2020/03/31 by R. L. Doretto
Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Atomic orbital #Ground state #Heisenberg model #Mean field theory #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Valence bond theory #Von Neumann entropy #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.102.014415
published as Phys. Rev. B 102, 014415 (2020) · 21 pages, 11 figures, final version
openalex publication_date 2020/07/10 · arxiv created 2020/07/14 · arxiv updated 2020/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We study a system of N interacting triplons (the elementary excitations of a valence-bond solid) described by an effective interacting boson model derived within the bond operator formalism in order to determine the stability and the properties of many-triplon states. In particular, we consider the square lattice spin-1/2\phantom\rule4pt0exJ1\ensuremath-J2 antiferromagnetic Heisenberg model, focus on the intermediate parameter region where a quantum paramagnetic phase sets in, and consider the columnar valence-bond solid as a reference state. Within the bond operator theory, the Heisenberg model is mapped into an effective boson model in terms of triplet operators t. The effective boson model is studied at the harmonic approximation and the energy of the triplons and the expansion of the triplon operators b in terms of the triplet operators t are determined. Such an expansion allows us to perform a second mapping and, therefore, determine an effective interacting boson model in terms of the triplon operators b. We then consider systems with a fixed number N of triplons and study the stability of many-triplon states within a mean-field approximation. We show that many-triplon states are stable, the lowest-energy ones are constituted by a small number of triplons, and the excitation gaps are finite. For J2=0.48J1 and 0.52J1, we also calculate spin-spin and dimer-dimer correlation functions, dimer order parameters, and the bipartite von Neumann entanglement entropy within our mean-field formalism in order to determine the properties of the many-triplon state as a function of the triplon number N. We find that the spin and the dimer correlations decay exponentially and that the entanglement entropy obeys an area law, regardless of the triplon number N. Moreover, only for J2=0.48J1, the spin correlations indicate that the many-triplon states with large triplon number N might display a more homogeneous singlet pattern than the columnar valence-bond solid. We also comment on possible relations between the many-triplon states with large triplon number N and gapped spin-liquid states.