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Register a new userThermal Hall effect in square-lattice spin liquids: A Schwinger boson mean-field study
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Motivated by recent transport measurements in high-$T_c$ cuprate superconductors in a magnetic field, we study the thermal Hall conductivity in materials with topological order, focusing on the contribution from neutral spinons. Specifically, different Schwinger boson mean-field ans{a}tze for the Heisenberg antiferromagnet on the square lattice are analyzed. We allow for both Dzyaloshinskii-Moriya interactions, and additional terms associated with scalar spin chiralities that break time-reversal and reflection symmetries, but preserve their product. It is shown that these scalar spin chiralities, which can either arise spontaneously or are induced by the orbital coupling of the magnetic field, can lead to spinon bands with nontrivial Chern numbers and significantly enhanced thermal Hall conductivity. Associated states with zero-temperature magnetic order, which is thermally fluctuating at any $T>0$, also show a similarly enhanced thermal Hall conductivity.
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We theoretically investigate, within the Schwinger-Boson mean-field theory, the transition from a gapped $Z_{2}$ quantum spin-liquid, in a $J_1$-$J_2$ Heisenberg spin-1/2 system in a honeycomb lattice, to a chiral $Z_2$ spin liquid phase under the presence of time-reversal symmetry breaking scalar chiral interaction (with amplitude $J_{chi}$), with non-trivial Chern bands of the excitations. We numerically obtain a phase diagram of such $J_1$-$J_2$-$J_{chi}$ system, where different phases are distinguished based on the gap and the nature of excitation spectrum, topological invariant of the excitations, the nature of spin-spin correlation and the symmetries of the mean-field parameters. The chiral $Z_2$ state is characterized by non-trivial Chern number of the excitation bands and lack of long-range magnetic order, which leads to large thermal Hall coefficient.
Recent theoretical studies have found quantum spin liquid states with spinon Fermi surfaces upon the application of a magnetic field on a gapped state with topological order. We investigate the thermal Hall conductivity across this transition, describing how the quantized thermal Hall conductivity of the gapped state changes to an unquantized thermal Hall conductivity in the gapless spinon Fermi surface state. We consider two cases, both of potential experimental interest: the state with non-Abelian Ising topological order on the honeycomb lattice, and the state with Abelian chiral spin liquid topological order on the triangular lattice.
The Heisenberg antiferromagnet on the Kagom{e} lattice is studied in the framework of Schwinger-boson mean-field theory. Two solutions with different symmetries are presented. One solution gives a conventional quantum state with $mathbf{q}=0$ order for all spin values. Another gives a gapped spin liquid state for spin $S=1/2$ and a mixed state with both $mathbf{q}=0$ and $sqrt{3}times sqrt{3}$ orders for spin $S>1/2$. We emphasize that the mixed state exhibits two sets of peaks in the static spin structure factor. And for the case of spin $S=1/2$, the gap value we obtained is consistent with the previous numerical calculations by other means. We also discuss the thermodynamic quantities such as the specific heat and magnetic susceptibility at low temperatures and show that our result is in a good agreement with the Mermin-Wagner theorem.
Recent experiments on several cuprate compounds have identified an enhanced thermal Hall response in the pseudogap phase. Most strikingly, this enhancement persists even in the undoped system, which challenges our understanding of the insulating parent compounds. To explain these surprising observations, we study the quantum phase transition of a square-lattice antiferromagnet from a confining Neel state to a state with coexisting Neel and semion topological order. The transition is driven by an applied magnetic field and involves no change in the symmetry of the state. The critical point is described by a strongly-coupled conformal field theory with an emergent global $SO(3)$ symmetry. The field theory has four different formulations in terms of $SU(2)$ or $U(1)$ gauge theories, which are all related by dualities; we relate all four theories to the lattice degrees of freedom. We show how proximity of the confining Neel state to the critical point can explain the enhanced thermal Hall effect seen in experiment.
The adsorbed atoms exhibit tendency to occupy a triangular lattice formed by periodic potential of the underlying crystal surface. Such a lattice is formed by, e.g., a single layer of graphane or the graphite surfaces as well as (111) surface of face-cubic center crystals. In the present work, an extension of the lattice gas model to $S=1/2$ fermionic particles on the two-dimensional triangular (hexagonal) lattice is analyzed. In such a model, each lattice site can be occupied not by only one particle, but by two particles, which interact with each other by onsite $U$ and intersite $W_{1}$ and $W_{2}$ (nearest and next-nearest-neighbor, respectively) density-density interaction. The investigated hamiltonian has a form of the extended Hubbard model in the atomic limit (i.e., the zero-bandwidth limit). In the analysis of the phase diagrams and thermodynamic properties of this model with repulsive $W_{1}>0$, the variational approach is used, which treats the onsite interaction term exactly and the intersite interactions within the mean-field approximation. The ground state ($T=0$) diagram for $W_{2}leq0$ as well as finite temperature ($T>0$) phase diagrams for $W_{2}=0$ are presented. Two different types of charge order within $sqrt{3} times sqrt{3}$ unit cell can occur. At $T=0$, for $W_{2}=0$ phase separated states are degenerated with homogeneous phases (but $T>0$ removes this degeneration), whereas attractive $W_2<0$ stabilizes phase separation at incommensurate fillings. For $U/W_{1}<0$ and $U/W_{1}>1/2$ only the phase with two different concentrations occurs (together with two different phase separated states occurring), whereas for small repulsive $0<U/W_{1}<1/2$ the other ordered phase also appears (with tree different concentrations in sublattices). The qualitative differences with the model considered on hypercubic lattices are also discussed.
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