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arXiv:1002.4593 · Physical Review B

AKLT models with quantum spin glass ground states

Chris R. Laumann, S. A. Parameswaran, Shivaji L. Sondhi, Francesco Zamponi

Published May 17, 2010• 18 citations
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Abstract

We study AKLT models on locally treelike lattices of fixed connectivity and find that they exhibit a variety of ground states depending upon the spin, coordination, and global (graph) topology. We find (a) quantum paramagnetic or valence-bond solid ground states, (b) critical and ordered N\'eel states on bipartite infinite Cayley trees, and (c) critical and ordered quantum vector spin glass states on random graphs of fixed connectivity. We argue, in consonance with a previous analysis [C. R. Laumann, S. A. Parameswaran, and S. L. Sondhi, Phys. Rev. B 80, 144415 (2009)], that all phases are characterized by gaps to local excitations. The spin glass states we report arise from random long-ranged loops which frustrate N\'eel ordering despite the lack of randomness in the coupling strengths.

DOI
10.1103/physrevb.81.174204

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We study AKLT models on locally treelike lattices of fixed connectivity and find that they exhibit a variety of ground states depending upon the spin, coordination, and global (graph) topology. We find (a) quantum paramagnetic or valence-bond solid ground states, (b) critical and ordered N'eel states on bipartite infinite Cayley trees, and (c) critical and ordered quantum vector spin glass states on random graphs of fixed connectivity. We argue, in consonance with a previous analysis [C. R. Laumann, S. A. Parameswaran, and S. L. Sondhi, Phys. Rev. B 80, 144415 (2009)], that all phases are characterized by gaps to local excitations. The spin glass states we report arise from random long-ranged loops which frustrate N'eel ordering despite the lack of randomness in the coupling strengths.
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 SSS is an integer multiple MMM 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)O(3)O(3) model on the same lattice, where the temperature is given by T=1/MT=1/MT=1/M. In dimensions d=1d=1d=1 and 2 this mapping implies that all AKLT states are quantum disordered. We consider AKLT states in d=3d=3d=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 SSS some form of N\'eel 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=2S=2S=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=3S=3S=3 state are disordered. The disordered AKLT models we report here are a significant addition to the catalog of magnetic Hamiltonians in d=3d=3d=3 with ground states known to lack order on account of strong quantum fluctuations.
Abstract. We study the structure of quantum ground states of simplex solid models, which are generalizations of the valence bond construction for quantum antiferromagnets originally proposed by Affleck, Kennedy, Lieb, and Tasaki (AKLT) (1987 Phys. Rev. Lett . 59 799). Whereas the AKLT states are created by application of bond singlet operators for spins, the simplex solid construction is based on N -simplex singlet operators for spins. In both cases, a discrete one-parameter family of translationally-invariant models with exactly solvable ground states is defined on any regular lattice, and the equal time ground state correlations are given by the finite temperature correlations of an associated classical model on the same lattice, owing to the product form of the wave functions when expressed in a coherent state representation. We study these classical companion models via a mix of Monte Carlo simulations, mean-field arguments, and low-temperature effective field theories. Our analysis reveals that the ground states of edge- and face-sharing cubic lattice simplex solid models are long range ordered for sufficiently large values of the discrete parameter, whereas the ground states of the models on the kagome (2D) and hyperkagome (3D) lattices are always quantum disordered. The kagome simplex solid exhibits strong local order absent in its three-dimensional hyperkagome counterpart, a contrast that we rationalize with arguments similar to those leading to ‘order by disorder’.
Unveiling nonmagnetic phase and many-body entanglement in two-dimensional random quantum magnets Sr2_22​CuTe1−x_{1-x}1−x​Wx_xx​O6_66​
We apply a random-plaquette J1J_1J1​-J2J_2J2​ model on the square lattice to capture the physics of a series of spin-1/21/21/2 Heisenberg antiferromagnet compounds Sr2_22​CuTe1−x_{1-x}1−x​Wx_xx​O6_66​. With the input of experimentally relevant coupling strengths, our exact diagonalization (ED) study probes the ground state properties beyond previous linear spin-wave approach. An intermediate range of x∈[0.08,0.55]x \in [0.08, 0.55]x∈[0.08,0.55] is identified for a nonmagnetic phase without the long-range Néel or stripe order. The absence of both valence-bond-glass order and spin-glass non-ergodic dynamics renders its nature intriguing. Deep inside this phase around x=0.3x = 0.3x=0.3, we observe signatures potentially linked to randomness-induced short-range spin-liquid-like (SLL) states, including close to zero spin-freezing parameter, vanishing spin-spin correlation beyond nearest neighbors, almost uniform static spin structure factor, as well as a broad tail in the dynamical spin structure factor. The nonmagnetic phase also features multipartite entanglement in the ground state witnessed by quantum Fisher information (QFI), which exhibits universal scaling behaviors at quantum critical points.
The large-N limit of a nearest-neighbor SU(N) antiferromagnet on a bipartite lattice exhibits in dimensions d\ensuremath{\ge}2 a zero-temperature phase transition between a N\'eel ordered state and a resonating-valence-bond state. Here it is shown in d=1,2 that topological effects produce spin-Peierls or valence-bond-solid order in the non-N\'eel phase with a ground-state degeneracy which varies periodically with ``spin'' for fixed N with periodicity given by the coordination number of the lattice. Thus a non-N\'eel phase of the spin-(1/2 Heisenberg model on a square lattice would be a spin-Peierls state with a fourfold degeneracy due to broken lattice rotational symmetry.
We study the structure of quantum ground states of simplex solid models, which are generalizations of the valence bond construction for quantum antiferromagnets originally proposed by Affleck, Kennedy, Lieb, and Tasaki (AKLT) [Phys. Rev. Lett. 59, 799 (1987)]. Whereas the AKLT states are created by application of bond singlet operators for SU(2) spins, the simplex solid construction is based on N-simplex singlet operators for SU(N) spins. In both cases, a discrete one-parameter family of translationally-invariant models with exactly solvable ground states is defined on any regular lattice, and the equal time ground state correlations are given by the finite temperature correlations of an associated classical model on the same lattice, owing to the product form of the wave functions when expressed in a CP^{N-1} coherent state representation. We study these classical companion models via a mix of Monte Carlo simulations, mean-field arguments, and low-temperature effective field theories. Our analysis reveals that the ground states of SU(4) edge- and SU(8) face-sharing cubic lattice simplex solid models are long range ordered for sufficiently large values of the discrete parameter, whereas the ground states of the SU(3) models on the kagome (2D) and hyperkagome (3D) lattices are always quantum disordered. The kagome simplex solid exhibits strong local order absent in its three-dimensional hyperkagome counterpart, a contrast that we rationalize with arguments similar to those leading to `order by disorder'.