Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice

Abstract

We provide numerical evidence in favor of spontaneous chiral symmetry breaking and the concomitant appearance of an Abelian chiral spin liquid for three-component fermions on the triangular lattice described by an SU(3) symmetric Hubbard model with hopping amplitude −t (t > 0) and on-site interaction U . This chiral phase is stabilized in the Mott phase with one particle per site in the presence of a uniform π-flux per plaquette, and in the Mott phase with two particles per site without any flux. Our approach relies on effective spin models derived in the strong-coupling limit in powers of t/U for general SU(N ) and arbitrary uniform charge flux per plaquette, which are subsequently studied using exact diagonalizations and variational Monte Carlo simulations for N = 3, as well as on exact diagonalizations of the SU(3) Hubbard model on small clusters. Up to third order in t/U , and for the time-reversal symmetric cases (flux 0 or π), the low-energy description is given by the J-K model with Heisenberg coupling J and real ring exchange K. The phase diagram in the full J-K parameter range contains, apart from three already known, magnetically long-range ordered phases, two previously unreported phases: i) a lattice nematic phase breaking the lattice rotation symmetry and ii) a spontaneous timereversal and parity symmetry breaking Abelian chiral spin liquid. For the Hubbard model, an investigation that includes higher-order itinerancy effects supports the presence of a phase transition inside the insulating region, occurring at (t/U )c ≈ 0.07 [(U/t)c ≈ 13] between the three-sublattice magnetically ordered phase at small t/U and this Abelian chiral spin liquid. arXiv:1802.03179v2 [cond-mat.str-el]

Structure of spin correlations in high-temperature SU(N) quantum magnets

“…The ground state physics of the spin Hamiltonian (2) has been explored for many values of N and lattice geometries over the last decades, see, e.g., Refs. [5,52,[78][79][80][81][82][83][84][85][86][89][90][91][92][93][94][95][96][97], and in most cases the structure of the ground states differs qualitatively from the Manhattan picture advocated in the previous section. Based on the current understanding, we expect only bipartite lattices with N = 2 to show a common sign structure of correlations from high to low temperatures.…”

“…The original proposals and the subsequent experimental work motivated a broad range of theoretical and computational works on various aspects of SU(N ) quantum magnets . A significant effort was put into understanding the ground state (T = 0) phase diagrams of quantum spin models in the fundamental representation of SU(N ) [52,[78][79][80][81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97].…”

“…The inclusion of the 3 P 0 clock state leads to a multiorbital SU(N ) Hubbard model, which is interesting in itself[115][116][117][118], but not the topic of the present work.2 This is the formula valid for the fundamental representation. At higher order in t/U , new terms in the spin model can be generated (see, e.g., Ref [97]…”

Fragility of the nematic spin liquid induced by diagonal couplings in the square-lattice SU(3) model

“…The search for novel quantum phases has also been extended to spin S = 1 systems both experimentally [9][10][11][12][13] and theoretically [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] . There are several spin-1 materials that have been reported to host spin-liquid ground states, such as the triangular layered materials NiGa 2 S 4 9 , Ba 3 NiSb 2 O 9 10,11 , and the layered honeycomb-lattice material 6HB-Ba 3 NiSb 2 O 9 12 .…”

Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets

“…The original proposals and the subsequent experimental work motivated a broad range of theoretical and computational works on various aspects of SU(N ) quantum magnets . A significant effort was put into understanding the ground state (T = 0) phase diagrams of quantum spin models in the fundamental representation of SU(N ) [51,[75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92].…”