We develop a systematic large-N expansion based on the Schwinger boson representation of SU(4) coherent states of dimers for the paradigmatic spin-1/2 bilayer square lattice Heisenberg antiferromagnet. This system exhibits a quantum phase transition between a quantum paramagnetic state and a N & eacute;el order state, driven by the coupling constant g = J'/J, which is defined as the ratio between the interdimer J' and intradimer J exchange interactions. We demonstrate that this approach accurately describes static and dynamic properties on both sides of the quantum phase transition. The critical coupling constant gc 0.42 and the dynamic spin structure factor reproduce quantum Monte Carlo results with high precision. Notably, the 1/N corrections reveal the longitudinal mode of the magnetically ordered phase along with the overdamping caused by its decay into the two-magnon continuum. The present large-N SU(4) Schwinger boson theory can be extended to more general cases of quantum paramagnets that undergo a quantum phase transition into magnetically ordered states.

We analyze the temperature evolution of the anomalous magnetic spectrum of the spin-1/2 triangular quantum Heisenberg antiferromagnet, which is proximate to a quantum phase transition leading to a spin-liquid phase. Recently, its low-energy excitations have been identified with two-spinon bound states, well defined in an ample region of the Brillouin zone. In this work, we compute the thermal magnetic spectrum within a Schwinger boson approach, incorporating Gaussian fluctuations around the saddle-point approximation. In order to account for a finite N & eacute;el temperature T N , we incorporate an exchange interaction between triangular layers. As temperature rises, the dispersion relation of the two-spinon bound states, representing single-magnon excitations, remains unchanged but becomes mixed with the thermally activated spinon continuum. Consequently, a crossover occurs at a temperature T * 0.75TN, defining a terminated Goldstone regime between T * and T N , where only the magnons close to the Goldstone modes survive as well-defined excitations, up to the N & eacute;el temperature. Our results support the idea that the fractionalization of magnons near a transition to a disordered phase can be extended to more realistic quasi-two-dimensional frustrated antiferromagnets.

The S = 1/2 triangular lattice antiferromagnet (TLAF) is a paradigmatic example of frustrated quantum magnetism. An ongoing challenge involves understanding the influence of exchange anisotropy on the collective behavior within such systems. Using inelastic neutron scattering (INS) and advanced calculation techniques, we have studied the low and high-temperature spin dynamics of Ba2La2CoTe2O12 (BLCTO): a Co2+-based Jeff = 1/2 TLAF that exhibits 120° order below TN = 3.26 K. We determined the spin Hamiltonian by fitting the energy-resolved paramagnetic excitations measured at T > TN, revealing exceptionally strong easy-plane XXZ anisotropy. Below TN, the excitation spectrum exhibits a high energy continuum having a larger spectral weight than the single-magnon modes, suggesting a scenario characterized by a spinon confinement length that markedly exceeds the lattice spacing. We conjecture that this phenomenon arises from the proximity to a quantum melting point, even under strong easy-plane XXZ anisotropy. Finally, we highlight characteristic flat features in the excitation spectrum, which are connected to higher-order van Hove singularities in the magnon dispersion directly induced by easy-plane XXZ anisotropy. Our results provide a rare experimental insight into the nature of highly anisotropic S = 1/2 TLAFs between the Heisenberg and XY limits. A TLAF is an archetypal geometrically frustrated magnetic system, which serves as the foundation for many exotic states, including quantum spin-liquids. Here, Park et al perform INS measurements on BLCTO, which, combined with theoretical calculations, reveal distinctive fingerprints of spinon excitations, thereby suggesting proximity to a spin liquid even in the presence of strong XXZ anisotropy.

The Heisenberg triangular-lattice quantum spin liquid and its phase transitions to nearby magnetic orders have received much theoretical attention, but clear experimental manifestations of these states are rare. Here we demonstrate that a spin-half delafossite material, namely, KYbSe 2 , shows close proximity to the triangular-lattice Heisenberg quantum spin liquid. Using neutron scattering, we identify a diffuse continuum with a sharp lower bound within the measured spectra. Applying entanglement witnesses to the data indicates multipartite entanglement spread between its neighbours, and an analysis of its magnetic-exchange couplings reveals close proximity to the theoretical quantum spin-liquid phase. The key features of the data are reproduced by Schwinger boson theory and tensor network calculations with a substantial next-nearest-neighbour coupling. The strength of the dynamical structure factor at the Brillouin-zone K point shows a scaling collapse down to 0.3 K, indicating the existence of a second-order quantum phase transition. Comparing this with previous theoretical work suggests that the proximate phase at a larger next-nearest-neighbour coupling is a gapped ℤ_2 spin liquid, resolving a long-debated issue.

Recent inelastic neutron scattering (INS) experiments of the triangular antiferromagnet Ba$_3$CoSb$_2$O$_9$ revealed strong deviations from semiclassical theories. We demonstrate that key features of the INS data are well reproduced by a parton Schwinger boson theory beyond the saddle-point approximation. The measured magnon dispersion is well reproduced by the dispersion of two-spinon bound states (poles of the emergent gauge fields propagator), while the low-energy continuum scattering is reproduced by a quasifree two-spinon continuum, suggesting that a free-spinon gas is a good initial framework to study magnetically ordered states near a quantum melting point.

The Schwinger boson theory provides a natural path for treating quantum spin systems with large quantum fluctuations. In contrast to semi-classical treatments, this theory allows us to describe a continuous transition between magnetically ordered and spin liquid states, as well as the continuous evolution of the corresponding excitation spectrum. The square lattice Heisenberg antiferromagnet is one of the first models that was approached with the Schwinger boson theory. Here we revisit this problem to reveal several subtle points that were omitted in previous treatments and that are crucial to further develop this formalism. These points include the freedom for the choice of the saddle point (Hubbard-Stratonovich decoupling and choice of the condensate) and the 1/N expansion in the presence of a condensate. A key observation is that the spinon condensate leads to Feynman diagrams that include contributions of different order in 1/N, which must be accounted to get a qualitatively correct excitation spectrum. We demonstrate that a proper treatment of these contributions leads to an exact cancellation of the single-spinon poles of the dynamical spin structure factor, as expected for a magnetically ordered state. The only surviving poles are the ones arising from the magnons (two-spinon bound states), which are the true collective modes of an ordered magnet.

E. A. Ghioldi,1, 2 Shang-Shun Zhang,1, 3 Yoshitomo Kamiya,4 L. O. Manuel,2 A. E. Trumper,2 and C. D. Batista1, 5, ∗ 1Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA 2Instituto de Física Rosario (CONICET) and Universidad Nacional de Rosario, Boulevard 27 de Febrero 210 bis, (2000) Rosario, Argentina 3School of Physics and Astronomy and William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA 4School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China 5Shull Wollan Center A Joint Institute for Neutron Sciences, Oak Ridge National Laboratory, TN 37831. USA

The Heisenberg triangular lattice quantum spin liquid and the phase transitions to nearby magnetic orders have received much theoretical attention, but clear experimental manifestations of these states are rare. This work investigates a new spin-half Yb$^{3+}$ delafossite material, KYbSe$_2$, whose inelastic neutron scattering spectra reveal a diffuse continuum with a sharp lower bound. Applying entanglement witnesses to the data reveals significant multipartite entanglement spread between its neighbors, and analysis of its magnetic exchange couplings shows close proximity to the triangular lattice Heisenberg quantum spin liquid. Key features of the data are reproduced by Schwinger-boson theory and tensor network calculations with a significant second-neighbor coupling $J_2$. The strength of the dynamical structure factor at the $K$ point shows a scaling collapse in $\hbar\omega/k_\mathrm{B}T$ down to 0.3 K, indicating a second-order quantum phase transition. Comparing this to previous theoretical work suggests that the proximate phase at larger $J_2$ is a gapped $\mathbb{Z}_2$ spin liquid, resolving a long-debated issue. We thus show that KYbSe$_2$ is close to a spin liquid phase, which in turn sheds light on the theoretical phase diagram itself.

We investigate the interplay between spatial anisotropy and further exchange interactions in the spin1/2 Heisenberg antiferromagnetic model on a triangular lattice. We use the Schwinger boson theory by including Gaussian fluctuations above the mean-field approach. The phase diagram exhibits a strong reduction of the long-range collinear and incommensurate spiral regions with respect to the mean-field ones. This reduction is accompanied by the emergence of its short-range order counterparts, leaving an ample room for zero-flux and nematic spin-liquid regions. Remarkably, within the neighborhood of the spatially isotropic line, there is a range where the spirals are so fragile that only the commensurate 120 degrees Neel ones survive. The good agreement with recent variational Monte Carlo predictions gives support to the rich phase diagram induced by spatial anisotropy.

We investigate the interplay between spatial anisotropy and further exchange interactions in the spin-1/2 Heisenberg antiferromagnetic model on a triangular lattice. We use the Schwinger boson theory by including Gaussian fluctuations above the mean-field approach. The phase diagram exhibits a strong reduction of the long range collinear and incommensurate spirals regions with respect to the mean-field ones. This reduction is accompanied by the emergence of its short range order counterparts, leaving an ample room for 0-flux and nematic spin liquid regions. Remarkably, within the neighborhood of the spatially isotropic line, there is a range where the spirals are so fragile that only the commensurate 120^∘ Néel ones survive. The good agreement with recent variational Monte Carlo predictions gives support to the rich phase diagram induced by spatial anisotropy.

Partial disorder-the microscopic coexistence of long-range magnetic order and disorder-is a rare phenomenon that has been experimentally and theoretically reported in some Ising- or easy plane-spin systems, driven by entropic effects at finite temperatures. Here, we present an analytical and numerical analysis of the S=1/2 Heisenberg antiferromagnet on the sqrt[3]×sqrt[3]-distorted triangular lattice, which shows that its quantum ground state has partial disorder in the weakly frustrated regime. This state has a 180° Néel ordered honeycomb subsystem coexisting with disordered spins at the hexagon center sites. These central spins are ferromagnetically aligned at short distances, as a consequence of a Casimir-like effect originated by the zero-point quantum fluctuations of the honeycomb lattice.

Large-$S$ and large-$N$ theories (spin value $S$ and spinor component number $N$) are complementary, and sometimes conflicting, approaches to quantum magnetism. While large-$S$ spin-wave theory captures the correct semiclassical behavior, large-$N$ theories, on the other hand, emphasize the quantumness of spin fluctuations. In order to evaluate the possibility of the non-trivial recovery of the semiclassical magnetic excitations within a large-$N$ approach, we compute the large-$S$ limit of the dynamic spin structure of the triangular lattice Heisenberg antiferromagnet within a Schwinger boson spin representation. We demonstrate that, only after the incorporation of Gaussian ($1/N$) corrections to the saddle-point ($N=\infty$) approximation, we are able to exactly reproduce the linear spin wave theory results in the large-$S$ limit. The key observation is that the effect of $1/N$ corrections is to cancel out exactly the main contribution of the saddle-point solution; while the collective modes (magnons) consist of two spinon bound states arising from the poles of the RPA propagator. This result implies that it is essential to consider the interaction of the spinons with the emergent gauge fields and that the magnon dispersion relation should not be identified with that of the saddle-point spinons.

We compute the zero-temperature dynamical structure factor S(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 degrees 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 break 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 semiclassical 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 deconfined spin-liquid state.

We compute the zero temperature dynamical structure factor $S({\bf q},\omega)$ of the triangular lattice Heisenberg model using a Schwinger Boson approach that includes the Gaussian fluctuations ($1/N$ correction) of the saddle point solution. While the ground state of this model exhibits a well-known 120$^{\circ}$ magnetic ordering, the excitation spectrum revealed by $S({\bf q},\omega)$ has a strong quantum character that is not captured by low-order $1/S$ expansions. The low-energy magnons consist of two spinon bound states confined by gauge fluctuations of the auxiliary fields, which can produce internal structure of the magnon peaks. In addition, the high-energy continuum of spinon modes extends up to about three times the single-magnon bandwidth.

We investigate, using the density-matrix renormalization group, the evolution of the Nagaoka state with t' hopping that frustrates the hole kinetic energy in the U = infinity Hubbard model on the square and anisotropic triangular lattices. We find that the Nagaoka ferromagnet survives up to a rather small t'(c)/t similar to 0.2. At this critical value, there is a transition to an antiferromagnetic phase that depends on the lattice: a Q = ( Q, 0) spiral order, which continuously evolves with t', for the triangular lattice and the usual Q = (pi, pi) Neel order for the square lattice. Remarkably, the local magnetization takes its classical value for all considered t' (t'/t <= 1). Our results show that the recently found classical kinetic antiferromagnetism, a perfect counterpart of Nagaoka ferromagnetism, is a generic phenomenon in these kinetically frustrated electronic systems.

We investigate the effect of dimensional crossover in the ground state of the antiferromagnetic spin-$1$ Heisenberg model on the anisotropic triangular lattice that interpolates between the regime of weakly coupled Haldane chains ($J^{\prime}\! \!\ll\!\! J$) and the isotropic triangular lattice ($J^{\prime}\!\!=\!\!J$). We use the density-matrix renormalization group (DMRG) and Schwinger boson theory performed at the Gaussian correction level above the saddle-point solution. Our DMRG results show an abrupt transition between decoupled spin chains and the spirally ordered regime at $(J^{\prime}/J)_c\sim 0.42$, signaled by the sudden closing of the spin gap. Coming from the magnetically ordered side, the computation of the spin stiffness within Schwinger boson theory predicts the instability of the spiral magnetic order toward a magnetically disordered phase with one-dimensional features at $(J^{\prime}/J)_c \sim 0.43$. The agreement of these complementary methods, along with the strong difference found between the intra- and the interchain DMRG short spin-spin correlations; for sufficiently large values of the interchain coupling, suggests that the interplay between the quantum fluctuations and the dimensional crossover effects gives rise to the one-dimensionalization phenomenon in this frustrated spin-$1$ Hamiltonian.

We investigate the spin dynamics of the square-lattice spin- Heisenberg antiferromagnet by means of an improved mean-field Schwinger boson calculation. By identifying both, the long-range Néel and the RVB-like components of the ground state, we propose an educated guess for the mean-field magnetic excitation consisting on a linear combination of local and bond spin flips to compute the dynamical structure factor. Our main result is that when this magnetic excitation is optimized in such a way that the corresponding sum rule is fulfilled, we recover the low- and high-energy spectral weight features of the experimental spectrum. In particular, the anomalous spectral weight depletion at found in recent inelastic neutron scattering experiments can be attributed to the interference of the triplet bond excitations of the RVB component of the ground state. We conclude that the Schwinger boson theory seems to be a good candidate to adequately interpret the dynamic properties of the square-lattice Heisenberg antiferromagnet.

We investigate the excitation spectrum of the triangular-lattice antiferromagnetic XXZ model using series expansion and mean field Schwinger boson approaches. The single-magnon spectrum computed with series expansion exhibits rotonic minima at the middle points of the edges of the Brillouin zone, for all values of the anisotropy parameter in the range 0 <= J(z)/J <= 1. Based on the good agreement with series expansion for the single-magnon spectrum, we compute the full dynamical magnetic structure factor within the mean field Schwinger boson approach to investigate the relevance of the XXZ model for the description of the unusual spectrum found recently in Ba3CoSb2O9. In particular, we obtain an extended continuum above the spin wave excitations, which is further enhanced and brought closer to those observed in Ba3CoSb2O9 with the addition of a second neighbor exchange interaction approximately 15% of the nearest-neighbor value. Our results support the idea that excitation continuum with substantial spectral-weight are generically present in two-dimensional frustrated spin systems and fractionalization in terms of bosonic spinons presents an efficient way to describe them.

We study, by means of the density matrix renormalization group, the infinite U Hubbard model--with one hole doped away from half filling--in triangular and square lattices with frustrated hoppings, which invalidate Nagaoka's theorem. We find that these kinetically frustrated models have antiferromagnetic ground states with classical local magnetization in the thermodynamic limit. We identify the mechanism of this kinetic antiferromagnetism with the release of the kinetic energy frustration, as the hole moves in the established antiferromagnetic background. This release can occur in two different ways: by a nontrivial spin Berry phase acquired by the hole, or by the effective vanishing of the hopping amplitude along the frustrating loops.