model and simple first-order perturbation estimates.

arXiv:cond-mat/9801228Jan 22, 19980 citations

A density matrix renormalization group (DMRG) algorithm is presented for the Bethe lattice with connectivity

Z=3

and antiferromagnetic exchange between nearest-neighbor spins

s=1/2

or 1 sites in successive generations

g

. The algorithm is accurate for

s=1

sites. The ground states are magnetic with spin

S(g)={2}^{g}s

, staggered magnetization that persists for large

g>20

, and short-range spin correlation functions that decrease exponentially. A finite energy gap to

S>S(g)

leads to a magnetization plateau in the extended lattice. Closely similar DMRG results for

s

=

1/2 and 1 are interpreted in terms of an analytical three-site model.

The half-filled Hubbard model on the Bethe lattice with coordination number

z=3

is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy

E

, average local magnetization $$, its fluctuations $ - < \hat S_z>^2$ and various spin correlation functions $ - < S_z(i)> < S_z(j)>$ are determined as a function of the Coulomb interaction strength $U/t$. The calculated local magnetic moments $$ increase monotonically with increasing Coulomb repulsion

U/t

forming an antiferromagnetic spin-density-wave state which matches the two sublattices of the bipartite Bethe lattice. At large

U/t

, $$ is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins ($|< S_z(i)>|\simeq 0.35$ for $U/t\to +\infty$). $ - < S_z(i)>^2$ shows a maximum for $U/t=2.4$--2.9 which results from the interplay between the usual increase of $$ with increasing

U/t

and the formation of important permanent moments $$ at large

U/t

. NN sites show antiferromagnetic spin correlations which increase with increasing Coulomb repulsion. In contrast next NN sites are very weakly correlated over the whole range of

U/t

. The accuracy of the DMRG results is discussed by comparison with tight-binding exact results, independent DMRG calculations for the Heisenberg model and simple first-order perturbation estimates.