Frédéric Michaud

Antiferromagnetic Spin-S Chains with Exactly Dimerized Ground States

We show that spin S Heisenberg spin chains with an additional three-body interaction of the form (S(i-1)·S(i))(S(i)·S(i+1))+H.c. possess fully dimerized ground states if the ratio of the three-body interaction to the bilinear one is equal to 1/[4S(S+1)-2]. This result generalizes the Majumdar-Ghosh point of the J1-J2 chain, to which the present model reduces for S=1/2. For S=1, we use the density matrix renormalization group method to show that the transition between the Haldane and the dimerized phases is continuous with a central charge c=3/2. Finally, we show that such a three-body interaction appears naturally in a strong-coupling expansion of the Hubbard model, and we discuss the consequences for the dimerization of actual antiferromagnetic chains.

Realization of higher Wess-Zumino-Witten models in spin chains

Building on the generalization of the exactly dimerized Majumdar-Ghosh ground state to arbitrary spin S for the Heisenberg chain with a three-site term (Si-1 . S-i)(S-i . Si+1) + H.c., we use density-matrix renormalization group simulations and exact diagonalizations to determine the nature of the dimerization transition for S = 1, 3/2, and 2. The resulting central charge and critical exponent are in good agreement with the SU(2)(k=2S) Wess-Zumino-Witten values c = 3k/(2 + k) and eta = 3/(2 + k). Since the three-site term that induces dimerization appears naturally if exchange interactions are calculated beyond second order, these results suggest that SU(2)(k>1) Wess-Zumino-Witten models might finally be realized in actual spin chains. DOI: 10.1103/PhysRevB.87.140404

Frustration- induced plateaus in S >= 1/2 Heisenberg spin ladders

We study the T=0 magnetization of frustrated two-leg spin ladders with arbitrary value of the spin S. In the strong-rung limit, we use degenerate perturbation theory to prove that frustration leads to magnetization plateaus at fractional values of the magnetization for all spins S and to determine the critical ratios of parallel to diagonal inter-rung couplings for the appearance of these plateaus. These ratios depend both on the plateau and on the spin. To confirm these results and to investigate the properties of these ladders away from the strong-coupling limit, we have performed extensive density-matrix renormalization-group calculations for S <= 2. For large enough inter-rung couplings, all plateaus simply disappear, leading to a magnetization curve typical of integer-spin chains in a magnetic field. The intermediate region turns out to be surprisingly rich however, with, upon increasing the inter-rung couplings, the development of magnetization jumps and, in some cases, the appearance of one or more phase transitions inside a given plateau.

Theory of inelastic light scattering in spin-1 systems: Resonant regimes and detection of quadrupolar order

Motivated by the lack of an obvious spectroscopic probe to investigate nonconventional order such as quadrupolar orders in spin S > 1/2 systems, we present a theoretical approach to inelastic light scattering for spin-1 quantum magnets in the context of a two-band Hubbard model. In contrast to the S = 1/2 case, where the only type of local excited state is a doubly occupied state of energy U, several local excited states with occupation up to four electrons are present. As a consequence, we show that two distinct resonating scattering regimes can be accessed depending on the incident photon energy. For (h) over bar omega(in) less than or similar to U, the standard Loudon-Fleury operator remains the leading term of the expansion as in the spin-1/2 case. For (h) over bar omega(in) less than or similar to 4U, a second resonant regime is found with a leading term that takes the form of a biquadratic coupling similar to(S-i . S-j)(2). Consequences for the Raman spectra of S = 1 magnets with magnetic or quadrupolar order are discussed. Raman scattering appears to be a powerful probe of quadrupolar order.

Berry phase investigation of spin-S ladders

We investigate the properties of antiferromagnetic spin-S ladders with the help of local Berry phases defined by imposing a twist on one or a few local bonds. In gapped systems with time-reversal symmetry, these Berry phases are quantized, hence able in principle to characterize different phases. In the case of a fully frustrated ladder where the total spin on a rung is a conserved quantity that changes abruptly upon increasing the rung coupling, we show that two Berry phases are relevant to detect such phase transitions: the rung Berry phase defined by imposing a twist on one rung coupling, and the twist Berry phase defined by twisting the boundary conditions along the legs. In the case of nonfrustrated ladders, we have followed the fate of both Berry phases when interpolating between standard ladders and dimerized spin chains, with the surprising conclusion that, at least far enough from dimerized chains, they define different domains in parameter space. A careful investigation of the spin gap and of edge states shows that a change of twist Berry phase is associated with a quantum phase transition at which the bulk gap closes, and at which, with appropriate boundary conditions, edge states appear or disappear, while a change of rung Berry phase is not necessarily associated with a quantum phase transition. The difference is particularly acute for regular ladders, in which the twist Berry phase does not change at all upon increasing the rung coupling from zero to infinity while the rung Berry phase changes 2S times. By analogy with the fully frustrated ladder, these changes are interpreted as crossovers between domains in which the rungs are in different states of total spin from 0 in the strong rung limit to 2S in the weak rung limit. This interpretation is further supported by the observation that these crossovers turn into real phase transitions as a function of rung coupling if one rung is strongly ferromagnetic, or equivalently if one rung is replaced by a spin 2S impurity.

Intermediate magnetization plateaus in the spin-1/2 Ising-Heisenberg and Heisenberg models on two-dimensional triangulated lattices

The ground state and zero-temperature magnetization process of the spin-1/2 Ising-Heisenberg model on two-dimensional triangles-in-triangles lattices is exactly calculated using eigenstates of the smallest commuting spin clusters. Our ground-state analysis of the investigated classical--quantum spin model reveals three unconventional dimerized or trimerized quantum ground states besides two classical ground states. It is demonstrated that the spin frustration is responsible for a variety of magnetization scenarios with up to three or four intermediate magnetization plateaus of either quantum or classical nature. The exact analytical results for the Ising-Heisenberg model are confronted with the corresponding results for the purely quantum Heisenberg model, which were obtained by numerical exact diagonalizations based on the Lanczos algorithm for finite-size spin clusters of 24 and 21 sites, respectively. It is shown that the zero-temperature magnetization process of both models is quite reminiscent and hence, one may obtain some insight into the ground states of the quantum Heisenberg model from the rigorous results for the Ising-Heisenberg model even though exact ground states for the Ising-Heisenberg model do not represent true ground states for the pure quantum Heisenberg model.