Using exact diagonalizations, Green's function Monte Carlo simulations and high-order perturbation theory, we study the low-energy properties of the two-dimensional spin-1/2 compass model on the square lattice defined by the Hamiltonian H=-Sigma(r)(J(x)sigma(r)(x)sigma(r+ex)(x)+J(z)sigma(r)(z)sigma(r+ez)(z)). When J(x)not equal J(z), we show that, on clusters of dimension L x L, the low-energy spectrum consists of 2(L) states which collapse onto each other exponentially fast with L, a conclusion that remains true arbitrarily close to J(x)=J(z). At that point, we show that an even larger number of states collapse exponentially fast with L onto the ground state, and we present numerical evidence that this number is precisely 2 x 2(L). We also extend the symmetry analysis of the model to arbitrary spins and show that the twofold degeneracy of all eigenstates remains true for arbitrary half-integer spins but does not apply to integer spins, in which cases the eigenstates are generically nondegenerate, a result confirmed by exact diagonalizations in the spin-1 case. Implications for Mott insulators and Josephson junction arrays are briefly discussed.

Quantum compass model on the square lattice

BECCA F;
2005-01-01

Abstract

Using exact diagonalizations, Green's function Monte Carlo simulations and high-order perturbation theory, we study the low-energy properties of the two-dimensional spin-1/2 compass model on the square lattice defined by the Hamiltonian H=-Sigma(r)(J(x)sigma(r)(x)sigma(r+ex)(x)+J(z)sigma(r)(z)sigma(r+ez)(z)). When J(x)not equal J(z), we show that, on clusters of dimension L x L, the low-energy spectrum consists of 2(L) states which collapse onto each other exponentially fast with L, a conclusion that remains true arbitrarily close to J(x)=J(z). At that point, we show that an even larger number of states collapse exponentially fast with L onto the ground state, and we present numerical evidence that this number is precisely 2 x 2(L). We also extend the symmetry analysis of the model to arbitrary spins and show that the twofold degeneracy of all eigenstates remains true for arbitrary half-integer spins but does not apply to integer spins, in which cases the eigenstates are generically nondegenerate, a result confirmed by exact diagonalizations in the spin-1 case. Implications for Mott insulators and Josephson junction arrays are briefly discussed.
2005
Pubblicato
http://link.aps.org/doi/10.1103/PhysRevB.72.024448
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2939710
 Avviso

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 109
  • ???jsp.display-item.citation.isi??? 106
social impact