Valence Bond Solid Phase Research Articles

Finite-temperature properties of quantum Lifshitz transitions between valence-bond solid phases: An example of local quantum criticality

We study the finite-temperature properties of quantum magnets close to a continuous quantum phase transition between two distinct valence-bond solid phases in two spatial dimension. Previous work has shown that such a second order quantum ``Lifshitz'' transition is described by a free field theory and is hence tractable, but is nevertheless nontrivial. At $T>0$, we show that while correlation functions of certain operators exhibit $\ensuremath{\omega}∕T$ scaling, they do not show analogous scaling in space. In particular, in the scaling limit, all such correlators are purely local in space, although the same correlators at $T=0$ decay as a power law. This provides a valuable microscopic example of a certain kind of local quantum criticality. The local form of the correlations arises from the large density of soft modes present near the transition that are excited by temperature. We calculate exactly the autocorrelation function for such operators in the scaling limit. Going beyond the scaling limit by including irrelevant operators leads to finite spatial correlations that are also obtained.

Quantum criticality and deconfinement in phase transitions between valence bond solids

We consider spin-half quantum antiferromagnets in two spatial dimensions in the quantum limit, where the spins are in a valence bond solid (VBS) phase. The transitions between two such VBS phases is studied. In some cases, an interesting second order transition controlled by a fixed line with varying critical exponents if found. A specific example is provided by an antiferromagnetically coupled bilayer system on the honeycomb lattice where a continuous quantum phase transition can generically exist between two VBS phases. Furthermore, these critical points are deconfined, in the sense that gapped spin-1/2 spinon excitations emerge right at the transition. The low energy physics of this critical point (upto marginally irrelevant interactions) contains just a free quadratically dispersing `photon'. The phase structure on one side of this continuous transition is very intricate consisting of a series of infinitely closely spaced further transitions in a `devil's staircase' form. Analogies with previous examples of deconfined quantum criticality are emphasized. Closely related transitions in single layer systems are explored. These are second order only at some multicritical points. The solvable Rokshar-Kivelson point of quantum dimer models of single layer systems is found to correspond to a very special non-generic multicritical point

Valence-bond crystal phase of the crossed-chain quantum spin model

Using a series expansion based on the flow-equation method we study the ground state energy and the elementary triplet excitations of a generalized model of crossed spin-1/2 chains starting from the limit of decoupled quadrumers. The triplet dispersion is shown to be very sensitive to the inter-quadrumer frustration, exhibiting a line of almost complete localization as well as lines of quantum phase transitions limiting the stability of the valence-bond solid phase. In the vicinity of the checkerboard-point a finite window of exchange couplings is found with a non-zero spin-gap, consistent with known results from exact diagonalization. The ground state energy is lower than that of the bare quadrumer case for all exchange couplings investigated. In the limiting situation of the fully frustrated checkerboard magnet our results agree with earlier series expansion studies.

High-Tcferromagnetism in theSrB6family: A case of doped spin-1 Mott insulator in a valence-bond solid phase

Doped divalent hexaborides such as ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{B}}_{6}$ exhibit a high ${T}_{c}$ ferromagnetism. We isolate a degenerate pair of $2p$ orbitals of boron with two valence electrons, invoke electron correlation and Hund coupling, to suggest that the undoped state is better viewed as a spin-1 Mott insulator; it is predicted to be a type of $3d$ Haldane gap phase with a spin gap $\ensuremath{\sim}0.1\mathrm{eV},$ much smaller than the charge gap of $>1.0\mathrm{eV}$ seen in angle-resolved photoemission spectroscopy. The experimentally seen high ${T}_{c}$ ``ferromagnetism'' is argued to be a complex magnetic order in disguise---either a canted six-sublattice antiferromagnetic $(\ensuremath{\approx}120\ifmmode^\circ\else\textdegree\fi{})$ order or its quantum melted version, a chiral spin liquid state, arising from a type of double-exchange mechanism.