Frustration and Multicriticality in the Antiferromagnetic Spin-1 Chain

We study the spin $S=1$ Heisenberg chain, with nearest neighbor, next nearest neighbor ($\alpha$) and biquadratic ($\beta$) interactions using a combination of the density matrix renormalization group (DMRG), an analytic variational matrix product state wavefunction, and non-Abelian bosonization. We study the effect of frustration ($\alpha>0$) on the Haldane phase with $-1\leq \beta < 1$ which reveals a rich phase diagram. For $-1<\beta<\beta^\ast$, we establish the existence of a spontaneously dimerized phase for large $\alpha>\alpha_c$, separated from the Haldane phase by the critical line $\alpha_c(\beta)$ of second-order phase transitions connected to the Takhtajan--Babudjian integrable point $\alpha_c(\beta=-1)=0$. In the opposite regime, $\beta>\beta^\ast$, the transition from the Haldane phase becomes first-order into the next nearest neighbor (NNN) AKLT phase. Based on field theoretical arguments and DMRG calculations, we conjecture that these two regimes are separated by a multicritical point ($\beta^\ast, \alpha^\ast$) of a different universality class, described by the $SU(2)_4$ Wess--Zumino--Witten critical theory. From the DMRG calculations we estimate this multicritical point to lie in the range $-0.2<\beta^\ast<-0.15$ and $0.47<\alpha^\ast < 0.53$. We find that the dimerized and NNN-AKLT phases are separated by a line of first-order phase transitions that terminates at the multicritical point. Inside the Haldane phase, we show the existence of two incommensurate crossovers: the Lifshitz transition and the disorder transition of the first kind, marking incommensurate correlations in momentum and real space, respectively. We show these crossover lines stretch across the entire $(\beta,\alpha)$ phase diagram, merging into a single incommensurate-to-commensurate transition line for negative $\beta\lesssim \beta^\ast$ outside the Haldane phase.Comment: 25 pages, 24 figures, updated with published versio

Quantum Phases of the Shastry-Sutherland Kondo Lattice: Implications for the Global Phase Diagram of Heavy Fermion Metals

Considerable recent theoretical and experimental efforts have been devoted to the study of quantum criticality and novel phases of antiferromagnetic heavy-fermion metals. In particular, quantum phase transitions have been discovered in the compound Yb$_2$Pt$_2$Pb. These developments have motivated us to study the competition between the RKKY and Kondo interactions on the Shastry-Sutherland lattice. We determine the zero-temperature phase diagram as a function of magnetic frustration and Kondo coupling within a slave-fermion approach. Pertinent phases include the Shastry-Sutherland valence bond solid and heavy Fermi liquid. In the presence of antiferromagnetic order, our zero-temperature phase diagram is remarkably similar to the global phase diagram proposed earlier based on general grounds. We discuss the implications of our results for the experiments on Yb$_2$Pt$_2$Pb and other geometrically frustrated heavy fermion compounds.Comment: 5 pages 4 figures - Supplementary Material 4 pages 6 figures. Updated with published versio

Cluster Extended Dynamical Mean Field Approach and Unconventional Superconductivity

The extended dynamical mean field theory has played an important role in the study of quantum phase transitions in heavy fermion systems. In order to incorporate the physics of unconventional superconductivity, we develop a cluster version of the extended dynamical mean field theory. In this approach, we show how magnetic order and superconductivity develop as a result of inter-site spin exchange interactions, and analyze in some detail the form of correlation functions. We also discuss the methods that can be used to solve the dynamical equations associated with this approach. Finally, we consider different settings in which our approach can be applied, including the periodic Anderson model for heavy fermion systems.Comment: 15 pages, 2 figures, Replaced with published versio