Majorana spin liquid and dimensional reduction in Cs2CuCl4

Abstract

The low-temperature behavior of the magnetic insulator Cs2CuCl4 can be modeled by an anisotropic triangular lattice spin-1/2 Heisenberg antiferromagnet with two different exchange couplings J and J' = J/3. We show that in a wide range of magnetic fields the experimentally observed field dependence of the crossover temperature T_c for spin-liquid behavior can be explained within a mean-field theory based on the representation of spin operators in terms of Majorana fermions. We also show that for small magnetic fields the specific heat and the spin susceptibility both exhibit a maximum as a function of temperature at T_c = J/2. In the spin-liquid regime, the Majorana fermions can only propagate along the direction of the strongest bond, in agreement with the dimensional reduction scenario advanced by Balents [Nature (London) 464, 199 (2010)].Comment: 9 pages, 8 figure

Spin-liquid phase in a spatially anisotropic frustrated antiferromagnet: A Schwinger boson mean-field approach

“…This indicates that SB-MF is unable to describe paramagnetic phases occurring, for instance, in the experimental phase diagram of Cs 2 CuCl 4 . This is in contrast to recent work using a spin representation based on Majorana fermions [45] which consistently describes the transition line from the spin-liquid to the paramagnetic phase. Further work which goes beyond the mean-field treatment presented here is needed to describe paramagnetic phases stabilized by temperature.…”

Properties and application of SO(3) Majorana representation of spin: Equivalence with Jordan-Wigner transformation and exact Z2 gauge theories for spin models

“…We also show that the conditions we apply to fix the Majorana Hilbert space can be mapped into standard form of Gauss law in Z 2 gauge theory. To this end, our study is different from previous studies 29,31 in that no approximation is introduced in obtaining the Z 2 gauge theories. Unfortunately the resulting Z 2 gauge theory does not take the standard form 34 and contain some non-trivial features.…”

“…Defining a mapping between spin operators and a fermion coupled to a string-operator of Chern-Simons gauge field 23 , the 2d Jordan-Wigner transformation maps the quantum XY model in 2d into a model of complex fermion coupled to a Chern-Simons gauge theory (Some details of the 2d Jordan-Wigner transformation are given in Appendix B). Besides the Jordan-Wigner (JW) transformation, there is another non-local representation of spin, which is the SO(3) Majorana representation 8,20,[24][25][26][27][28][29][30][31] . In the SO(3) Majorana representation, each spin operator is represented by three Majorana fermions.…”

“…Application of non-local 2d Jordan-Wigner transformation results in U(1) Chern-Simons gauge theories [21][22][23] . Mean field studies of various spin models 29,31 and exact solution of Kitaev model 8 using the SO(3) Majorana representation result in Z 2 gauge theories. Thus, it is conjectured that the application of the SO(3) Majorana representation can result in Z 2 lattice gauge theories because of the Z 2 redundancy mentioned above.…”

YbMgGaO4: A Triangular‐Lattice Quantum Spin Liquid Candidate

“…Unfortunately, a magnetic transition into the 3D long‐range‐ordered phase was observed below T N ≈ 0.6 K due to the small interlayer coupling, and the detailed B ‐ T phase diagrams was also reported . It had aroused interest of the community, due to its novel frustrated magnetism and continuous inelastic neutron scattering (INS) spin excitation, as well as the possible Majorana spin liquid phase . And Starykh et al.…”