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AIP Advances

Field-induced phase transitions of tetramer-singlet states in synthetic SU(4) magnets

Yuki Miyazaki, Daisuke Yamamoto, Giacomo Marmorini, Nobuo Furukawa

Published Feb 1, 2021• 4 citations
Publisher

Abstract

Phase transitions of quantum dimer magnets can be explained in terms of Bose-Einstein condensation of magnons. Here we consider a natural extension of the dimer magnets to SU(4)-symmetric tetramer systems, which could be created with four nuclear-spin components (named “u,” “d,” “c,” and “s”) of 173Yb atoms in optical superlattices. We apply the cluster mean-field approximation to the SU(4) Heisenberg model on a tetramerized square lattice, and study the phase transition phenomena in the presence of the field that creates a population imbalance between the two components u,d and the other two c,s. When the population of the four components is balanced, the ground state is approximately given by the direct product of local SU(4)-singlet states. When the field is applied, the population ratio of the components u and d is increased and the system eventually reaches a “saturated” state, which is a SU(2) system with only u and d. We show that in the saturation process, the system exhibits two successive step-like transitions, in contrast to the standard dimer magnets with continuous transition process associated with Bose-Einstein condensation of magnons. The intermediate phase in between the two step-like transitions is a nontrivial solid phase with alternating arrangement of the SU(4)-singlet and four-site resonating-valence-bond states.

DOI
10.1063/9.0000227

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Phase transitions of quantum dimer magnets can be explained in terms of Bose-Einstein condensation of magnons. Here we consider a natural extension of the dimer magnets to SU(4)-symmetric tetramer systems, which could be created with four nuclear-spin components (named “u,” “d,” “c,” and “s”) of 173Yb atoms in optical superlattices. We apply the cluster mean-field approximation to the SU(4) Heisenberg model on a tetramerized square lattice, and study the phase transition phenomena in the presence of the field that creates a population imbalance between the two components u,d and the other two c,s. When the population of the four components is balanced, the ground state is approximately given by the direct product of local SU(4)-singlet states. When the field is applied, the population ratio of the components u and d is increased and the system eventually reaches a “saturated” state, which is a SU(2) system with only u and d. We show that in the saturation process, the system exhibits two successive step-like transitions, in contrast to the standard dimer magnets with continuous transition process associated with Bose-Einstein condensation of magnons. The intermediate phase in between the two step-like transitions is a nontrivial solid phase with alternating arrangement of the SU(4)-singlet and four-site resonating-valence-bond states.
We study the quantum magnetism of the SU(4) Mott insulator in a square optical superlattice, in which atoms with four nuclear-spin components strongly interact with each other, in the presence of an external field that controls the imbalance between the population of two components and that of the other two. This is a natural extension of the physics of spin-dimer materials under strong magnetic field. We apply an extended linear flavor-wave theory based on four-site plaquettes and unveil the ground-state phase diagram and excitation spectra. When the population of the four components is balanced and the plaquesttes are weakly coupled, the ground state is approximately given by the direct product of local SU(4)-singlet states. In high-field, the system reaches a "saturated state" where only two components are present. Our main finding is a nontrivial intermediate phase, which has a checkerboard-like arrangement of the SU(4)-singlet and four-site resonating-valence-bond states.
In systems with many local degrees of freedom, high-symmetry points in the phase diagram can provide an important starting point for the investigation of their properties throughout the phase diagram. In systems with both spin and orbital (or valley) degrees of freedom such a starting point gives rise to SU(4)-symmetric models. Here we consider SU(4)-symmetric "spin'' models, corresponding to Mott phases at half-filling, i.e. the six-dimensional representation of SU(4). This may be relevant to twisted multilayer graphene. In particular, we study the SU(4) antiferromagnetic "Heisenberg'' model on the triangular lattice, both in the classical limit and in the quantum regime. Carrying out a numerical study using the density matrix renormalization group (DMRG), we argue that the ground state is non-magnetic. We then derive a dimer expansion of the SU(4) spin model. An exact diagonalization (ED) study of the effective dimer model suggests that the ground state breaks translation invariance, forming a valence bond solid (VBS) with a 12-site unit cell. Finally, we consider the effect of SU(4)-symmetry breaking interactions due to Hund's coupling, and argue for a possible phase transition between a VBS and a magnetically ordered state.
We study field-induced magnetic order in cubic lattices of dimers with antiferromagnetic Heisenberg interactions. The thermal critical exponents at the quantum phase transition from a spin liquid to a magnetically ordered phase are determined from stochastic series expansion quantum Monte Carlo simulations. These exponents are independent of the interdimer coupling ratios, and converge to the value obtained by considering the transition as a Bose-Einstein condensation of magnons, ${\ensuremath{\alpha}}_{\mathrm{BEC}}=\frac{3}{2}.$ The scaling results are of direct relevance to the spin-dimer systems TlCuCl3{\mathrm{TlCuCl}}_{3}TlCuCl3​ and KCuCl3,{\mathrm{KCuCl}}_{3},KCuCl3​, and explain the broad range of exponents reported for field-induced ordering transitions.
We numerically investigate the phase diagram of two-dimensional site-diluted coupled dimer systems in an external magnetic field. We show that this phase diagram is characterized by the presence of an extended Bose glass, not accessible to mean-field approximation, and stemming from the localization of two distinct species of bosonic quasiparticles appearing in the ground state. On the one hand, nonmagnetic impurities doped into the dimer-singlet phase of a weakly coupled dimer system are known to free up local magnetic moments. The deviations of these local moments from full polarization along the field can be mapped onto a gas of bosonic quasiparticles, which undergo condensation in zero and very weak magnetic fields, corresponding to transverse long-range antiferromagnetic order. An increasing magnetic field lowers the density of such quasiparticles to a critical value at which a quantum phase transition occurs, corresponding to the quasiparticle localization on clusters of local magnets (dimers, trimers, etc.) and to the onset of a Bose glass. Strong finite-size quantum fluctuations hinder further depletion of quasiparticles from such clusters, and thus lead to the appearance of pseudoplateaus in the magnetization curve of the system. On the other hand, site dilution hinders the field-induced Bose-Einstein condensation of triplet quasiparticles on the intact dimers, and it introduces instead a Bose glass of triplets. A thorough numerical investigation of the phase diagram for a planar system of coupled dimers shows that the two above-mentioned Bose glass phases are continuously connected, and they overlap in a finite region of parameter space, thus featuring a two-species Bose glass. The quantum phase transition from Bose glass to magnetically ordered phases in two dimensions is marked by novel universal exponents ($z\ensuremath{\approx}2$, $\ensuremath{\beta}\ensuremath{\approx}0.9$, and $\ensuremath{\nu}\ensuremath{\approx}1$). Hence we conclude that doped quantum antiferromagnets in a field represent an ideal setting for the study of fundamental dirty-boson physics.
It is evidenced that effective lattice-gas models of hard-core monomers and dimers afford a proper description of low-temperature features of spin-12\frac{1}{2}21​ Heisenberg diamond and octahedral chains. In addition to monomeric particles assigned within the localized-magnon theory to bound one- and two-magnon eigenstates, the effective monomer-dimer lattice-gas model includes dimeric particles assigned to a singlet-tetramer (singlet-hexamer) state as a cornerstone of dimer-tetramer (tetramer-hexamer) ground state of a spin-12\frac{1}{2}21​ Heisenberg diamond (octahedral) chain. The feasibility of the effective description is confirmed through the exact diagonalization and finite-temperature Lanczos methods. Both quantum spin chains display rich ground-state phase diagrams including discontinuous as well as continuous field-driven phase transitions, whereby the specific heat shows in vicinity of the former phase transitions an extraordinary low-temperature peak coming from a highly degenerate manifold of low-lying excitations.
Quantum phase transition at the saturation field is studied for a class of frustrated quantum antiferromagnets. The considered models include (i) the ${J}_{1}\mathrm{\text{\ensuremath{-}}}{J}_{2}$ frustrated square-lattice antiferromagnet with J2=12J1{J}_{2}=\frac{1}{2}{J}_{1}J2​=21​J1​ and (ii) the nearest-neighbor Heisenberg antiferromagnet on a face centered cubic lattice. In the fully saturated phase the magnon spectra for the two models have lines of degenerate minima. Transition into a partially magnetized state is treated via a mapping to a dilute gas of hard-core bosons and by complementary spin-wave calculations. Momentum dependence of the exact four-point boson vertex removes the degeneracy of the single-particle excitation spectra and selects the ordering wave vectors at $(\ensuremath{\pi},\ensuremath{\pi})$ and $(\ensuremath{\pi},0,0)$ for the two models. We predict a unique form for the magnetization curve $\ensuremath{\Delta}M=S\ensuremath{-}M\ensuremath{\simeq}{\ensuremath{\mu}}^{(d\ensuremath{-}1)/2}(\mathrm{log}\ensuremath{\mu}{)}^{(d\ensuremath{-}1)}$, where $\ensuremath{\mu}$ is a distance from the quantum critical point.