Derivation of a reduced effective model allows for a unified treatment and discussion of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}\phantom{\rule{4pt}{0ex}}S=1/2$ Heisenberg model on triangular and kagome lattices. Calculating thermodynamic quantities, i.e., the entropy
s(T) and uniform susceptibility ${\ensuremath{\chi}}_{0}(T)$, numerically on systems up to effectively
N=42 sites, we show by comparing to full-model results that low-
T properties are qualitatively well represented within the effective model. Moreover, we find in the spin-liquid regime similar variation of
s(T) and ${\ensuremath{\chi}}_{0}(T)$ in both models down to $T\ensuremath{\ll}{J}_{1}$. In particular, studied spin liquids appear to be characterized by the Wilson ratio vanishing at low
T, indicating that the low-lying singlets are dominating over the triplet excitations.
The
U(1) Dirac spin liquid might realize an exotic phase of matter whose low-energy properties are described by quantum electrodynamics in
2+1 dimensions, where gapless modes exist but spinons and gauge fields are strongly coupled. Its existence was proposed in frustrated Heisenberg models in the presence of frustrating superexchange interactions by the (Abrikosov) fermionic representation of the spin operators [Wen, Phys. Rev. B 65, 165113 (2002)], supplemented by the Gutzwiller projection. Here, we construct charge-
Q monopole excitations in the Heisenberg model on the triangular lattice with nearest-neighbor (
J1) and next-nearest-neighbor (
J2) couplings. In the highly frustrated regime, singlet and triplet monopoles with
Q=1 become gapless in the thermodynamic limit; in addition, the energies for generic
Q agree with field-theoretical predictions, obtained for a large number of gapless fermion modes. Finally, we consider localized gauge excitations, in which magnetic $\ensuremath{\pi}$ fluxes are concentrated in the triangular plaquettes (in analogy with
Z2 visons), showing that these kinds of states do not play a relevant role at low energies. All our findings lend support to a stable
U(1) Dirac spin liquid in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the triangular lattice.
We numerically study the Heisenberg models on triangular lattices by extending it from the simplest equilateral lattice with only the nearest-neighbor exchange interaction. We show that, by including an additional weak next-nearest-neighbor interaction, a quantum spin-liquid phase is stabilized against the antiferromagnetic order. The spin gap (triplet excitation gap) and spin correlation at long distances decay algebraically with increasing system size at the critical point between the antiferromagnetic phase and the spin-liquid phase. This algebraic behavior continues in the spin-liquid phase as well, indicating the presence of an unconventional critical (algebraic spin-liquid) phase characterized by the dynamical and anomalous critical exponents
z+η∼1. Unusually small triplet and singlet excitation energies found in extended points of the Brillouin zone impose constraints on this algebraic spin liquid.
The spin-
1/2 J1-
J2 Heisenberg model on the square lattice represents one of the simplest examples in which the effects of magnetic interactions may suppress magnetic order, eventually leading to a pure quantum phase with no local order parameters. This model has been extensively studied in the last three decades, with conflicting results. Here, by using Gutzwiller-projected wave functions and recently developed methods to assess the low-energy spectrum, we show the existence of a level crossing between the lowest-energy triplet and singlet excitations for ${J}_{2}/{J}_{1}\ensuremath{\approx}0.54$. This fact supports the existence of a phase transition between a gapless spin liquid (which is stable for $0.48\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.54$) and a valence-bond solid (for $0.54\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.6$), even though no clear sign of dimer order is visible in the correlations functions. These results, which confirm recent density-matrix renormalization calculations on cylindrical clusters [L. Wang and A. W. Sandvik, Phys. Rev. Lett. 121, 107202 (2018)], reconcile the contradicting results obtained within different approaches over the years.
Using micromechanical force magnetometry, we have measured the magnetization of the strong-leg spin-1/2 ladder compound (C(7)H(10)N)(2)CuBr(2) at temperatures down to 45 mK. Low-temperature magnetic susceptibility as a function of field exhibits a maximum near the critical field H(c) at which the magnon gap vanishes, as expected for a gapped one-dimensional antiferromagnet. Above H(c) a clear minimum appears in the magnetization as a function of temperature, as predicted by theory. In this field region, the susceptibility in conjunction with our specific-heat data yields the Wilson ratio R(W). The result supports the relation R(W)=4K, where K is the Tomonaga-Luttinger-liquid parameter.
We study Kondo physics in the algebraic spin liquid, recently proposed to describe
ZnCu3(OH)6Cl2 [Phys. Rev. Lett. {\bf 98}, 117205 (2007)]. Although spin dynamics of the algebraic spin liquid is described by massless Dirac fermions, this problem differs from the Pseudogap Kondo model, because the bulk physics in the algebraic spin liquid is governed by an interacting fixed point where well-defined quasiparticle excitations are not allowed. Considering an effective bulk model characterized by an anomalous critical exponent, we derive an effective impurity action in the slave-boson context. Performing the large-
Nσ analysis with a spin index
Nσ, we find an impurity quantum phase transition from a decoupled local-moment state to a Kondo-screened phase. We evaluate the impurity spin susceptibility and specific heat coefficient at zero temperature, and find that such responses follow power-law dependencies due to the anomalous exponent of the algebraic spin liquid. Our main finding is that the Wilson's ratio for the magnetic impurity depends strongly on the critical exponent in the zero temperature limit. We propose that the Wilson's ratio for the magnetic impurity may be one possible probe to reveal criticality of the bulk system.