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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\'eel order state, driven by the coupling constant $g = J'/J$, which is defined as the ratio between the inter-dimer $J'$ and intra-dimer $J$ 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 $g_c \approx 0.42$ 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-$N$ $SU(N)$ Schwinger boson theory can be extended to more general cases of quantum paramagnets that undergo a quantum phase transition into magnetically ordered states.

Ionic liquids have proved to be excellent heat transfer fluids and alternatives to common HTFs used in industries for heat exchangers and other heat transfer equipment. However, its industrial utilization depends on the cost per kg of its production, to be competitive for industrial applications with biphenyl and diphenyl oxide, alkylated aromatics, and dimethyl polysiloxane oils, which degrade above 200 {\deg}C and possess some environmental problems. The efficiency of a heat transfer fluid depends on the fundamental thermophysical properties influencing convective heat transfer (density, heat capacity, thermal conductivity, and viscosity), as these properties are necessary to calculate the heat transfer coefficients for different heat exchanger geometries. In Part 1, the thermophysical properties of pure 1-ethyl-3-methylimidazolium methanesulfonate $[C_{2}mim][CH_{3}SO_{3}]$ (CAS no. 145022-45-3), (ECOENG 110), produced by BASF, under the trade name of Basionics ST35, with an assay $\geq$97% with $\leq$0.5% water and $\leq$2% chloride ($Cl^{-}$), were presented, for temperatures slightly below room temperature and up to 355 K. In this paper, we report the thermophysical properties of mixtures of [C2mim][CH3SO3] with water, in the whole concentration range, at $P$ = 0.1 MPa. The properties measured were density and speed of sound (293.15 < $T$/K < 343.15), viscosity, electrical and thermal conductivities, refractive index (293.15 < $T$/K < 353.15), and infinite dilution diffusion coefficient of the ionic liquid in water (298.15 K).

We establish a technique to prove that a Koszul graded ring is prime or a domain using information about its Koszul dual. This is based on a general categorical result that expands on methods of J.Y. Guo, which proves that certain orbital rings are prime or domains. We apply this method to prove that if $A = kQ/I$ is a Koszul twisted Calabi-Yau algebra of dimension 2, such that $Q$ is connected with every vertex having outdegree at least 2, then $A$ is a prime piecewise domain. In particular, the preprojective algebra of a connected quiver whose underlying graph has minimum degree at least 2 is a prime piecewise domain., Comment: 24 pages

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 critical point. 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\'eel 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 $T^* \simeq 0.75 T_N$, defining a "terminated Goldstone regime" between $T^*$ and $T_N$, where only the Goldstone modes survives as well-defined magnon excitations, up to the N\'eel temperature. Our results support the idea that the fractionalization of magnons near a quantum critical point can be extended to more realistic quasi-2D frustrated antiferromagnets., Comment: 13 pages, 8 figures

Light-matter interactions can be used as a tool to realize novel many-body states of matter and to study the interplay between electronic and magnetic degrees of freedom. In particular, tightly bound many-body states that behave as coherent quasi-particles are rare, and may lead to unconventional technological applications beyond the semi-conductor paradigm, particularly if these excitations are bosonic and can condense. Two-dimensional magnetic systems present a pristine platform to realize and study such states. We construct a theory that explains the low-energy optical excitations at 1.476 eV and 1.498 eV observed by photoluminiscence, optical absorption, and RIXS in the van der Waals antiferromagnet NiPS$_3$. Using \textit{ab initio} methods, we construct a two-band Hubbard model for two \textit{effective} Ni orbitals of the original lattice. The dominant effective hopping corresponds to third-nearest neighbours. This model exhibits two triplet-singlet excitations of energy near two times the Hund exchange. From perturbation theory, we obtain an effective model for the movement of the singlets in an antiferromagnetic background, that we solve using a generalized self-consistent Born approximation. These singlet excitations, dressed by a cloud of magnons, move coherently as polaronic-like quasi-particles, "singlet polarons". Our theory explains the main features of the observed spectra., Comment: 8 pages, 4 figures

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{\deg} 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., Comment: 5 figures, Supplementary Information can be found on the journal's website

We propose a minimal setup for a quantum heat pump, consisting of two tunnel-coupled quantum dots, each hosting a single level and each being coupled to a different fermionic reservoir. The working principle relies on both non-Markovian system-bath coupling and driving induced resonant coupling. We describe the system using a reaction-coordinate mapping in combination with Floquet-Born-Markov theory and characterize its performance., Comment: 9 pages, 5 Figures

We investigate cases where the finite dual coalgebra of a twisted tensor product of two algebras is a crossed product coalgebra of their respective finite duals. This is achieved by interpreting the finite dual as a topological dual; in order to prove this, we show that the continuous dual is a strong monoidal functor on linearly topologized vector spaces whose open subspaces have finite codimension. We describe a sufficient condition for the result on finite dual coalgebras to be applied, and we this condition to particular constructions including Ore extensions, smash product algebras, and crossed product bialgebras., Comment: 24 pages. This paper includes material that was removed from an earlier version of arXiv:2111.07081

In order to diagnose the cause of some defects in the category of canonical hypergroups, we investigate several categories of hyperstructures that generalize hypergroups. By allowing hyperoperations with possibly empty products, one obtains categories with desirable features such as completeness and cocompleteness, free functors, regularity, and closed monoidal structures. We show by counterexamples that such constructions cannot be carried out within the category of canonical hypergroups. This suggests that (commutative) unital, reversible hypermagmas -- which we call mosaics -- form a worthwhile generalization of (canonical) hypergroups from the categorical perspective. Notably, mosaics contain pointed simple matroids as a subcategory, and projective geometries as a full subcategory., Comment: 51 pages, 3 figures. Minor corrections and updates throughout. Added Proposition 2.22 as a new source of examples. Corrected slight errors in some statements, especially in Subsections 3.1 and 3.3

This note exhibits a new set of 85 three-dimensional integer vectors that has no Kochen-Specker coloring. These vectors represent rank-1 projection matrices with entries in the rational subring $\mathbb{Z}[1/462]$. Consequences are given for (non)contextuality in a purely algebraic sense for partial rings of symmetric matrices over finitely generated rational subrings and $p$-adic integers., Comment: 8 pages

Local quantum phase transitions driven by Kondo correlations have been theoretically proposed in several magnetic nanosystems; however, clear experimental signatures are scant. Modeling a nickelocene molecule on a Cu(100) substrate as a two-orbital Anderson impurity with single-ion easy-plane anisotropy coupled to two conduction bands, we find that recent scanning tunneling spectra measured at different microscope tip heights reveal the existence of a topological quantum phase transition from the usual local Fermi liquid with high zero-bias conductance to a non-Landau Fermi liquid, characterized by a non-trivial quantized Luttinger integral, with a small conductance. The effects of intermediate valence, finite temperature, and structural relaxation of the molecule position allow us to explain the different observed behaviors., Comment: 6 pages, 4 figures. Accepted in SciPost Physics

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.

Value-at-Risk is one of the most popular risk management tools in the financial industry. Over the past 20 years several attempts to include VaR in the portfolio selection process have been proposed. However, using VaR as a risk measure in portfolio optimization models leads to problems that are computationally hard to solve. In view of this, few practical applications of VaR in portfolio selection have appeared in the literature up to now. In this paper, we propose to add the VaR criterion to the classical Mean-Variance approach in order to better address the typical regulatory constraints of the financial industry. We thus obtain a portfolio selection model characterized by three criteria: expected return, variance, and VaR at a specified confidence level. The resulting optimization problem consists in minimizing variance with parametric constraints on the levels of expected return and VaR. This model can be formulated as a Mixed-Integer Quadratic Programming (MIQP) problem. An extensive empirical analysis on seven real-world datasets demonstrates the practical applicability of the proposed approach. Furthermore, the out-of-sample performance of the optimal Mean-Variance-VaR portfolios seems to be generally better than that of the optimal Mean-Variance and Mean-VaR portfolios.

In pursuit of a noncommutative spectrum functor, we argue that the Heyneman-Sweedler finite dual coalgebra can be viewed as a quantization of the maximal spectrum of a commutative affine algebra, integrating prior perspectives of Takeuchi, Batchelor, Kontsevich-Soibelman, and Le Bruyn. We introduce fully residually finite-dimensional algebras $A$ as those with enough finite-dimensional representations to let $A^\circ$ act as an appropriate depiction of the noncommutative maximal spectrum of $A$; importantly, this class includes affine noetherian PI algebras. In the case of prime affine algebras that are module-finite over their center, we describe how the Azumaya locus is represented in the finite dual. This is used to describe the finite dual of quantum planes at roots of unity as an endeavor to visualize the noncommutative space on which these algebras act as functions. Finally, we discuss how a similar analysis can be carried out for other maximal orders over surfaces., Comment: 35 pages, 2 figures. Final version

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., Comment: 6 pages main text, 6 pages methods, 7 pages supplemental information

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., Comment: 25 pages, 12 figures

The paradigm of Landau's Fermi liquid theory has been challenged with the finding of a strongly interacting Fermi liquid that cannot be adiabatically connected to a non-interacting system. A spin-1 two-channel Kondo impurity with anisotropy D has a quantum phase transition between two topologically different Fermi liquids with a peak (dip) in the Fermi level for D < Dc (D > Dc). Extending this theory to general multi-orbital problems with finite magnetic field, we reinterpret in a unified and consistent fashion several experimental studies of iron phthalocyanine molecules on Au(111) that were previously described in disconnected and conflicting ways. The differential conductance shows a zero-bias dip that widens when the molecule is lifted from the surface (reducing the Kondo couplings) and is transformed continuously into a peak under an applied magnetic field. We reproduce all features and propose an experiment to induce the topological transition., Comment: 11 pages, 7 figures + supplementary materials

We calculate the quasiparticle dispersion and spectral weight of the quasiparticle that results when a hole is added to an antiferromagnetically ordered CuO$_2$ plane of a cuprate superconductor. We also calculate the magnon contribution to the quasiparticle spectral function. We start from a multiband model for the cuprates considered previously [Nat. Phys. \textbf{10}, 951 (2014)]. We map this model and the operator for creation of an O hole to an effective one-band generalized $t-J$ model, without free parameters. The effective model is solved using the state of the art self-consistent Born approximation. Our results reproduce all the main features of experiments. They also reproduce qualitatively the dispersion of the multiband model, giving better results for the intensity near wave vector $(\pi,\pi)$, in comparison with the experiments. In contrast to what was claimed in [Nat. Phys. \textbf{10}, 951 (2014)], we find that spin fluctuations play an essential role in the dynamics of the quasiparticle, and hence in both its weight and dispersion., Comment: 7 pages, 4 figures

We investigate the interplay between spatial anisotropy and further exchange interactions in the spin-$\frac{1}{2}$ 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 $120^{\circ}$ N\'eel ones survive. The good agreement with recent variational Monte Carlo predictions gives support to the rich phase diagram induced by spatial anisotropy., Comment: 8 pages, 8 figures

We study the low-temperature properties of the generalized Anderson impurity model in which two localized configurations, one with two doublets and the other with a triplet, are mixed by two degenerate conduction channels. By using the numerical renormalization group and the non-crossing approximation, we analyze the impurity entropy, its spectral density, and the equilibrium conductance for several values of the model parameters. Marked differences with respect to the conventional one-channel spin $s=1/2$ Anderson model, that can be traced as hallmarks of an impurity spin $S=1$, are found in the Kondo temperature, the width and position of the charge transfer peak, as well as the temperature dependence of the equilibrium conductance. Furthermore, we analyze the rich effects of a single-ion magnetic anisotropy $D$ on the Kondo behavior. In particular, as shown before, for large enough positive $D$ the system behaves as a "non-Landau" Fermi liquid that cannot be adiabatically connected to a non-interacting system turning off the interactions. For negative $D$ the Kondo effect is strongly suppressed. The model studied is suitable for a comprehensive analysis for recent investigations of a single Ni impurity embedded into an Au chain., Comment: 15 pages, 14 figures

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 initiate a study of the growth and matrix-valued Hilbert series of non-negatively graded twisted Calabi-Yau algebras that are homomorphic images of path algebras of weighted quivers, generalizing techniques previously used to investigate Artin-Schelter regular algebras and graded Calabi-Yau algebras. Several results are proved without imposing any assumptions on the degrees of generators or relations of the algebras. We give particular attention to twisted Calabi-Yau algebras of dimension d at most 3, giving precise descriptions of their matrix-valued Hilbert series and partial results describing which underlying quivers yield algebras of finite GK-dimension. For d = 2, we show that these are algebras with mesh relations. For d = 3, we show that the resulting algebras are a kind of derivation-quotient algebra arising from an element that is similar to a twisted superpotential., Comment: 49 pages

This is a general study of twisted Calabi-Yau algebras that are $\mathbb{N}$-graded and locally finite-dimensional, with the following major results. We prove that a locally finite graded algebra is twisted Calabi-Yau if and only if it is separable modulo its graded radical and satisfies one of several suitable generalizations of the Artin-Schelter regularity property, adapted from the work of Martinez-Villa as well as Minamoto and Mori. We characterize twisted Calabi-Yau algebras of dimension 0 as separable $k$-algebras, and we similarly characterize graded twisted Calabi-Yau algebras of dimension 1 as tensor algebras of certain invertible bimodules over separable algebras. Finally, we prove that a graded twisted Calabi-Yau algebra of dimension 2 is noetherian if and only if it has finite GK dimension., Comment: 54 pages. Title has been changed (formerly titled "A twisted Calabi-Yau toolkit"). Revisions to the writing throughout

We study a generalized Anderson model that mixes two localized configurations --one formed by two degenerate doublets and the other by a triplet with single-ion anisotropy $DS_z^2$-- by means of two degenerate conduction channels. The model has been derived for a single Ni impurity embedded into an O-doped Au chain. Using the numerical renormalization group, we find a topological quantum phase transition, at a finite value $D_c,$ between two regular Fermi liquid phases of high (low) conductance and topological number $2 I_L/\pi = 0$ (-1) for $D < D_c$ ($D > D_c$), where $I_L$ is the well-known Luttinger integral. At finite temperature the two phases are separated by a non-Fermi liquid phase with fractional impurity entropy $\frac{1}{2}{\rm ln}2$ and other properties which remind those of the two-channel Kondo model., Comment: 6 pages + Supplemental Material, 8 figures

Partial disorder --the microscopic coexistence of long-range magnetic order and disorder-- is a rare phenomenon, that has been experimental 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 $\sqrt{3}\times \sqrt{3}$-distorted triangular lattice, which shows that its quantum ground state has partial disorder in the weakly frustrated regime. This state has a 180$^\circ$ N\'eel 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., Comment: 6 pages + Supplemental Material. Final version to appear in Physical Review Letters

Tetragonal CuO (T-CuO) has attracted attention because of its structure similar to that of the cuprates. It has been recently proposed as a compound whose study can give an end to the long debate about the proper microscopic modeling for cuprates. In this work, we rigorously derive an effective one-band generalized $t\!-\!J$ model for T-CuO, based on orthogonalized Zhang-Rice singlets, and make an estimative calculation of its parameters, based on previous \textit{ab initio} calculations. By means of the self-consistent Born approximation, we then evaluate the spectral function and the quasiparticle dispersion for a single hole doped in antiferromagnetically ordered half-filled T-CuO. Our predictions show very good agreement with angle-resolved photoemission spectra and with theoretical multiband results. We conclude that a generalized $t\!-\!J$ model remains the minimal Hamiltonian for a correct description of single-hole dynamics in cuprates., Comment: 5 pages, 4 figures. Supplemental Material. To be published in Physical Review Letters

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., Comment: 28 pages + 8 figures. Extended version

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., Comment: 8 pages, 7 figures

We study the monoidal dagger category of Hilbert C*-modules over a commutative C*-algebra from the perspective of categorical quantum mechanics. The dual objects are the finitely presented projective Hilbert C*-modules. Special dagger Frobenius structures correspond to bundles of uniformly finite-dimensional C*-algebras. A monoid is dagger Frobenius over the base if and only if it is dagger Frobenius over its centre and the centre is dagger Frobenius over the base. We characterise the commutative dagger Frobenius structures as finite coverings, and give nontrivial examples of both commutative and central dagger Frobenius structures. Subobjects of the tensor unit correspond to clopen subsets of the Gelfand spectrum of the C*-algebra, and we discuss dagger kernels., Comment: 35 pages

We investigate, using the density matrix renormalization group, the evolution of the Nagaoka state with $t'$ hoppings that frustrate the hole kinetic energy in the $U=\infty$ Hubbard model on the anisotropic triangular lattice and the square lattice with second-nearest neighbor hoppings. We find that the Nagaoka ferromagnet survives up to a rather small $t'_c/t \sim 0.2.$ At this critical value, there is a transition to an antiferromagnetic phase, that depends on the lattice: a ${\bf Q}=(Q,0)$ spiral order, that continuously evolves with $t'$, for the triangular lattice, and the usual ${\bf Q}=(\pi,\pi)$ N\'eel order for the square lattice. Remarkably, the local magnetization takes its classical value for all considered $t'$ ($t'/t \le 1$). 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., Comment: 7 pages, 7 figures

In this paper we study right $S$-Noetherian rings and modules, extending of notions introduced by Anderson and Dumitrescu in commutative algebra to noncommutative rings. Two characterizations of right $S$-Noetherian rings are given in terms of completely prime right ideals and point annihilator sets. We also prove an existence result for completely prime point annihilators of certain $S$-Noetherian modules with the following consequence in commutative algebra: If a module $M$ over a commutative ring is $S$-Noetherian with respect to a multiplicative set $S$ that contains no zero-divisors for $M$, then $M$ has an associated prime., Comment: 8 pages; corrections made to Example 1 and Theorem 2.3

Combining ab initio calculations and effective models derived from them, we discuss the electronic structure of oxygen doped gold chains when one Au atom is replaced by any transition-metal atom of the $3d$ series. The effect of O doping is to bring extended Au $5d_{xz}$ and $5d_{yz}$ states to the Fermi level, which together with the Au states of zero angular momentum projection, lead to three possible channels for the screening of the magnetism of the impurity. For most 3d impurities the expected physics is similar to that of the underscreened Kondo model, with singular Fermi liquid behavior. For Fe and Co under a tetragonal crystal field introduced by leads, the system might display a non-Fermi liquid behavior. Ni and Cu impurities are described by a $S = 1$ two channel Kondo model and an SU(4) impurity Anderson model in the intermediate valence regime, respectively. In both cases, the system is a Fermi liquid, but the conductance shows some observable differences with the ordinary SU(2) Anderson model., Comment: 18 pages, 5 figures and 5 tables

The Anderson impurity model is studied by means of the self-consistent hybridization expansions in its non-crossing (NCA) and one-crossing (OCA) approximations. We have found that for the one-channel spin-$1/2$ particle-hole symmetric Anderson model, the NCA results are qualitatively wrong for any temperature, even when the approximation gives the exact threshold exponents of the ionic states. Actually, the NCA solution describes an overscreened Kondo effect, because it is the same as for the two-channel infinite-$U$ single level Anderson model. We explicitly show that the NCA is unable to distinguish between these two very different physical systems, independently of temperature. Using the impurity entropy as an example, we show that the low temperature values of the NCA entropy for the symmetric case yield the limit $S_{imp}(T=0)\rightarrow \ln\sqrt{2},$ which corresponds to the zero temperature entropy of the overscreened Kondo model. Similar pathologies are predicted for any other thermodynamic property. On the other hand, we have found that the OCA approach lifts the artificial mapping between the models and restores correct properties of the ground-state, for instance, a vanishing entropy at low enough temperatures $S_{imp}(T=0)\rightarrow0$. Our results indicate that the very well known NCA should be used with caution close to the symmetric point of the Anderson model., Comment: 9 pages, 3 figures. Accepted for publication in Physical Review B

We investigate how a C*-algebra could consist of functions on a noncommutative set: a discretization of a C*-algebra $A$ is a $*$-homomorphism $A \to M$ that factors through the canonical inclusion $C(X) \subseteq \ell^\infty(X)$ when restricted to a commutative C*-subalgebra. Any C*-algebra admits an injective but nonfunctorial discretization, as well as a possibly noninjective functorial discretization, where $M$ is a C*-algebra. Any subhomogenous C*-algebra admits an injective functorial discretization, where $M$ is a W*-algebra. However, any functorial discretization, where $M$ is an AW*-algebra, must trivialize $A = B(H)$ for any infinite-dimensional Hilbert space $H$., Comment: 16 pages. This paper supersedes arXiv:1412.1721

We investigate the spin dynamics of the square-lattice spin-1/2 Heisenberg antiferromagnet by means of an improved mean field Schwinger boson calculation. By identifying both, the long range N\'eel and the RVB-like components of the ground state, we propose an educated guess for the mean field triplet 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 triplet 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 $(\pi,0)$ 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., Comment: 6 pages with 3 figures

We assess the reliability of the one-crossing approximation (OCA) approach in quantitative description of the Mott transition in the framework of the dynamical mean field theory (DMFT). The OCA approach has been applied in the conjunction with DMFT to a number of heavy-fermion, actinide, transition metal compounds, and nanoscale systems. However, several recent studies in the framework of impurity models pointed out to serious deficiencies of OCA and raised questions regarding its reliability. Here we consider a single band Hubbard model on the Bethe lattice at finite temperatures and compare the results of OCA to those of a numerically exact quantum Monte Carlo (QMC) method. The temperature-local repulsion U phase diagram for the particle-hole symmetric case obtained by OCA is in good agreement with that of QMC, with the metal-insulator transition captured very well. We find, however, that the insulator to metal transition is shifted to higher values of U and, simultaneously, correlations in the metallic phase are significantly overestimated. This counter-intuitive behavior is due to simultaneous underestimations of the Kondo scale in the metallic phase and the size of the insulating gap. We trace the underestimation of the insulating gap to that of the second moment of the high-frequency expansion of the impurity spectral density. Calculations for the system away from the particle-hole symmetric case are also presented and discussed.

By means of ab initio calculations we study the effect of O-doping of Au chains containing a nanocontact represented by a Ni atom as a magnetic impurity. In contrast to pure Au chains, we find that with a minimun O-doping the $5d_{xz,yz}$ states of Au are pushed up, crossing the Fermi level. We also find that for certain O configurations, the Ni atom has two holes in the degenerate $3d_{xz,yz}$ orbitals, forming a spin $S=1$ due to a large Hund interaction. The coupling between the $5d_{xz,yz}$ Au bands and the $3d_{xz,yz}$ of Ni states leads to a possible realization of a two-channel $S=1$ Kondo effect. While this kind of Kondo effect is commonly found in bulk systems, it is rarely observed in low dimensions. The estimated Kondo scale of the system lies within the present achievable experimental resolution in transport measurements. Another possible scenario for certain atomic configurations is that one of the holes resides in a $3d_{z^2}$ orbital, leading to a two-stage Kondo effect, the second one with SU(4) symmetry.

We characterize the diagonalizable subalgebras of End(V), the full ring of linear operators on a vector space V over a field, in a manner that directly generalizes the classical theory of diagonalizable algebras of operators on a finite-dimensional vector space. Our characterizations are formulated in terms of a natural topology (the "finite topology") on End(V), which reduces to the discrete topology in the case where V is finite-dimensional. We further investigate when two subalgebras of operators can and cannot be simultaneously diagonalized, as well as the closure of the set of diagonalizable operators within End(V). Motivated by the classical link between diagonalizability and semisimplicity, we also give an infinite-dimensional generalization of the Wedderburn-Artin theorem, providing a number of equivalent characterizations of left pseudocompact, Jacoboson semisimple rings that parallel various characterizations of artinian semisimple rings. This theorem unifies a number of related results in the literature, including the structure of linearly compact, Jacobson semsimple rings and cosemisimple coalgebras over a field., Comment: 39 pages

Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying a special property must be prime. We present a "Prime Ideal Principle" that gives a uniform method of proving such facts, generalizing the Prime Ideal Principle for commutative rings due to T.Y. Lam and the author. Old and new "maximal implies prime" results are presented, with results touching on annihilator ideals, polynomial identity rings, the Artin-Rees property, Dedekind-finite rings, principal ideals generated by normal elements, strongly noetherian algebras, and just infinite algebras., Comment: 22 pages

The C*-algebra of bounded operators on the separable infinite-dimensional Hilbert space cannot be mapped to a W*-algebra in such a way that each unital commutative C*-subalgebra C(X) factors normally through $\ell^\infty(X)$. Consequently, there is no faithful functor discretizing C*-algebras to AW*-algebras, including von Neumann algebras, in this way., Comment: 5 pages. Please note that arXiv:1607.03376 supersedes this paper. It significantly strengthens the main results and includes positive results on discretization of C*-algebras

We investigate the excitation spectrum of the triangular-lattice antiferromagnetic $XXZ$ model using series expansions and mean field Schwinger bosons approaches. The single-magnon spectrum computed with series expansions exhibits rotonic minima at the middle points of the edges of the Brillouin zone, for all values of the anisotropy parameter in the range $0\leq J^z/J\leq1$. Based on the good agreement with series expansions 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 $Ba_3CoSb_2O_9$. In particular, we obtain an extended continuum above the spin wave excitations, which is further enhanced and brought closer to those observed in $Ba_3CoSb_2O_9$ 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 {\it bosonic} spinons presents an efficient way to describe them., Comment: 8 pages, 4 figures

We study the infinite U Hubbard model with one hole doped away half-filling, in triangular and square lattices with frustrated hoppings that invalidate Nagaoka's theorem, by means of the density matrix renormalization group. 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 occurs in two different ways: by a non-trivial spin-Berry phase acquired by the hole or by the effective vanishing of the hopping amplitude along the frustrating loops., Comment: 12 pages and 4 figures, with Supplementary Material. To be published in Phys. Rev. Lett

We study the occurrence of symmetry breakings, at zero and finite temperatures, in the J_1-J_3 antiferromagnetic Heisenberg model on the square lattice using Schwinger boson mean field theory. For spin-1/2 the ground state breaks always the SU(2) symmetry with a continuous quasi-critical transition at J_3/J_1=0.38, from N\'eel to spiral long range order, although local spin fluctuations considerations suggest an intermediate disordered regime around 0.35 < J_3/J_1 < 0.5, in qualitative agreement with recent numerical results. At low temperatures we find a Z_2 broken symmetry region with short range spiral order characterized by an Ising-like nematic order parameter that compares qualitatively well with classical Monte Carlo results. At intermediate temperatures the phase diagram shows regions with collinear short range orders: for J_3/J_1<1 N\'eel (\pi,\pi) correlations and for J_3/J_1>1 a novel phase consisting of four decoupled third neighbour sublattices with N\'eel (\pi,\pi) correlations in each one. We conclude that the effect of quantum and thermal fluctuations is to favour collinear correlations even in the strongly frustrated regime., Comment: 17 pages, accepted for publication in Journal of Physics: condensed Matter

Joint measurability of sharp quantum observables is determined pairwise, and so can be captured in a graph. We prove the converse: any graph, whose vertices represent sharp observables, and whose edges represent joint measurability, is realised by quantum theory. This leads us to show that it is not always possible to use Neumark dilation to turn unsharp observables into sharp ones with the same joint measurability relations, highlighting a caveat in the church of the larger Hilbert space"., Comment: 5 pages

We prove that operator algebras that have enough projections are completely determined by those projections, their symmetries, and the action of the latter on the former. This includes all von Neumann algebras and all AW*-algebras. We introduce active lattices, which are formed from these three ingredients. More generally, we prove that the category of AW*-algebras is equivalent to a full subcategory of active lattices. Crucial ingredients are an equivalence between the category of piecewise AW*-algebras and that of piecewise complete Boolean algebras, and a refinement of the piecewise algebra structure of an AW*-algebra that enables recovering its total structure., Comment: 26 pages

There are two fundamental obstructions to representing noncommutative rings via sheaves. First, there is no subcanonical coverage on the opposite of the category of rings that includes all covering families in the big Zariski site. Second, there is no contravariant functor F from the category of rings to the category of ringed categories whose composite with the global sections functor is naturally isomorphic to the identity, such that F restricts to the Zariski spectrum functor Spec on the category of commutative rings (in a compatible way with the natural isomorphism). Both of these no-go results are proved by restricting attention to matrix rings., Comment: 13 pages; final version

Every commuting set of normal matrices with entries in an AW*-algebra can be simultaneously diagonalized. To establish this, a dimension theory for properly infinite projections in AW*-algebras is developed. As a consequence, passing to matrix rings is a functor on the category of AW*-algebras., Comment: 24 pages. Comments very welcome!

We study the low temperature properties of the triangular-lattice Heisenberg antiferromagnet with a mean field Schwinger spin-1/2 boson scheme that reproduces quantitatively the zero temperature energy spectrum derived previously using series expansions. By analyzing the spin-spin and the boson density-density dynamical structure factors, we identify the unphysical spin excitations that come from the relaxation of the local constraint on bosons. This allows us to reconstruct a free energy based on the physical excitations only, whose predictions for entropy and uniform susceptibility seem to be reliable within the temperature range $0< T <0.3J, which is difficult to access by other methods. The high values of entropy, also found in high temperature expansions studies, can be attributed to the roton-like narrowed dispersion at finite temperatures., Comment: 16 pages, 5 figures