Classical and quantum order in hyperkagome antiferromagnets

Abstract

Motivated by recent experiments and density functional theory calculations on a choloalite PbCuTe2O6, which possesses a Cu-based three-dimensional hyperkagome lattice, we propose and study a J1-J2-J3 antiferromagnetic Heisenberg model on a hyperkagome lattice. In the classical limit, possible ground states are analyzed by two triangle rules, i.e., the "hyperkagome triangle rule" and the "isolated triangle rule", and classical Monte-Carlo simulations are exploited to identify possible classical magnetic ordering and explore the phase diagram. In the quantum regime, Schwinger boson theory is applied to study possible quantum spin liquid states and long-range magnetically ordered states on an equal footing. These quantum states with bosonic partons are classified and analyzed by using projective symmetry group (PSG). It is found that there are only four types of algebraic PSGs allowed by the space group P 4132 on a hyperkagome lattice. Moreover, there are only two types of PSGs that are compatible with the J1-J2-J3 Heisenberg model. These two types of Z2 bosonic states are distinct by the gauge-invariant flux on the elementary ten-site loops on the hyperkagome network, called zero-flux state and π-flux state respectively. Both the zero-flux state and the π-flux state are able to give rise to quantum spin liquid states as well as magnetically ordered states. And the zero-flux states and the π-flux states can be distinguished by the spin spectral function S(q, ω), which can be measured by inelastic neutron scattering experiments.

Beyond the Freshman's Dream: Classical fractal spin liquids from matrix cellular automata in three-dimensional lattice models

“…The second lattice we consider is the hyperhyperkagome (HHK) or 'distorted-windmill' structure. This is realized by the magnetic lattice of β-Mn as well as PbCuTe 2 O 6 , both of which have been investigated in the context of frustrated magnetism and spin liquids [27,28,30,32,33] The crystal structure is displayed in Fig. 3, along with the positions of each sublattice α i .…”

“…Rather than deform the model and lattice to ensure a description in terms of scalar CAs, we instead identify two different lattices of corner-sharing trianglestrillium [24,25], and hyperhyperkagome (HHK) [26][27][28] -on which the Baxter-Wu three-spin interaction can be imposed on each plaquette. Both of these lattices have been previously investigated with Heisenbergtype nearest-neighbor spin-spin interactions, in the context of seeking classical and quantum spin liquids stabilized by geometrical frustration [27][28][29][30][31][32][33]. We find that rather than the 'conventional' classical spin liquid behaviour with an extensive T = 0 entropy, the trillium and HHK Baxter-Wu models instead exhibit fractal symmetries with ground state degeneracies that contribute subextensively to the entropy as T → 0, a hallmark of a classical fractal spin liquid of the NM type.…”

Mechanism of current noise spectrum in a nonequilibirum Kondo dot system

“…The present study is based on the well-established dissipaton equation of motion (DEOM) approach [27][28][29][30][31]. This is a nonperturbative and accurate method, having been extensively explored in the study of quantum impurity problems [27,[32][33][34][35][36][37]. These include the recent noise spectrum evaluations, with the identification of Coulomb blockade assisted Rabi interference in a doubledot Aharonov-Bohm interferometer [37].…”

Equilibrium and transient thermodynamics: A unified dissipaton-space approach

“…[19][20][21][22] Demonstrated examples beyond the HEOM evaluations include the Fano interference, [23] Herzberg-Teller vibronic coupling, [24] quantum transport shot noise spectrums. [25][26][27] The recently developed phase-space DEOM theory enables also the evaluations on various thermal transport problems, including the dynamical heat correlation functions. [22] This paper consists of two major and closely related topics.…”

“…[29] The unified DEOM theory would facilitate the evaluations on various systemand-bath entanglement properties of strongly correlated quantum impurity systems. [19][20][21][22][23][24][25][26][27] To complete this topic, we present the equilibrium DEOM solutions in Appendix A, and further the imaginary-time DEOM in Appendix B. While the imaginary-time formalism focuses on equilibrium thermodynamics only, the real-time DEOM accesses also nonequilibrium and/or transient analogues.…”