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Register a new userDimer phases in quantum antiferromagnets with orbital degeneracy
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We study and solve the ground-state problem of a microscopic model for a family of orbitally degenerate quantum magnets. The orbital degrees of freedom are assumed to have directional character and are represented by static Potts-like variables. In the limit of vanishing Hunds coupling, the ground-state manifold of such a model is spanned by the hard-core dimer (spin singlet) coverings of the lattice. The extensive degeneracy of dimer coverings is lifted at a finite Hunds coupling through an order-out-of-disorder mechanism by virtual triplet excitations. The relevance of our results to several experimentally studied systems is discussed.
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We study spin-wave interactions in quantum antiferromagnets by expressing the usual magnon annihilation and creation operators in terms of Hermitian field operators representing transverse staggered and ferromagnetic spin fluctuations. In this parameterization, which was anticipated by Anderson in 1952, the two-body interaction vertex between staggered spin fluctuations vanishes at long wavelengths. We derive a new effective action for the staggered fluctuations only by tracing out the ferromagnetic fluctuations. To one loop order, the renormalization group flow agrees with the nonlinear-$sigma$-model approach.
Field-induced excitation gaps in quantum spin chains are an interesting phenomenon related to confinements of topological excitations. In this paper, I present a novel type of this phenomenon. I show that an effective magnetic field with a fourfold screw symmetry induces the excitation gap accompanied by dimer orders. The gap and dimer orders induced so exhibit characteristic power-law dependence on the fourfold screw-symmetric field. Moreover, the field-induced dimer order and the field-induced Neel order coexist when the external uniform magnetic field, the fourfold screw-symmetric field, and the twofold staggered field are applied. This situation is in close connection with a compound [Cu(pym)(H$_2$O)$_4$]SiF$_6$ [J. Liu et al., Phys. Rev. Lett. 122, 057207 (2019)]. In this paper, I discuss a mechanism of field-induced dimer orders by using a density-matrix renormalization group method, a perturbation theory, and quantum field theories.
Motivated by the recent synthesis of the spin-1 A-site spinel NiRh$_{text 2}$O$_{text 4}$, we investigate the classical to quantum crossover of a frustrated $J_1$-$J_2$ Heisenberg model on the diamond lattice upon varying the spin length $S$. Applying a recently developed pseudospin functional renormalization group (pf-FRG) approach for arbitrary spin-$S$ magnets, we find that systems with $S geq 3/2$ reside in the classical regime where the low-temperature physics is dominated by the formation of coplanar spirals and a thermal (order-by-disorder) transition. For smaller local moments $S$=1 or $S$=1/2 we find that the system evades a thermal ordering transition and forms a quantum spiral spin liquid where the fluctuations are restricted to characteristic momentum-space surfaces. For the tetragonal phase of NiRh$_{text 2}$O$_{text 4}$, a modified $J_1$-$J_2^-$-$J_2^perp$ exchange model is found to favor a conventionally ordered Neel state (for arbitrary spin $S$) even in the presence of a strong local single-ion spin anisotropy and it requires additional sources of frustration to explain the experimentally observed absence of a thermal ordering transition.
We map the problem of the orbital excitation (orbiton) in a 2D antiferromagnetic and ferroorbital ground state onto a problem of a hole in 2D antiferromagnet. The orbiton turns out to be coupled to magnons and can only be mobile on a strongly renormalized scale by dressing with magnetic excitations. We show that this leads to a dispersion relation reflecting the two-site unit cell of the antiferromagnetic background, in contrast to the predictions based on a mean-field approximation and linear orbital-wave theory.
We calculate the bipartite von Neumann and second Renyi entanglement entropies of the ground states of spin-1/2 dimerized Heisenberg antiferromagnets on a square lattice. Two distinct dimerization patterns are considered: columnar and staggered. In both cases, we concentrate on the valence bond solid (VBS) phase and describe such a phase with the bond-operator representation. Within this formalism, the original spin Hamiltonian is mapped into an effective interacting boson model for the triplet excitations. We study the effective Hamiltonian at the harmonic approximation and determine the spectrum of the elementary triplet excitations. We then follow an analytical procedure, which is based on a modified spin-wave theory for finite systems and was originally employed to calculate the entanglement entropies of magnetic ordered phases, and calculate the entanglement entropies of the VBS ground states. In particular, we consider one-dimensional (line) subsystems within the square lattice, a choice that allows us to consider line subsystems with sizes up to $L = 1000$. We combine such a procedure with the results of the bond-operator formalism at the harmonic level and show that, for both dimerized Heisenberg models, the entanglement entropies of the corresponding VBS ground states obey an area law as expected for gapped phases. For both columnar-dimer and staggered-dimer models, we also show that the entanglement entropies increase but do not diverge as the dimerization decreases and the system approaches the Neel--VBS quantum phase transition. Finally, the entanglement spectra associated with the VBS ground states are presented.
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