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Register a new userExceptional Symmetry of G$_2$ in Spin-$frac{3}{2}$ Fermion Systems
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As the smallest exceptional Lie group and the automorphism group of the non-associative algebra of octonions, G$_2$ is often employed for describing exotic symmetry structures. We prove a G$_2$ symmetry in a Hubbard-like model with spin-$frac{3}{2}$ fermions in a bipartite lattice, which lies in the intersection of two SO(7) algebras connected by the structure constants of octonions. Depending on the representations of the order parameters, the G$_2$ symmetry can be spontaneously broken into either an SU(3) one associated with an $S^6$ Goldstone manifold, or, into an SU(2)$times$U(1) with a Grassmannian Goldstone manifold $mbox{Gr}_5^+(mathbb{R}^7)$. In the quantum disordered states, quantum fluctuations generate the effective SU(3) and SU(2)$times$U(1) gauge theories for low energy fermions.
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Correlated band theory implemented as a combination of density functional theory with exact diagonalization [DFT+U(ED)] of the Anderson impurity term with Coulomb repulsion $U$ in the open 14-orbital $5f$ shell is applied to UTe$_2$. The small gap for $U$=0, evidence of the half-filled $j=frac{5}{2}$ subshell of $5f^3$ uranium, is converted for $U$=3 eV to a flat band semimetal with small heavy-carrier Fermi surfaces that will make properties sensitive to pressure, magnetic field, and off-stoichiometry, as observed experimentally. The predicted Kondo temperature around 100 K matches the experimental values from resistivity. The electric field gradients for the two Te sites are calculated by DFT+U(ED) to differ by a factor of seven, indicating a strong site distinction, while the anisotropy factor $eta=0.18$ is similar for all three sites. The calculated uranium moment $<M^2>^{1/2}$ of 3.5$mu_B$ is roughly consistent with the published experimental Curie-Weiss values of 2.8$mu_B$ and 3.3$mu_B$ (which are field-direction dependent), and the calculated separate spin and orbital moments are remarkably similar to Hunds rule values for an $f^3$ ion. The $U$=3 eV spectral density is compared with angle-integrated and angle-resolved photoemission spectra, with agreement that there is strong $5f$ character at, and for several hundred meV below, the Fermi energy. Our results support the picture that the underlying ground state of UTe$_2$ is that of a half-filled $j=frac{5}{2}$ subshell with two half-filled $m_j=pmfrac{1}{2}$ orbitals forming a narrow gap by hybridization, then driven to a conducting state by configuration mixing (spin-charge fluctuations). UTe$_2$ displays similarities to UPt$_3$ with its $5f$ dominated Fermi surfaces rather than a strongly localized Kondo lattice system.
It was proposed in [(https://doi.org/10.1103/PhysRevLett.114.145301){Chen et al., Phys. Rev. Lett. $mathbf{114}$, 145301 (2015)}] that spin-2 chains display an extended critical phase with enhanced SU$(3)$ symmetry. This hypothesis is highly unexpected for a spin-2 system and, as we argue, would imply an unconventional mechanism for symmetry emergence. Yet, the absence of convenient critical points for renormalization group perturbative expansions, allied with the usual difficulty in the convergence of numerical methods in critical or small-gapped phases, renders the verification of this hypothetical SU$(3)$-symmetric phase a non-trivial matter. By tracing parallels with the well-understood phase diagram of spin-1 chains and searching for signatures robust against finite-size effects, we draw criticism on the existence of this phase. We perform non-Abelian density matrix renormalization group studies of multipolar static correlation function, energy spectrum scaling, single-mode approximation, and entanglement spectrum to shed light on the problem. We determine that the hypothetical SU$(3)$ spin-2 phase is, in fact, dominated by ferro-octupolar correlations and also observe a lack of Luttinger-liquid-like behavior in correlation functions that suggests that is perhaps not critical. We further construct an infinite family of spin-$S$ systems with similar ferro-octupolar-dominated quasi-SU$(3)$-like phenomenology; curiously, we note that the spin-3 version of the problem is located in a subspace of exact G$_2$ symmetry, making this a point of interest for search of Fibonacci topological properties in magnetic systems.
The Kondo-Spin Glass competition is studied in a theoretical model of a Kondo lattice with an intra-site Kondo type exchange interaction treated within the mean field approximation, an inter-site quantum Ising exchange interaction with random couplings among localized spins and an additional transverse field in the x direction, which represents a simple quantum mechanism of spin flipping. We obtain two second order transition lines from the spin-glass state to the paramagnetic one and then to the Kondo state. For a reasonable set of the different parameters, the two second order transition lines do not intersect and end in two distinct QCP.
We report on the synthesis of a new $gamma$-phase of the spin $S$~=~$frac{3}{2}$ compound SrCo$_2$(PO$_4$)$_2$ together with a detailed structural, magnetic and thermodynamic properties. The $gamma$-phase of SrCo$_2$(PO$_4$)$_2$ crystallizes in a triclinic crystal structure with the space group $Pbar{1}$. Susceptibility and specific heat measurements reveal that SrCo$_2$(PO$_4$)$_2$ orders antiferromagnetically below $T_{rm N}simeq 8.5$,K and the nature of ordering is three dimensional (3D). The magnetic isotherm at temperatures below $T_{rm N}$ shows a field-induced spin-flop transition, related to the magnetocrystalline anisotropy, at an applied field of $sim$~4.5~Tesla. Remarkably, heat capacity shows magnetic-field-induced transitions at $T_{rm N1}$ = 3.6 K and $T_{rm N2}$ = 7.4 K. The magnetic long range ordering (LRO) is also confirmed in both the Knight shift and spin-lattice relaxation rate ($1/T_{1}$) of the $^{31}$P-NMR measurements. However, below the LRO we have not detected any NMR signal due to faster relaxation. We have detected two structurally different phosphorous sites in $gamma$-phase of SrCo$_{2}$(PO$_{4}$)$_{2}$ and they shift differently with temperature.
In this work we study the possible occurrence of topological insulators for 2D fermions of high spin. They can be realized in cold fermion systems with ground-state atomic spin $F>tfrac{1}{2}$, if the optical potential is properly designed, and spin-orbit coupling is relevant. The latter is shown to be induced by letting the fermions interact with a specially tuned arrangement of polarized laser beams. When the system is subject to a perpendicular magnetic field, time reversal symmetry is broken but the ensuing Hamiltonian is still endowed with a mirror symmetry. Topological insulators for fermions of higher spins are fundamentally distinct from those pertaining to spin $frac{1}{2}$. The underlying physics reveals a plethora of positive and negative mirror Chern numbers, respectively corresponding to chiral and anti-chiral edge states. Here, for simplicity, we concentrate on the case $F=tfrac{3}{2}$ (which is suitable for $^{6}$Li or $^2$H atoms) but extension to higher spins (such as $^{40}$K whose ground-state spin is $F=tfrac{9}{2}$), is straightforward.
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