The A-Cycle Problem In XY model with Ring Frustration

Traditionally, the transverse spin-1/2 XY model is mapped to a fermionic "c-cycle" problem, where the prior periodic boundary condition is applied to the fermionic chain and the additional boundary term has been neglected. However, the "a-cycle" problem (the original problem without any approximation) has not been treated seriously up to now. In this paper, we consider the XY model with ring frustration and diagonalize it without any approximation with the help of parity constraint. Then two peculiar gapless phases have been found.Comment: 6 pages, 1 figures, to appear in Modern Physics Letters

Potential thermoelectric materials CsMI3\mathrm{CsMI_3} (M=Sn and Pb) in perovskite structures from the first-principles calculations

The thermoelectric properties of halide perovskites $\mathrm{CsMI_3}$ (M=Sn and Pb) are investigated from a combination of first-principles calculations and semiclassical Boltzmann transport theory by considering both the electron and phonon transport. The electronic part is performed using a modified Becke and Johnson (mBJ) exchange potential, including spin-orbit coupling (SOC), while the phonon part is computed using generalized gradient approximation (GGA). It is found that SOC has remarkable detrimental effect on n-type power factor, while has a negligible influence in p-type doping, which can be explained by considering SOC effect on conduction and valence bands. Calculated results show exceptionally low lattice thermal conductivities in $\mathrm{CsSnI_3}$ and $\mathrm{CsPbI_3}$, and the corresponding room-temperature lattice thermal conductivity is 0.54 $\mathrm{W m^{-1} K^{-1}}$ and 0.25 $\mathrm{W m^{-1} K^{-1}}$. At 1000 K, the maximal figure of merit $ZT$ is up to 0.63 and 0.64 for $\mathrm{CsSnI_3}$ and $\mathrm{CsPbI_3}$ with scattering time $\tau$=$10^{-14}$ s, and the peak $ZT$ is 0.49 and 0.41 with $\tau$=$10^{-15}$ s. These results make us believe that $\mathrm{CsMI_3}$ (M=Sn and Pb) in perovskite structures may be potential thermoelectric materials.Comment: 6 pages, 6 figure

Pressure enhanced thermoelectric properties in Mg2Sn

Pressure dependence of electronic structures and thermoelectric properties of $\mathrm{Mg_2Sn}$ are investigated by using a modified Becke and Johnson (mBJ) exchange potential, including spin-orbit coupling (SOC). The corresponding value of spin-orbit splitting at $\Gamma$ point is 0.47 eV, which is in good agreement with the experimental value 0.48 eV. With the pressure increasing, the energy band gap first increases, and then decreases. In certain doping range, the power factor for n-type has the same trend with energy band gap, when the pressure increases. Calculated results show that the pressure can lead to significantly enhanced power factor in n-type doping below the critical pressure, and the corresponding lattice thermal conductivity near the critical pressure shows the relatively small value. These results make us believe that thermoelectric properties of $\mathrm{Mg_2Sn}$ can be improved in n-type doping by pressure.Comment: 4 pages, 6 figure

Spin-orbital coupling effect on power factor in semiconducting transition-metal dichalcogenide monolayers

The electronic structures and thermoelectric properties of semiconducting transition-metal dichalcogenide monolayers $\mathrm{MX_2}$ (M=Zr, Hf, Mo, W and Pt; X=S, Se and Te) are investigated by combining first-principles and Boltzmann transport theory, including spin-orbital coupling (SOC). It is found that the gap decrease increases from S to Te in each cation group, when the SOC is opened. The spin-orbital splitting has the same trend with gap reducing. Calculated results show that SOC has noteworthy detrimental effect on p-type power factor, while has a negligible influence in n-type doping except W cation group, which can be understood by considering the effects of SOC on the valence and conduction bands. For $\mathrm{WX_2}$ (X=S, Se and Te), the SOC leads to observably enhanced power factor in n-type doping, which can be explained by SOC-induced band degeneracy, namely bands converge. Among all cation groups, Pt cation group shows the highest Seebeck coefficient, which leads to best power factor, if we assume scattering time is fixed. Calculated results show that $\mathrm{MS_2}$ (M=Zr, Hf, Mo, W and Pt) have best p-type power factor for all cation groups, and that $\mathrm{MSe_2}$ (M=Zr and Hf), $\mathrm{WS_2}$ and $\mathrm{MTe_2}$ (M=Mo and Pt) have more wonderful n-type power factor in respective cation group. Therefore, these results may be useful for further theoretical prediction or experimental search of excellent thermoelectric materials from semiconducting transition-metal dichalcogenide monolayers.Comment: 8 pages, 8 figure

Entanglement in the scattering process by local impurity

We study entanglement in the scattering processes by fixed impurity and Kondo impurity. The fixed impurity plays a role as spin state filter that is employed to concentrate entanglement between the scattering particle and the unscattering particle. One Kondo impurity can entangle two noninteracting scattering particles while one scattering particle can entangle two separate noninteracting Kondo impurities.Comment: 8 page

Projective symmetry group classification of Z3Z_3 parafermion spin liquids on a honeycomb lattice

To study exotic excitations described by parafermions in the possible spin liquid states of SU($n$) spin systems, we introduce a parafermion parton approach. The SU($n$) spin operators can be represented by clock and shift matrices, which are shown to be the polynomials of parafermion operators in the parafermion representation. We find that SU($n$) spins can be decomposed into $n$ parafermion matrices of degree one. In this decomposition, the spin has a $\{\bigotimes{\rm SU}(n)\}^{n-1}$ gauge symmetry. As an application, we study the one-dimensional three-state clock model and generalized Kitaev model by a mean-field theory, both of them have been proved to be related to parafermion excitations. We find that with the symmetries of translations, $6$-fold rotation and combination of parity and time reversal, there are $9$ types and $102$ solutions for two-dimensional $Z_3$ parafermion spin liquids on the honeycomb lattice. On the contrast, there are $9$ types and $36$ solutions if both parity and time-reversal symmetries are present. Our results provide a novel route for the systematic search of new types of spin liquids with exotic anyon excitations.Comment: 13 pages, 1 figure

Spectral properties of the square-lattice antiferromagnetic J1-J2 Heisenberg model: confinement and deconfinement of spinons

Based on the mapping between $s=1/2$ spin operators and hard-core bosons, we extend the cluster perturbation theory to spin systems and study the whole excitation spectrum of the antiferromagnetic $J_{1}$-$J_{2}$ Heisenberg model on the square lattice. In the N\'eel phase for $J_{2}\lesssim0.4J_{1}$, in addition to the dominant magnon excitation, there is an obvious continuum close to $(\pi,0)$ in the Brillouin zone indicating the deconfined spin-1/2 spinon excitations. In the stripe phase for $J_{2}\gtrsim0.6J_{1}$, we find similar high-energy two-spinon continuums at $(\pi/2,\pi/2)$ and $(\pi/2,\pi)$, respectively. The intermediate phase is characterized by a spectrum with completely deconfined broad continuum, which is attributed to a $Z_{2}$ quantum spin liquid with the aid of a variational-Monte-Carlo analysis.Comment: 7 pages, 6 figure

The A-Cycle Problem for Transverse Ising Ring

Traditionally, the transverse Ising model is mapped to the fermionic c-cycle problem, which neglects the boundary effect due to thermodynamic limit. If persisting on a perfect periodic boundary condition, we can get a so-called a-cycle problem that has not been treated seriously so far (Lieb et al., 1961 \textit{Ann. of Phys.} \textbf{16} 407). In this work, we show a little surprising but exact result in this respect. We find the odevity of the number of lattice sites, $N$, in the a-cycle problem plays an unexpected role even in the thermodynamic limit, $N\rightarrow\infty$, due to the boundary constraint. We pay a special attention to the system with $N(\in Odd)\rightarrow\infty$, which is in contrast to the one with $N(\in Even)\rightarrow\infty$, because the former suffers a ring frustration. As a new effect, we find the ring frustration induces a low-energy gapless spectrum above the ground state. By proving a theorem for a new type of Toeplitz determinant, we demonstrate that the ground state in the gapless region exhibits a peculiar longitudinal spin-spin correlation. The entangled nature of the ground state is also disclosed by the evaluation of its entanglement entropy. At low temperatures, new behavior of specific heat is predicted. We also propose an experimental protocol for observing the new phenomenon due to the ring frustration.Comment: 24 pages, 9 figure

SU(NN) spin-wave theory: Application to spin-orbital Mott insulators

We present the application of the SU($N$) ($N>2$) spin-wave theory to spin-orbital Mott insulators whose ground states exhibit magnetic orders. When taking both the spin and orbital degrees of freedom into account rather than projecting onto the Kramers doublet, the lowest spin-orbital locking energy levels, due to the inevitable spin-orbital multipole exchange interactions, the SU($N$) spin-wave theory should take the place of the SU($2$) one. To implement the application, we introduce an efficient general local mean field approach which involves all the local fluctuations into the SU($N$) linear spin-wave theory. Our approach is tested firstly by calculating the multipolar spin-wave spectra of the SU($4$) antiferromagnetic model. Then we apply it to spin-orbital Mott insulators. It is revealed that the Hund's coupling would influence the effectiveness of the isospin-$1/2$ representation when the spin orbital coupling is not large enough. Besides, we also calculate the spin-wave spectra based on the first principle calculations for two concrete materials, $\alpha$-RuCl$_3$ and Sr$_2$IrO$_4$. The SU($N$) spin-wave theory appropriately depicts the low-energy magnons and the spin-orbital excitations qualitatively.Comment: 9 pages, 5 figure

Rigorous proof for the non-local correlation functions in the antiferromagnetic seamed transverse Ising ring

An unusual correlation function is conjectured by M. Campostrini et al. (Phys. Rev. E 91, 042123 (2015)) for the ground state of a transverse Ising chain with geometrical frustration in one of the translationally invariant cases. Later, we demonstrated the correlation function and showed its non-local nature in the thermodynamic limit based on the rigorous evaluation of a Toeplitz determinant (J. Stat. Mech. 113102 (2016)). In this paper, we prove rigorously that all the states that forming the lowest gapless spectrum (including the ground state) in the kink phase exhibit the same asymptotic correlation function. So, in a point of view of cannonical ensemble, the thermal correlation function is inert to temperature within the energy range of the lowest gapless spectrum.Comment: 8 pages, 0 figure