Search

The identification of low-energy thermal excitations in SmMnO3+δ degenerate states of spin and superconducting quantum liquids in magnetic fields H ≤ 3.5 kOe is presented. In the temperature interval 4.2–12 K, the Landau quantization of the low-energy magnetic excitations pair spectrum of Z2 quantum spin liquid is found in the system spinon-gauge field. The formation of a broad continuum of spinon pair excitations in the “weak magnetic field” regime (H = 100 Oe, 1 kOe) in the FC regime is explained in the framework of the Landau quantization models of the compressible spinon gas with fractional values of the factor ν filling three overlapping bands. In the regime of “strong magnetic field” (H = 3.5 kOe), the quantum oscillations of temperature dependences of “supermagnetization” of the incompressible spinon liquid were observed. They have the form of three narrow steps (plateaus), corresponding to a complete filling of the non-overlapping Landau bands with integer values of the filling factor by spinons. These results are evidence for the existence of vortex gauge field fluctuations with a high density in the magnetic fields H ≥ 100 Oe. The strong growth of vortex fluctuations can be explained by a second-kind phase transition in SmMnO3+δ in the form of the vortices condensation. Growth of the external dc magnetic field strength in the SmMnO3+δ samples in the interval of fields 0

(Quasi-)one-dimensional systems exhibit various fascinating properties such as Luttinger liquid behavior, Peierls transition, novel topological phases, and the accommodation of unique quasiparticles (e.g., spinon, holon, and soliton, etc.). Here we study molybdenum blue bronze A0.3MoO3 (A = K, Rb), a canonical quasi-one-dimensional charge-density-wave material, using laser-based angle-resolved photoemission spectroscopy. Our experiment suggests that the normal phase of A0.3MoO3 is a prototypical Luttinger liquid, from which the charge-density-wave emerges with decreasing temperature. Prominently, we observe strong renormalizations of band dispersions, which is recognized as the spectral function of Holstein polaron derived from band-selective electron-phonon coupling in the system. We argue that the strong electron-phonon coupling plays a dominant role in electronic properties and the charge-density-wave transition in blue bronzes. Our results not only reconcile the long-standing heavy debates on the electronic properties of blue bronzes but also provide a rare platform to study novel composite quasiparticles in Luttinger liquid materials., 19 pages, 4 figures, accepted by Nature Communications

We present a comprehensive study of a one-dimensional two-orbital model at and below quarter-filling that realizes a number of unconventional phases. In particular, we find an excitonic density wave in which excitons quasi-condense with finite center of mass momentum and an order parameter that changes phase with wave-vector $Q$. In this phase, excitons behave as hard-core bosons without charge order. In addition, excitons can pair to form bi-excitons in a state that is close to a charge density-wave instability. When pairing dominates over the inter-orbital repulsion, we encounter a regime in which one orbital is metallic, while the other forms a spin gapped superconductor, a genuine orbital selective paired state. All these results are supported by both, analytical and numerical calculations. By assuming a quasi-classical approximation, we solve the three-body hole-electron-spinon problem and show that excitons are held together by forming a bound state with spinons. In order to preserve the antiferromagnetic background, excitons acquire a dispersion that has a minimum away from $k=0$. The full characterization of the different phases is obtained by means of extensive density matrix renormalization group calculations., Long overdue

Two-dimensional triangular-lattice antiferromagnets are predicted under some conditions to exhibit a quantum spin liquid ground state with no energy barrier to create emergent, fractionalized spinon excitations that carry spin but no charge. Materials that realize this kind of spin liquid are expected to have a low-energy behaviour described by a spinon Fermi surface. Directly imaging the resulting spinons, however, is difficult due to their chargeless nature. Here we use scanning tunnelling spectroscopy to image density waves consistent with the predictions of spinon density modulation arising from a spinon Fermi surface instability in single-layer 1T-TaSe2. We confirm the existence of a triangular lattice of localized spins in this material by contacting it with a metallic 1H-TaSe2 substrate and measuring the Kondo effect. Spectroscopic imaging of isolated single-layer 1T-TaSe2 reveals long-wavelength super-modulations at Hubbard band energies, consistent with the predicted behaviour of itinerant spinons. These super-modulations allow the direct experimental measurement of the spinon Fermi wavevector, in good agreement with theoretical predictions for a two-dimensional quantum spin liquid. Some quantum spin liquids are expected to have an effective Fermi surface of fractionalized spinon excitations. The two-dimensional spin liquid candidate 1T-TaSe2 has charge density modulations that may be caused by an unstable spinon Fermi surface.

This paper considers modern ideas about the topological nature of superconductivity and the Mott–Hubbard state in strongly correlated systems. These systems are described in terms of spin and charge separation, i.e., deconfinement of spinons and holons in a gauge field. The role of orbital degrees of freedom is discussed. Analogies with topological insulators, quantum Hall effect, and Landau quantization are considered. The importance of the Chern–Simons term for the correct description of the Hubbard splitting is demonstrated.

Using a combination of neutron scattering, calorimetry, quantum Monte Carlo simulations, and analytic results we uncover confinement effects in depleted, partially magnetized quantum spin ladders. We show that introducing nonmagnetic impurities into magnetized spin ladders leads to the emergence of a new characteristic length L in the otherwise scale-free Tomonaga-Luttinger liquid (serving as the effective low energy model). This results in universal LT scaling of staggered susceptibilities. Comparison of simulation results with experimental phase diagrams of prototypical spin ladder compounds bis(2,3-dimethylpyridinium)tetrabromocuprate(II) (DIMPY) and bis(piperidinium)tetrabromocuprate(II) (BPCB) yields excellent agreement., Physical Review Letters, 128 (23), ISSN:0031-9007, ISSN:1079-7114

Anisotropic triangular antiferromagnets can host two primary spin excitations, namely, spinons and triplons. Here, we utilize polarization-resolved Raman spectroscopy to assess the statistics and dynamics of spinons in Ca3ReO5Cl2. We observe a magnetic Raman continuum consisting of one- and two-pair spinon-antispinon excitations as well as triplon excitations. The twofold rotational symmetry of the spinon and triplon excitations are distinct from magnons. The strong thermal evolution of spinon scattering is compatible with the bosonic spinon scenario. The quasilinear spinon hardening with decreasing temperature is envisaged as the ordering of one-dimensional topological defects. This discovery will enable a fundamental understanding of novel phenomena induced by lowering spatial dimensionality in quantum spin systems., Spinons are quasisparticles that can appear in anisotropic triangular lattices, however, probing the statistics and dynamics of such excitations is experimentally challenging. Here, Choi et al present Raman spectroscopy measurements of anisotropic triangular lattices, showing a bosonic evolution of the spinon scattering.

Quantum spin liquids are exotic states of matter that may be realized in frustrated quantum magnets and feature fractionalized excitations and emergent gauge fields. Here, we consider a gapless U(1) spin liquid with spinon Fermi pockets in two spatial dimensions. Such a state appears to be the most promising candidate to describe the exotic field-induced behavior observed in numerical simulations of the antiferromagnetic Kitaev honeycomb model. A similar such state may also be responsible for the recently-reported quantum oscillations of the thermal conductivity in the field-induced quantum paramagnetic phase of $\alpha$-RuCl$_3$. We consider the regime close to a Lifshitz transition, at which the spinon Fermi pockets shrink to small circles around high-symmetry points in the Brillouin zone. By employing renormalization group and mean-field arguments, we demonstrate that interactions lead to a gap opening in the spinon spectrum at low temperatures, which can be understood as a nesting instability of the spinon Fermi surface. This leads to proliferation of monopole operators of the emergent U(1) gauge field and confinement of spinons. While signatures of fractionalization may be observable at finite temperatures, the gapless U(1) spin liquid state with nested spinon Fermi pockets is ultimately unstable at low temperatures towards a conventional long-range-ordered ground state, such as a valence bond solid. Implications for Kitaev materials in external magnetic fields are discussed., Comment: 19 pages, 7 figures, 1 table; v2: added several minor improvements and references

Effective gauge theories based on slave particle construction are widely used to describe quantum number fractionalization in strongly correlated electron systems. However, even setting aside the debates on the confinement issue of the slave particles, there are still significant conflicts between theory and experiment. In particular, a ${T}^{2/3}$ specific heat anomaly has been predicted to be the smoking-gun signature of low-lying gauge fluctuation in a $U(1)$ spin liquid with a large spinon Fermi surface, which has, however, never been observed. Here we show that such an anomaly is actually an artifact of a Gaussian approximation and is absent when the no-double-occupancy constraint on the slave particles is strictly enforced. We also show that projective construction based on slave particle representation provides a unified understanding of the mechanism of spin fractionalization in one- and two-dimensional spin liquids.

Heavy fermion metals typically exhibit unconventional quantum critical point or quantum critical phase at zero temperature due to competition of Kondo effect and magnetism. Previous theories were often based on certain local type of assumptions and a fully consistent explanation of experiments has not been achieved. Here we develop an efficient algorithm for the Schwinger boson approach to explore the effect of spatial correlations on the Kondo lattice and introduce the concept of nonlocal Kondo effect in the quantum critical region with deconfined spinons. We predict a global phase diagram containing a non-Fermi liquid quantum critical phase with a hidden holon Fermi surface and a partially enlarged electron Fermi surface for strong quantum fluctuations while a single quantum critical point for weak quantum fluctuations. This explains the unusual metallic spin liquid recently reported in the frustrated Kondo lattice CePdAl and resolves the Fermi volume puzzle in YbRh$_2$Si$_2$. Our theory highlights the importance of nonlocal physics and provides a unified understanding of heavy fermion quantum criticality., 11 pages, 6 figures

We show how Oshikawa's theorem for the Fermi surface volume of the Kondo lattice can be extended to the $\mathrm{SU}(N)$ symmetric case. By extending the theorem, we can show that the mechanism of Fermi surface expansion seen in the large $N$ mean-field theory is directly linked to the expansion of the Fermi surface in a spin-$\frac{1}{2}$ Kondo lattice. This linkage enables us to interpret the expansion of the Fermi surface in a Kondo lattice as a fractionalization of the local moments into heavy electrons. Our method allows extension to a pure U(1) spin liquid, where we find the volume of the spinon Fermi surface by applying a spin twist, analogous to Oshikawa's, [Phys. Rev. Lett. 84, 3370 (2000)] flux insertion. Lastly, we discuss the possibility of interpreting the ${\mathrm{FL}}^{*}$ phase characterized by a small Fermi surface in the absence of symmetry breaking, as a nontopological coexistence of such a U(1) spin liquid and an electronic Fermi liquid.

Recent experiments suggest a quantum spin liquid ground state in the material ${\mathrm{PbCuTe}}_{2}{\mathrm{O}}_{6}$, where $S=1/2$ moments are coupled by antiferromagnetic Heisenberg interactions into a three-dimensional structure of corner sharing triangles dubbed the hyper-hyperkagome lattice. It exhibits a richer connectivity, and thus likely a stronger geometric frustration, than the relatively well studied hyperkagome lattice. Here, we investigate the possible quantum spin liquids in the $S=1/2$ hyper-hyperkagome magnet using the complex fermion mean field theory. Extending the results of a previous projective symmetry group analysis, we identify only two ${\mathbb{Z}}_{2}$ spin liquids and a $U(1)$ spin liquid that are compatible with the hyper-hyperkagome structure. The $U(1)$ spin liquid has a spinon Fermi surface. For the ${\mathbb{Z}}_{2}$ spin liquids, one has a small excitation gap, while the other is gapless and proximate to the $U(1)$ spin liquid. We show that the gapped and gapless spin liquids can in principle be distinguished by heat capacity measurements. Moreover, we calculate the dynamical spin structure factors of all three spin liquids and find that they highly resemble the inelastic neutron scattering spectra of ${\mathrm{PbCuTe}}_{2}{\mathrm{O}}_{6}$. Implications of our work to the experiments, as well as its relations to the existing theoretical studies, are discussed.

Here, the authors report the discovery of novel types of U(1) and \ensuremath{\mathbb{Z}}${}_{2}$ quantum spin liquids on the pyrochlore lattice through a projective symmetry group classification. The classification highlights a special type of U(1) spin liquid, possessing an unusual symmetry-protected gapless multi-nodal-line structure in the spinon bands. The effect of gauge fluctuations for such a nodal structure is discussed. The leading contributions to the low-temperature specific heat are calculated, providing a clear experimental diagnostic of this U(1) spin liquid.

Pursuing fractionalized particles that do not bear properties of conventional measurable objects, exemplified by bare particles in the vacuum such as electrons and elementary excitations such as magnons, is a challenge in physics. Here we show that a machine-learning method for quantum many-body systems that has achieved state-of-the-art accuracy reveals the existence of a quantum spin liquid (QSL) phase in the region $0.49\lesssim J_2/J_1\lesssim0.54$ convincingly in spin-1/2 frustrated Heisenberg model with the nearest and next-nearest neighbor exchanges, $J_1$ and $J_2$, respectively, on the square lattice. This is achieved by combining with the cutting-edge computational schemes known as the correlation ratio and level spectroscopy methods to mitigate the finite-size effects. The quantitative one-to-one correspondence between the correlations in the ground state and the excitation spectra enables the reliable identification and estimation of the QSL and its nature. The spin excitation spectra containing both singlet and triplet gapless Dirac-like dispersions signal the emergence of gapless fractionalized spin-1/2 Dirac-type spinons in the distinctive QSL phase. Unexplored critical behavior with coexisting and dual power-law decays of N\'{e}el antiferromagnetic and dimer correlations is revealed. The power-law decay exponents of the two correlations differently vary with $J_2/J_1$ in the QSL phase and thus have different values except for a single point satisfying the symmetry of the two correlations. The isomorph of excitations with the cuprate $d$-wave superconductors implies a tight connection between the present QSL and superconductivity. This achievement demonstrates that the quantum-state representation using machine learning techniques, which had mostly been limited to benchmarks, is a promising tool for investigating grand challenges in quantum many-body physics., Comment: 18 pages, 17 figures, 2 tables, accepted for publication in Phys. Rev. X

An analytic method is proposed to compute the surface energy and elementary excitations of the XXZ spin chain with generic non-diagonal boundary fields. For the gapped case, in some boundary parameter regimes the contributions of the two boundary fields to the surface energy are non-additive. Such a correlation effect between the two boundaries also depends on the parity of the site number $N$ even in the thermodynamic limit $N\to\infty$. For the gapless case, contributions of the two boundary fields to the surface energy are additive due to the absence of long-range correlation in the bulk. Although the $U(1)$ symmetry of the system is broken, exact spinon-like excitations, which obviously do not carry spin-$\frac12$, are observed. The present method provides an universal procedure to deal with quantum integrable systems either with or without $U(1)$ symmetry., 6 pages, 4 figures

An effective Hamiltonian describing fluctuation effects in the magnetic phases of the Hubbard model in terms of spinon excitations is derived. A comparison of spin-rotational Kotliar-Ruckenstein slave boson and Ribeiro-Wen dopon representations is performed. The quantum transition into the half-metallic ferromagnetic state with vanishing of spin-down Fermi surface is treated as the topological Lifshitz transition in the quasimomentum space. The itinerant-localized magnetism transitions and Mott transition in antiferromagnetic state are considered in the topological context. Related metal-insulator transitions in Heusler alloys are discussed., 5 pages, Physics Letters A, the printed version is slightly corrected and extended

A spin- [Formula: see text] lattice Heisenberg Kagome antiferromagnet (KAFM) is a prototypical frustrated quantum magnet, which exhibits exotic quantum spin liquids that evade long-range magnetic order due to the interplay between quantum fluctuation and geometric frustration. So far, the main focus has remained on the ground-state properties; however, the theoretical consensus regarding the magnetic excitations is limited. Here, we study the dynamic spin structure factor (DSSF) of the KAFM by means of the density matrix renormalization group. By comparison with the well-defined magnetically ordered state and the chiral spin liquid sitting nearby in the phase diagram, the KAFM with nearest neighbor interactions shows distinct dynamical responses. The DSSF displays important spectral intensity predominantly in the low-frequency region around the [Formula: see text] point in momentum space and shows a broad spectral distribution in the high-frequency region for momenta along the boundary of the extended Brillouin zone. The excitation continuum identified from momentum- and energy-resolved DSSF signals emergent spinons carrying fractional quantum numbers. These results capture the main observations in the inelastic neutron scattering measurements of herbertsmithite and indicate the spin liquid nature of the ground state. By tracking the DSSF across quantum-phase transition between the chiral spin liquid and the magnetically ordered phase, we identify the condensation of two-spinon bound state driving the quantum-phase transition.

We study Z2 topologically ordered states enriched by translational symmetry by employing a recently developed two-dimensional (2D) bosonization approach that implements an exact Z2 charge-flux attachment in the lattice. Such states can display “weak symmetry breaking” of translations, in which both the Hamiltonian and ground state remain fully translational invariant but the symmetry is “broken” by its anyon quasiparticles, in the sense that its action maps them into a different superselection sector. We demonstrate that this phenomenon occurs when the fermionic spinons form a weak topological superconductor in the form of a 2D stack of one-dimensional Kitaev wires, leading to the amusing property that there is no local operator that can transport the π-flux quasiparticle across a single Kitaev wire of fermonic spinons without paying an energy gap in spite of the vacuum remaining fully translational invariant. We explain why this phenomenon occurs hand in hand with other previously identified peculiar features such as ground-state degeneracy dependence on the size of the torus and the appearance of dangling boundary Majorana modes in certain Z2 topologically ordered states. Moreover, by extending the Z2 charge-flux attachment to open lattices and cylinders, we construct a plethora of exactly solvable models providing an exact description of their dispersive Majorana gapless boundary modes. We also review the Z×(Z2)3 classification of 2D BdG Hamiltonians (class D) enriched by translational symmetry and provide arguments on its robust stability against interactions and self-averaging disorder that preserve translational symmetry.

The spin-orbit entangled nature of the magnetic moments in Kitaev materials is expected to give rise to a quantum spin liquid (QSL) state with fractional excitations. Using resonant inelastic x-ray scattering under a magnetic field, here the authors map the excitation spectra of $\ensuremath{\beta}$-Li${}_{2}$IrO${}_{3}$. They observe a dichotomy between a magnon-like response at low energies, originating from intertwined field-induced ground states, and a multi-spinon-like continuum at higher energies, originating from pairwise excitations of long-lived Majorana fermions of the proximate QSL.

We study a quantum quench in which a magnetic impurity is suddenly coupled to Hubbard chains, whose low-energy physics is described by Tomonaga-Luttinger liquid theory. Using the time-dependent density-matrix renormalization-group (tDMRG) technique, we analyze the propagation of charge, spin and entanglement in the chains after the quench and relate the light-cone velocities to the dispersion of holons and spinons. We find that the local magnetization at the impurity site decays faster if we increase the interaction in the chains, even though the spin velocity decreases. We derive an analytical expression for the relaxation of the impurity magnetization which is in good agreement with the tDMRG results at intermediate timescales, providing valuable insight into the time evolution of the Kondo screening cloud in interacting systems., 11 pages, 5 figures

We study the impact of trimerization (breathing) of the nearest-neighbor (NN) exchange on the planar XY spin-1/2 ferromagnet on the kagome lattice, including additional four-site ring exchange. For uniform NN exchange, this model has previously been shown to transit from a long-range ordered ferromagnet into a Z2 quantum spin liquid by virtue of the ring exchange. Using quantum Monte-Carlo calculations, based on the stochastic series expansion, we present results for the spin stiffness, the quantum phase diagram, the longitudinal static, as well as the transverse dynamic structure factor. Our results corroborate 3D XY universality also at finite trimerization and suggest a simple continuation of the quantum critical point of the uniform case into a line in terms of rescaled exchange parameters. Moreover, at any trimerization and in the ordered phase the elementary excitations can be understood very well in terms of linear spin wave theory, while beyond the critical line, in the spin liquid phase we find signatures of spinon continua., 9 pages, 8 figures

We describe a solvable model of a quantum transition in a single band model involving a change in the size of the electron Fermi surface without any symmetry breaking. In a model with electron density $1-p$, we find a 'large' Fermi surface state with the conventional Luttinger volume $1-p$ of electrons for $p>p_c$, and a first order transition to a 'small' Fermi surface state with a non-Luttinger volume $p$ of holes for $p, Comment: 43 pages, 18 figures. Added a phase diagram as a function of doping. Discussion on 1/M corrections and comments in the introduction are added

We find that the Schwinger Boson mean field theory(SBMFT) supplemented with Gutzwiller projection provides an exceedingly accurate description for the ground state of the spin-$\frac{1}{2}$ triangular lattice antiferromagnetic Heisenberg model(spin-$\frac{1}{2}$ TLHAF). However, we find the SBMFT fails even qualitatively in the description of the dynamical behavior of the system. In particular, the SBMFT fails to predict the Goldstone mode in the magnetic ordered phase. We show that the coherent peak in the two-spinon continuum in the presence of spinon condensate should not be interpreted as a magnon mode. The SBMFT also predicts incorrectly a gapless longitudinal spin fluctuation mode in the magnetic ordered phase. We show that these failures are related to the following facts: (1)Spinon condensation fails to provide a consistent description of the order parameter manifold of the 120 degree ordered phase. (2)There lacks in the SBMFT the coupling between the uncondensed spinon and the spinon condensate, which breaks both the spin rotational and the translational symmetry. (3)There lacks in the SBMFT the rigidity that is related to the no double occupancy constraint on the spinon system. We show that such failures of the SBMFT is neither restricted to the spin-$\frac{1}{2}$ TLHAF nor to the magnetic ordered phase. We proposed a generalized SBMFT to resolve the first two issues and a new formalism to address the third issue., 12 pages, 7 figures

We present numerical solutions of the spectral functions of $t$-$J$ models with random and all-to-all exchange and global SU($M$) spin rotation symmetry. The solutions are obtained from the saddle-point equations of the large volume limit, followed by the large $M$ limit. These saddle point equations involve Green's functions for fractionalized spinons and holons carrying emergent U(1) gauge charges, obeying relations similar to those of the Sachdev-Ye-Kitaev (SYK) models. The low frequency spectral functions are compared with an analytic analysis of the operator scaling dimensions, with good agreement. We also compute the low frequency and temperature behavior of gauge-invariant observables: the electron Green's function, the local spin susceptibility and the optical conductivity; along with the temperature dependence of the d.c. resistivity. The time reparameterization soft mode (equivalent to the boundary graviton in holographically dual models of two-dimensional quantum gravity) makes important contributions to all observables, and provides a linear-in-temperature contribution to the d.c. resistivity., 40 pages, 15 figures

We study the dynamical spin excitations of the one-dimensional $S=1$ Heisenberg antiferromagnetic chain with single-ion anisotropy by using quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation function. Using the transverse dynamic spin structure factor, we observe the quantum phase transition with a critical point between the topological Haldane gapped phase and the trivial phase. At the quantum critical point, we find a broad continuum characterized by the Tomonaga-Luttinger liquid, and its dynamical signatures are similar to a $S=1/2$ Heisenberg antiferromagnetic chain. The broad continuum can be seen as a dynamical signature of spinons. We further identify that the elementary excitations are fractionalized spinons in the critical state.

A spin-1/2 Heisenberg antiferromagnetic chain is one of the most important paradigmatic models in quantum magnetism. Its ground state is a spin singlet, while the excitation spectrum is formed by gapless fractional excitations, spinons. The presence of alternating g-tensors and/or the staggered Dzyaloshinskii-Moriya interaction results in opening the energy gap $$\varDelta \propto H^{2/3}$$ Δ ∝ H 2 / 3 , once the magnetic field H is applied. A fairly good understanding of this phenomenon was achieved in the framework of the sine-Gordon quantum-field theory, taking into account the effective transverse staggered field induced by the applied uniform field. The theory predicts solitons and antisolitons as elementary excitations, as well as their bound states, breathers. Here, I review recent high-field electron spin resonance spectroscopy studies of such systems, focusing on peculiarities of their spin dynamics in the sine-Gordon regime and beyond.

At strong repulsion, the triangular-lattice Hubbard model is described by $s=1/2$ spins with nearest-neighbor antiferromagnetic Heisenberg interactions and exhibits conventional 120$^\circ$ order. Using the infinite density matrix renormalization group and exact diagonalization, we study the effect of the additional four-spin interactions naturally generated from the underlying Mott-insulator physics of electrons as the repulsion decreases. Although these interactions have historically been connected with a gapless ground state with emergent spinon Fermi surface, we find that at physically relevant parameters, they stabilize a chiral spin-liquid (CSL) of Kalmeyer-Laughlin (KL) type, clarifying observations in recent studies of the Hubbard model. We then present a self-consistent solution based on mean-field rewriting of the interaction to obtain a Hamiltonian with similarities to the parent Hamiltonian of the KL state, providing a physical understanding for the origin of the CSL., Comment: 7+15 pages, 4+17 figures

Quantum spin systems exhibit an enormous range of collective excitations, but their spin waves, gapped triplons, fractional spinons, or yet other modes are generally held to be mutually exclusive. Here we show by neutron spectroscopy on SeCuO$_3$ that magnons, triplons, and spinons are present simultaneously. We demonstrate that this is a consequence of a structure consisting of two coupled subsystems and identify all the interactions of a minimal magnetic model. Our results serve qualitatively to open the field of multi-excitation spin systems and quantitatively to constrain the complete theoretical description of one member of this class of materials., 8 pages, 5 figures

We study the antiferromagnetic spin-half Heisenberg ladder in the presence of an additional frustrating rung spin which is motivated and relevant also for the description of real two-dimensional materials such as the two-dimensional trimer magnet Ba$_4$Ir$_3$O$_{10}$. We study the zero-temperature phase diagram, where we combine numerical and analytical methods into an overall consistent description. All numerical simulations are also accompanied by studies of the dynamical spin structure factor obtained via the density matrix renormalization group. Overall, we find in the regime of strong rung coupling a gapped dimerized phase related to competing symmetry sectors in Hilbert space that ultimately results in frustration-driven spin-Peierls transition. In the weak rung-coupling regime, the system is uniform, yet shows a gapped spinon continuum together with a sharp coherent low-energy branch which renders the system critical overall. In either case, the additional rung spin quickly get sidelined and nearly decouple once their bare coupling to the ladder drops somewhat below the direct Heisenberg coupling of the legs., Comment: 14 + 3 pages, 13 figures; fixes of typos and minor textual changes

We demonstrate a remarkable property of metallic Fermi liquids: the transverse conductivity assumes a universal value in the quasi-static ($\omega \rightarrow 0$) limit for wavevectors $q$ in the regime $l_{\rm mfp}^{-1} \ll q \ll p_{\rm F}$, where $l_{\rm mfp}$ is the mean free path and $p_{\rm F}$ is the Fermi momentum. This value is $(e^2/h) \mathcal{R}_{\rm FS}/q$ in two dimensions (2D), where $\mathcal{R}_{\rm FS}$ measures the local radius of curvature of the Fermi surface in momentum space. Even more surprisingly, we find that U(1) spin liquids with a spinon Fermi surface have the same universal transverse conductivity. This means such spin liquids behave effectively as metals in this regime, even though they appear insulating in standard transport experiments. Moreover, we show that transverse current fluctuations result in a universal low-frequency magnetic noise that can be directly probed by a spin qubit, such as a nitrogen-vacancy center in diamond, placed at a distance $z$ above of the 2D metal or spin liquid. Specifically the magnetic noise is given by $C\omega \mathcal{P}_{\rm FS}/z$, where $\mathcal{P}_{\rm FS}$ is the perimeter of the Fermi surface in momentum space and $C$ is a combination of fundamental constants of nature. Therefore these observables are controlled purely by the geometry of the Fermi surface and are independent of kinematic details of the quasi-particles, such as their effective mass and interactions. This behavior can be used as a new technique to measure the size of the Fermi surface of metals and as a smoking gun probe to pinpoint the presence of the elusive spinon Fermi surface in two-dimensional systems. We estimate that this universal regime is within reach of current nitrogen-vacancy center spectroscopic techniques for several spinon Fermi surface candidate materials., Comment: 34 pages, 9 figures

We introduce an entanglement entropy analysis to quantitatively identify the confinement and deconfinement of the spinons in the spin excitations of quantum magnets. Our proposal is implemented by the parton construction of a honeycomb-lattice antiferromagnet exhibiting high-energy anomalous spectra. To obtain the quasiparticles of spin excitations for entanglement entropy calculations, we develop an effective Hamiltonian using the random phase approximation. We elaborate quantitatively the deconfinement-to-confinement transition of spinons in the anomalous spectra with the increase of the Hubbard interaction, indicating the avoided fractionalization of magnons in the strong interaction regime. Meanwhile, the Higgs mode at the {\Gamma}0 point is fractionalized into four degenerate spinon pairs, although it appears as a sharp well-defined peak in the spectra. Our work extends our understanding of the deconfinement of the spinon and its coexistence with the magnon in quantum magnets., Comment: 6 pages, 4 figures

The theory for the vanishing of N\'eel order in the spin $S=1/2$ square lattice antiferromagnet has been the focus of attention for many decades. A consensus appears to have emerged in recent numerical studies on the antiferromagnet with first and second neighbor exchange interactions (the $J_1$-$J_2$ model): a gapless spin liquid is present for a narrow window of parameters between the vanishing of the N\'eel order and the onset of a gapped valence bond solid state. We propose a deconfined critical SU(2) gauge theory for a transition into a stable $\mathbb{Z}_2$ spin liquid with massless Dirac spinon excitations; on the other side the critical point, the SU(2) spin liquid (the `$\pi$-flux' phase) is presumed to be unstable to confinement to the N\'eel phase. We identify a dangerously irrelevant coupling in the critical SU(2) gauge theory, which contributes a logarithm-squared renormalization. This critical theory is also not Lorentz invariant, and weakly breaks the SO(5) symmetry which rotates between the N\'eel and valence bond solid order parameters. We also propose a distinct deconfined critical U(1) gauge theory for a transition into the same gapless $\mathbb{Z}_2$ spin liquid; on the other side of the critical point, the U(1) spin liquid (the `staggered flux' phase) is presumed to be unstable to confinement to the valence bond solid. This critical theory has no dangerously irrelevant coupling, dynamic critical exponent $z \neq 1$, and no SO(5) symmetry. All of these phases and critical points are unified in a SU(2) gauge theory with Higgs fields and fermionic spinons which can naturally realize the observed sequence of phases with increasing $J_2/J_1$: N\'eel, gapless $\mathbb{Z}_2$ spin liquid, and valence bond solid., Comment: 49 pages, 10 figures

We study the spreading of entanglement produced by the time evolution of a local fermionic excitation created above the ground state of the XXZ chain. The resulting entropy profiles are investigated via density-matrix renormalization group calculations, and compared to a quasiparticle ansatz. In particular, we assume that the entanglement is dominantly carried by spinon excitations traveling at different velocities, and the entropy profile is reproduced by a probabilistic expression involving the density fraction of the spinons reaching the subsystem. The ansatz works well in the gapless phase for moderate values of the XXZ anisotropy, eventually deteriorating as other types of quasiparticle excitations gain spectral weight. Furthermore, if the initial state is excited by a local Majorana fermion, we observe a nontrivial rescaling of the entropy profiles. This effect is further investigated in a conformal field theory framework, carrying out calculations for the Luttinger liquid theory. Finally, we also consider excitations creating an antiferromagnetic domain wall in the gapped phase of the chain, and find again a modified quasiparticle ansatz with a multiplicative factor., Comment: 29 pages, 10 figures, error in Fig. 1 corrected + minor changes

We study a generalization of the two-dimensional transverse-field Ising model, combining both ferromagnetic and antiferromagnetic two-body interactions, that hosts exact global and local ${\mathbb{Z}}_{2}$ gauge symmetries. Using exact diagonalization and stochastic series expansion quantum Monte Carlo methods, we confirm the existence of the topological phase in line with previous theoretical predictions. Our simulation results show that the transition between the confined topological phase and the deconfined paramagnetic phase is of first order, in contrast to the conventional ${\mathbb{Z}}_{2}$ lattice gauge model in which the transition maps onto that of the standard Ising model and is continuous. We further generalize the model by replacing the transverse field on the gauge spins with a ferromagnetic $XX$ interaction while keeping the local gauge symmetry intact. We find that the ${\mathbb{Z}}_{2}$ topological phase remains stable, while the paramagnetic phase is replaced by a ferromagnetic phase. The topological-ferromagnetic quantum phase transition is also of first order. For both models, we discuss the low-energy spinon and vison excitations of the topological phase and their avoided level crossings associated with the first-order quantum phase transitions.

We study the effect of Dzyaloshinskii-Moriya (DM) interaction on the triangular lattice U(1) quantum spin liquid (QSL) which is stabilized by ring-exchange interactions. A weak DM interaction introduces a staggered flux to the U(1) QSL state and changes the density of states at the spinon Fermi surface. If the DM vector contains in-plane components, then the spinons gain nonzero Berry phase. The resultant thermal conductances ${\ensuremath{\kappa}}_{xx}$ and ${\ensuremath{\kappa}}_{xy}$ qualitatively agree with the experimental results on the material ${\mathrm{EtMe}}_{3}\mathrm{Sb}[\mathrm{Pd}(\mathrm{dmit}{)}_{2}{]}_{2}$. Furthermore, owing to perfect nesting of the Fermi surface, a spin density wave state is triggered by larger DM interactions. On the other hand, when the ring-exchange interaction decreases, another antiferromagnetic (AFM) phase with 120\ifmmode^\circ\else\textdegree\fi{} order shows up which is proximate to a U(1) Dirac QSL. We discuss the difference of the two AFM phases from their static structure factors and excitation spectra.

Anomalous metals are observed in numerous experiments on disordered two-dimensional systems proximate to superconductivity. A characteristic feature of an anomalous metal is that its low temperature conductivity has a weakly temperature dependent value, significantly higher than that of a disordered Fermi liquid. We propose a dynamical mean-field model of an anomalous metal: interacting electrons similar in structure to that of the well-studied universal Hamiltonian of mesoscopic metallic grains, but with independent random interactions between pairs of sites, involving Cooper pair hopping and spin exchange. We find evidence for critical anomalous phases or points between a superconducting phase and a disordered Fermi liquid phase in this model. Our results are obtained by a renormalization group analysis in a weak coupling limit, and a complementary solution at large $M$ when the spin symmetry is generalized to USp($M$). The large $M$ limit describes the anomalous metal by fractionalization of the electron into spinons, holons, and doublons, with these partons forming critical non-Fermi liquids in the Sachdev-Ye-Kitaev class. We compute the low temperature conductivity in the large $M$ limit, and find temperature-independent values moderately enhanced from that in the disordered metal., Comment: 54 pages, 5 figures

We report gapless quantum spin liquid behavior in the layered triangular ${\mathrm{Sr}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}$ system. X-ray diffraction shows superlattice reflections associated with atomic site ordering into triangular Cu planes well separated by Sb planes. Muon spin relaxation measurements show that the $S=\frac{1}{2}$ moments at the magnetically active Cu sites remain dynamic down to 65 mK in spite of a large antiferromagnetic exchange scale evidenced by a large Curie-Weiss temperature ${\ensuremath{\theta}}_{\mathrm{CW}}\ensuremath{\simeq}\ensuremath{-}143\text{ }\text{ }\mathrm{K}$ as extracted from the bulk susceptibility. Specific heat measurements also show no sign of long-range order down to 0.35 K. The magnetic specific heat (${C}_{m}$) below 5 K reveals a ${C}_{m}=\ensuremath{\gamma}T+\ensuremath{\alpha}{T}^{2}$ behavior. The significant ${T}^{2}$ contribution to the magnetic specific heat invites a phenomenology in terms of the so-called Dirac spinon excitations with a linear dispersion. From the low-$T$ specific heat data, we estimate the dominant exchange scale to be $\ensuremath{\sim}36\text{ }\text{ }\mathrm{K}$ using a Dirac spin liquid ansatz which is not far from the values inferred from microscopic density functional theory calculations ($\ensuremath{\sim}45\text{ }\text{ }\mathrm{K}$) as well as high-temperature susceptibility analysis ($\ensuremath{\sim}70\text{ }\text{ }\mathrm{K}$). The linear specific heat coefficient is about $18\text{ }\text{ }\mathrm{mJ}/\mathrm{mol}\text{ }{\mathrm{K}}^{2}$ which is somewhat larger than for typical Fermi liquids.

We find that the best resonating valence bond (RVB) state of the spin-$\frac{1}{2}$ kagome antiferromagnetic Heisenberg model (spin-$\frac{1}{2}$ KAFH) is described by a ${Z}_{2}$ mean field ansatz belonging to the ${Z}_{2}[0,\ensuremath{\pi}]\ensuremath{\beta}$ class, which hosts a mean field spinon dispersion very different from that of the widely studied $U(1)$ Dirac spin liquid state. However, we find that the physical spin fluctuation spectrum calculated from the Gutzwiller projected random phase approximation (RPA) (GRPA) theory above such an RVB state is actually gapless and is almost identical to that above the $U(1)$ Dirac spin liquid state. We find that such a peculiar behavior can be attributed to the unique flat band physics on the kagome lattice, which makes the mapping between the mean field ansatz and the RVB state noninjective. We find that the spin fluctuation spectrum of the spin-$\frac{1}{2}$ KAFH is not at all featureless, but is characterized by a prominent spectral peak at about $0.25J$ around the $\mathbf{M}$ point, which is immersed in a broad continuum extending to $2.7J$. Based on these results, we argue that the spectral peak below 2 meV in the inelastic neutron scattering spectrum of hebertsmithite ${\mathrm{ZnCu}}_{3}{(\mathrm{OH})}_{6}{\mathrm{Cl}}_{2}$, which has been attributed to the contribution of ${\mathrm{Cu}}^{2+}$ impurity spins occupying the ${\mathrm{Zn}}^{2+}$ site, should rather be understood as the intrinsic contribution from the kagome layer. We propose to verify such a picture by measuring the Knight shift on the Cu site, rather than the O site, which is almost blind to the spin fluctuation at the $\mathbf{M}$ point as a result of the strong antiferromagnetic correlation between nearest neighboring spins on the kagome lattice.

This work presents the inelastic neutron scattering spectrum on the spin-1/2 anisotropic triangular lattice antiferromagnetCa_3 ReO_5 Cl_2 , and show that the spinon-like continuum coexists with dispersive modes due to the formation of bound spinon pairs.