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Register a new userSchwinger boson approach for the dynamical mean-field theory of the Kondo lattice
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We apply the dynamical large-$N$ Schwinger boson technique as an impurity solver for the dynamical mean-field theory calculations of the Kondo lattice model. Our approach captures the hybridization physics through the DMFT self-consistency that is missing in the pure Schwinger boson calculations with independent electron baths. The resulting thermodynamic and transport properties are in qualitative agreement with more rigorous calculations and give the correct crossover behavior over a wide temperature range from the local moment regime to the Fermi liquid. Our method may be further extended to combine with the density functional theory for efficient material calculations.
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We compute the zero temperature dynamical structure factor $S({bf q},omega)$ of the triangular lattice Heisenberg model (TLHM) using a Schwinger boson approach that includes the Gaussian fluctuations ($1/N$ corrections) of the saddle point solution. While the ground state of this model exhibits a well-known 120$^{circ}$ magnetic ordering, experimental observations have revealed a strong quantum character of the excitation spectrum. We conjecture that this phenomenon arises from the proximity of the ground state of the TLHM to the quantum melting point separating the magnetically ordered and spin liquid states. Within this scenario, magnons are described as collective modes (two spinon-bound states) of a spinon condensate (Higgs phase) that spontaneously breaks the SU(2) symmetry of the TLHM. Crucial to our results is the proper account of this spontaneous symmetry breaking. The main qualitative difference relative to semi-classical treatments ($1/S$ expansion) is the presence of a high-energy spinon continuum extending up to about three times the single-magnon bandwidth. In addition, the magnitude of the ordered moment ($m=0.224$) agrees very well with numerical results and the low energy part of the single-magnon dispersion is in very good agreement with series expansions. Our results indicate that the Schwinger boson approach is an adequate starting point for describing the excitation spectrum of some magnetically ordered compounds that are near the quantum melting point separating this Higgs phase from the {it deconfined} spin liquid state.
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.
We investigate the periodic Anderson model with $bm{k}$-dependent $c$-$f$ mixing reproducing the point nodes of the hybridization gap by using the dynamical mean-field theory combined with the exact diagonalization method. At low temperature below a coherence temperature $T_0$, the imaginary part of the self-energy is found to be proportional to $T^2$ and the pseudogap with two characteristic energies $tilde{it Delta}_1$ and $tilde{it Delta}_2$ is clearly observed for $Tll T_0$, while the pseudogap is smeared with increasing $T$ and then disappears at high temperature $T simg T_0$ due to the evolution of the imaginary self-energy. When the Coulomb interaction between $f$ electrons $U$ increases, $tilde{it Delta}_1$, $tilde{it Delta}_2$, and $T_0$ together with $T_{rm max}$ at which the magnetic susceptibility is maximum decrease in proportion to the renormalization factor $Z$ resulting in a heavy-fermion semiconductor with a large mass enhancement $m^*/m=Z^{-1}$ for large $U$. We also examine the effect of the external magnetic field $H$ and find that the magnetization $M$ shows two metamagnetic anomalies $H_1$ and $H_2$ corresponding to $tilde{it Delta}_1$ and $tilde{it Delta}_2$ which are reduced due to the effect of $H$ together with $Z$. Remarkably, $Z^{-1}$ is found to be largely enhanced due to $H$ especially for $H_1 siml H siml H_2$, where the field induced heavy-fermion state is realized. The obtained results seem to be consistent with the experimental results observed in the anisotropic Kondo semiconductors such as CeNiSn.
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.
The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter.
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