From SU(2)5 to SU(2)3 Wess-Zumino-Witten transitions in a frustrated spin-52 chain

We investigate the properties of a frustrated spin-5/2 chain with next-nearest-neighbor two- and three-site interactions, with two questions in mind: the nature of the transition into the dimerized phase induced by the three-site interaction, and the possible presence of a critical floating phase at intermediate values of the nextnearest-neighbor interaction. We provide strong evidence that the continuous transition into the dimerized phase, which has been found to be generically in the Wess-Zumino-Witten SU(2)2S universality class up to spin S = 2, is SU(2)5 only at two isolated points of the phase diagram, and that it is SU(2)3 in between, in agreement with the presence of two relevant operators allowed by symmetry for SU(2)5, and with the conservation of the parity of the level index along the renormalization flow between SU(2)k theories with different values of k. We also find that the dimerization induced by the next-nearest-neighbor interaction is a three step process, with first a small partially dimerized phase followed by a broad critical floating phase with incommensurate correlations before the fully dimerized phase is reached. Implications for the iron oxide Bi3FeMo2O12 are briefly discussed.

Dimerization and exotic criticality in spin-S chains

Natalia Chepiga

In this thesis we have studied the emergence of spontaneously dimerized phases in frustrated spin-S chains, with emphasis on the nature of the critical lines between the dimerized and non-dimerized phases. The main numerical method used in this thesis is the Density Matrix Renormalization Group (DMRG). The DMRG algorithm is a relatively old and well established method for the investigation of the ground-state. In this thesis, we show how to use this algorithm to calculate the excitation spectra of one-dimensional critical systems, known in the context of conformal field theory as conformal towers of states. We have demonstrated that the method works very well for two simple minimal models (the transverse-field Ising model and the three-state Potts model), and we have used it systematically to identify the universality classes and the underlying conformal field theories of various one-dimensional spin systems. It has been known for a long time that the transition to a spontaneously dimerized phase in a spin-1 chain can be either continuous, in the Wess-Zumino-Witten (WZW) SU(2) level 2 universality class, or first order. By combining a careful numerical investigation with a conformal field theory analysis, we were able to detect in a frustrated spin-1 chain with competing next-nearest-neighbor and three-site interactions the presence of yet another type of continuous phase transition that belongs to the Ising universality class. In contrast to the WZW SU(2) level 2 critical line, at which the singlet-triplet gap closes, the Ising transition occurs entirely in the singlet sector, while the singlet-triplet gap remains open. The use of the standard DMRG approach, along the lines mentioned above, has allowed us to provide explicit numerical evidence for the presence of a conformal tower of singlets inside the spin gap. Moreover, according to field theory, a WZW SU(2) level k critical line can turn into a first order transition due to the presence of a marginal operator in the WZW SU(2) level k model. A careful investigation of the conformal towers along the critical lines has allowed us to find the precise location of this point in both S=1 and S=3/2 chains. We have also shown that the nature of the continuous dimerization transitions is related to the topological properties of the corresponding phases, and that the phase diagrams of various frustrated spin chains can be effectively extracted by looking at the local topological order parameter - the degeneracy of the lowest state in the entanglement spectrum. When coupled with the conformal field theory of open systems, DMRG appears to be an extremely powerful tool to characterize not only the phase diagram and the ground-state correlations of quantum one-dimensional systems, but also the excitation spectrum and the conformal structure along critical lines.

EPFL2017

Spontaneous dimerization, critical lines, and short-range correlations in a frustrated spin-1 chain

Natalia Chepiga, Frédéric Mila

We report on a detailed investigation of the spin-1 J1−J2−J3 Heisenberg model, a frustrated model with nearest-neighbor coupling J1, next-nearest neighbor coupling J2, and a three-site interaction J3[(Si−1⋅Si)(Si⋅Si+1)+H.c.] previously studied in [Phys. Rev. B 93, 241108(R) (2016)]. Using density matrix renormalization group (DMRG) and exact diagonalizations, we show that the phase boundaries between the Haldane phase, the next-nearest neighbor Haldane phase, and the dimerized phase can be very accurately determined by combining the information deduced from the dimerization, the ground-state energy, the entanglement spectrum and the Berry phase. By a careful investigation of the finite-size spectrum, we also show that the transition between the next-nearest neighbor Haldane phase and the dimerized phase is in the Ising universality class all along the critical line. Furthermore, we justify the conformal embedding of the SU(2)2 Wess-Zumino-Witten conformal field theory in terms of a boson and an Ising field, and we explicitly derive a number of consequences of this embedding for the spectrum along the SU(2)2 transition line between the Haldane phase and the dimerized phase. We also show that the solitons along the first-order transition line between the Haldane phase and the dimerized phase carry a spin-1/2, while the domain walls between different dimerization domains inside the dimerized phase carry a spin 1. Finally, we show that short-range correlations change character in the Haldane and dimerized phases through disorder and Lifshitz lines, as well as through the development of short-range dimer correlations in the Haldane phase, leading to a remarkably rich phase diagram.

2016

Dimerization transitions in spin-1 chains

Natalia Chepiga, Frédéric Mila

We study spontaneous dimerization transitions in a Heisenberg spin-1 chain with additional next-nearest-neighbor and three-site interactions using extensive numerical simulations and a conformal field-theory analysis. We show that the transition can be second order in the Wess-Zumino-Witten (WZW) SU(2)2 or Ising universality class, or first order. We argue that these features are generic because of a marginal operator in the WZW SU(2)2 model and because of two topologically distinct nondimerized phases with or without edge states. We also provide explicit numerical evidence of conformal towers of singlets inside the spin gap at the Ising transition. Implications for other models are briefly discussed.

2016

Dimerization and exotic criticality in spin-S chains

Natalia Chepiga

EPFL2017