TY - JOUR

T1 - Order and disorder in AKLT antiferromagnets in three dimensions

AU - Parameswaran, Siddharth A.

AU - Sondhi, Shivaji Lal

AU - Arovas, Daniel P.

PY - 2009/1/5

Y1 - 2009/1/5

N2 - The models constructed by Affleck, Kennedy, Lieb, and Tasaki (AKLT) [Phys. Rev. Lett. 59, 799 (1987)] describe a family of quantum antiferromagnets on arbitrary lattices, where the local spin S is an integer multiple M of half the lattice coordination number. The equal-time quantum correlations in their ground states may be computed as finite temperature correlations of a classical O (3) model on the same lattice, where the temperature is given by T=1/M. In dimensions d=1 and 2 this mapping implies that all AKLT states are quantum disordered. We consider AKLT states in d=3 where the nature of the AKLT states is now a question of detail depending upon the choice of lattice and spin; for sufficiently large S some form of Néel order is almost inevitable. On the unfrustrated cubic lattice, we find that all AKLT states are ordered, while for the unfrustrated diamond lattice the minimal S=2 state is disordered while all other states are ordered. On the frustrated pyrochlore lattice, we find (conservatively) that several states starting with the minimal S=3 state are disordered. The disordered AKLT models we report here are a significant addition to the catalog of magnetic Hamiltonians in d=3 with ground states known to lack order on account of strong quantum fluctuations.

AB - The models constructed by Affleck, Kennedy, Lieb, and Tasaki (AKLT) [Phys. Rev. Lett. 59, 799 (1987)] describe a family of quantum antiferromagnets on arbitrary lattices, where the local spin S is an integer multiple M of half the lattice coordination number. The equal-time quantum correlations in their ground states may be computed as finite temperature correlations of a classical O (3) model on the same lattice, where the temperature is given by T=1/M. In dimensions d=1 and 2 this mapping implies that all AKLT states are quantum disordered. We consider AKLT states in d=3 where the nature of the AKLT states is now a question of detail depending upon the choice of lattice and spin; for sufficiently large S some form of Néel order is almost inevitable. On the unfrustrated cubic lattice, we find that all AKLT states are ordered, while for the unfrustrated diamond lattice the minimal S=2 state is disordered while all other states are ordered. On the frustrated pyrochlore lattice, we find (conservatively) that several states starting with the minimal S=3 state are disordered. The disordered AKLT models we report here are a significant addition to the catalog of magnetic Hamiltonians in d=3 with ground states known to lack order on account of strong quantum fluctuations.

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U2 - 10.1103/PhysRevB.79.024408

DO - 10.1103/PhysRevB.79.024408

M3 - Article

AN - SCOPUS:59249107224

SN - 1098-0121

VL - 79

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 2

M1 - 024408

ER -