Deconfined quantum criticality represents an exotic state of matter that is characterized by emergent symmetry and fractionalized spin excitations. However, its stabilization in frustrated quantum magnets and corresponding spectral signatures have remained elusive. Here, we investigate the spin excitation spectra of the highly frustrated S = 1/2 antiferromagnetic (AFM) Shastry-Sutherland model, tracing the evolution of low-energy collective modes across the transition from the Néel AFM phase to the plaquette valence bond solid (PVBS) phase. We show that the magnon bands in the AFM state exhibit opposite chiralities and a non-relativistic splitting, arising from the altermagnetic nature as dictated by the underlying lattice symmetry. We further uncover two remarkable low-lying excitations: a Higgs mode in the longitudinal excitation channel and an S = 0 excitation with vanishing spectral weight. Upon approaching the AFM-to-PVBS transition, both these modes soften concurrently with the lowest-energy triplet and singlet modes of the PVBS state. The energy gap closing of the Higgs mode, together with the nearly degenerate velocities of S = 1 and S = 0 excitations, provides direct spectral evidence that the AFM-to-PVBS transition is proximate to a deconfined quantum critical point with emergent O(4) symmetry. Our results help clarify the spectral fingerprint of deconfined quantum criticality and advance the understanding of symmetry-enhanced quantum phase transitions more broadly.

We present a theoretical study of the low-energy physics of a quarter-hole-filled two-orbital bilayer Hubbard model motivated by transition-metal bilayer systems with strong orbital-selective interlayer hybridization. By explicitly treating the strong interlayer bonding of dz2 orbitals within a molecular orbital basis and projecting out high-energy electronic states, we derive a low-energy effective Kugel-Khomskii Hamiltonian describing the interplay between electron spin and emergent layer pseudospin degrees of freedom. We map out a rich ground state phase diagram featuring diverse spin and charge ordered states. These include conventional ferromagnetic and antiferromagnetic phases with layer staggered charge densities, a layer-coherent phase characterized by spontaneous interlayer quantum coherence, and a novel maximally spin-layer-entangled phase with a hidden composite spin-layer order. We show that this exotic hidden ordered phase arises from the spontaneous breaking of an emergent O(4) symmetry down to a O(3), manifesting a unique excitation spectrum with three entangled gapless Goldstone modes. Our results uncover a geometrically driven mechanism for realizing composite entanglement in strongly correlated bilayer systems and provide a concrete theoretical framework relevant to bilayer nickelate superconductors and other multi-component correlated materials.

Spectroscopic measurements in model 1D correlated systems offer insights for understanding their two-dimensional counterparts, which include the cuprate and iron pnictide/chalcogenide superconductors. A major challenge is the identification of such correlated systems with dominantly 1D physics. In this Letter, inelastic neutron scattering measurements on NaFe_{0.53}Cu_{0.47}As single crystal directly reveal quasi-1D spin excitations, resulting from atomic order that leads to magnetic Fe and nonmagnetic Cu chains. The dominant exchange interaction is antiferromagnetic along the chain [SJ_{∥}≈90.1(3)  meV], whereas the inter-chain couplings are much weaker [SJ_{⊥}≈-2.4(1)  meV and SJ_{c}≈0.15(5)  meV]. The quasi-1D spin excitations in NaFe_{0.53}Cu_{0.47}As stem from both the Néel and stripe vectors, with Néel excitations sensitive to Fe impurities on the Cu site. The spin excitations in quasi-1D NaFe_{0.53}Cu_{0.47}As and quasi-2D FeSe exhibit a striking resemblance, suggesting a common origin for their coexistent stripe and Néel excitations. Our findings demonstrate magnetic dilution in NaFeAs leads to dimension reduction of its magnetic degree of freedom, presenting a strategy for discovering low-dimensional quantum materials.

The phase diagram of iron-based superconductors contains a host of electronic orders, which are intimately connected with their superconductivity. Here we analyze the fluctuations of one type of nematic order in another. Our analysis leads to an emergent U(1) symmetry at a first-order transition between a nematic phase and a $C_4$-symmetric charge-ordered phase. We characterize the continuous symmetry in terms of a certain hidden Lie algebra that links the different orders. This emergent symmetry leads to a Goldstone mode at the transition and causes softening of excitations in the nematic and charge sectors near the transition. The underlying physics bears a resemblance to the anisotropic XZ spin model, with the nematic order and charge $C_4$ order parameters playing the roles of the $x$ and $z$ components of the magnetization vector, respectively. We provide the experimental evidence in support of the proposed effects, and discuss the general implications of our results for the physics of iron-based superconductors and other correlated systems.

Simulating U(1) quantum gauge theories with spatial dimensions greater than one is of great physical significance. Here we propose a simple realization of U(1) gauge theory with Rydberg and Rydberg-dressed atom arrays. Within the experimentally accessible range, we find that the various aspects of the U(1) gauge theory can be well simulated, such as the emergence of topological sectors, incommensurability, and the Rokhsar-Kivelson point that hosts deconfined charge excitations and degenerate topological sectors. Our proposal is promising to implement experimentally and exhibits pronounced quantum dynamics.

Shastry-Sutherland magnet is a typical frustrated spin system hosting rich phases. While the Heisenberg limit has been extensively studied, the role of spin-orbit coupling is not well explored. Motivated by newly discovered rare-earth Shastry-Sutherland magnets, we construct a generic effective-spin model that describes the interactions between Kramers doublet local moments on a Shastry-Sutherland lattice. Due to the strong spin-orbit coupling, the model takes the form of extended XYZ interactions on both intra- and inter-dimer bonds. We show that, in addition to the conventional "singlet" dimer phase, strong spin-orbit coupling can stabilize peculiar "triplet" dimer phases. These "triplet" dimer phases, though fully gapped, respond immediately to magnetic fields and evolve smoothly into the fully polarized phase. We present that the recently discovered Shastry-Sutherland magnet Yb_2Be_2GeO_7 belongs to the "triplet" dimer phase, and discuss the implication of our results to a broad class of quantum magnets in general.

Rydberg blockade effect provides a convenient platform for simulating locally constrained many-body systems, such as quantum dimer models and quantum loop models, especially their novel phases like topological orders and gapless quantum spin ice (QSI) phases. To discuss the possible phase diagram containing different QSIs in three-dimensional (3D) Rydberg arrays, we have constructed an extended Rokhsar-Kivelson (RK) Hamiltonian with equal weight superposition ground state in different fillings at the RK point. Therefore, the perfect QSIs with fixed local dimer filling and their monomer-doped states can be simulated directly by Monte Carlo sampling. Using single-mode approximation, the excitations of dimers and monomers have also been explored in different fillings. We find that, in the thermodynamical limit, even doping a small amount of monomers can disrupt the topological structure and lead to the existence of off-diagonal long-range order. However, in a finite size (as in cold-atom experiment), the property of QSI will be kept in a certain region like a crossover after doping. The phase diagram containing different QSIs and off-diagonal order phases is proposed.

Recent numerical and theoretical studies on the two-dimensional $J$-$Q_3$ model suggests that the deconfined quantum critical point is actually a $SO(5)$-symmetry-enhanced first-order phase transition that is spontaneously broken to $O(4)$. However, this conclusion has mainly relied on finite-size scaling of the entanglement entropy, lacking direct evidence from physical observables.} Here, we investigate the dynamical spectra of spin and bond operators at the deconfined critical point of the $J$-$Q_3$ model using large-scale quantum Monte Carlo simulations, and contrasting them with the well-established $\mathrm{O(3)}$ Wilson-Fisher criticality in the $J_1$-$J_2$ Heisenberg model. Although both models exhibit two gapless magnon modes in the Néel phase, their critical behaviors diverge strikingly. At the $J_1$-$J_2$ critical point, the Higgs mode becomes gapless, yielding three gapless modes that reflect the full restoration of the $\mathrm{O(3)}$ symmetry. {In the $J$-$Q_3$ model, we instead observe four gapless transverse modes at the either side of the transition. This spectral feature, together with the entanglement entropy results, provides direct evidence for the weakly first-order scenario that the deconfined quantum critical point exhibits an emergent $\mathrm{SO(5)}$ symmetry that spontaneously breaks to $\mathrm{O(4)}$.

Motivated by the rapid experimental progress on the rare-earth Shastry-Sutherland lattice magnets, we propose a generic effective spin model that describes interacting non-Kramers local moments on the Shastry-Sutherland lattice. We point out that the local moments consist of both magnetic dipole and quadrupole components and the effective model turns out to be an extended XYZ model with an intrinsic field that accounts for the crystal field splitting. We then study the ground-state phase diagram of the model and find that pure quadrupole orders, which are invisible to conventional experimental probes, can be stabilized over a broad regime. In particular, we show that a hidden ``1/3 magnetization plateau'' with quadrupole orders generally exists and discuss its experimental signatures. Finally, we discuss the relevance of our results to the rare-earth Shastry-Sutherland lattice magnets Pr$_{2}$Ga$_{2}$BeO$_{7}$ and Pr$_{2}$Be$_{2}$GeO$_{7}$.

Phase transitions in condensed matter are a source of exotic emergent properties. We study the fully frustrated bilayer Heisenberg antiferromagnet to demonstrate that an applied magnetic field creates a previously unknown emergent criticality. The quantum phase diagram contains four states with distinctly different symmetries, all but one pair separated by first-order transitions. We show by quantum Monte Carlo simulations that the thermal phase diagram is dominated by a wall of discontinuities extending between the dimer-triplet phases and the singlet-containing phases. This wall is terminated at finite temperatures by a critical line, which becomes multicritical where the Berezinskii-Kosterlitz-Thouless (BKT) transition of the dimer-triplet antiferromagnet and the thermal Ising transition of the singlet-triplet crystal phase also terminate. The combination of merging symmetries leads to a 4-state Potts universality not contained in the microscopic Hamiltonian, which we interpret within the Ashkin-Teller model. Our results represent a systematic step in understanding emergent phenomena in quantum magnetic materials, including the “Shastry-Sutherland compound” SrCu 2 (BO 3 ) 2 .

We propose an extended compass model that hosts subsystem symmetries and has potential experimental relevance with 3d transition metal compounds. The subsystem symmetries strongly constrain the mobility of spin excitations and lead to profound consequences. At the quantum critical point we find the presence of "critical Bose surface" along the entire $k_x$ and $k_y$ axis. Across which we find a nodal-line spin liquid that undergoes nematic instability at low temperatures. In the ferro-quadrupole phase, we find that one excitation is immobile individually analogous to "fractons".

Frustrated quantum magnets can host a variety of exotic spin excitations, including fractionalized spin excitations coupled to emergent gauge fields at deconfined quantum critical points (DQCPs) and chiral magnons in altermagnets. Here, we investigate the spin excitation spectra of the highly frustrated S=1/2 antiferromagnetic (AFM) Shastry-Sutherland model, focusing on the evolution of low-energy collective modes from the Néel AFM phase to the plaquette valence bond solid (PVBS). We demonstrate that the AFM state exhibits altermagnetic behavior, characterized by a non-relativistic splitting between two chiral magnon bands. Furthermore, we identify two additional low-energy excitations: a Higgs mode in the longitudinal excitation channel and an S=0 excitation with vanishing spectral weight. As the system approaches the AFM-to-PVBS transition, both these modes soften along with the lowest-energy triplet and singlet modes in the PVBS state. The closing gap of the Higgs mode, combined with the nearly degenerate velocities of S=1 and S=0 excitations, provides spectral evidence that the AFM-to-PVBS transition is proximate to a DQCP with emergent O(4) symmetry. Our results help clarify the spectral signature of a broad class of symmetry enhanced quantum phase transitions including deconfined quantum criticality.

Phase transitions in condensed matter are often linked to exotic emergent properties. We study the fully frustrated bilayer Heisenberg antiferromagnet to demonstrate that an applied magnetic field creates a novel emergent criticality. The quantum phase diagram contains four states, the DS (singlets on every interlayer dimer bond), DTAF (all triplets with antiferromagnetic order), TC (a singlet-triplet checkerboard) and FM (saturated ferromagnet). The thermal phase diagram is dominated by a wall of discontinuities extending from the zero-field DTAF-DS transition to a quantum critical endpoint where the field drives the DTAF and TC into the FM. This first-order wall is terminated at finite temperatures by a line of critical points, where the Berezinskii-Kosterlitz-Thouless (BKT) transition of the DTAF and the thermal Ising transition of the TC also terminate. We demonstrate by quantum Monte Carlo simulations that the BKT transition does not change the Ising nature of the DTAF-DS critical line. By contrast, the combination of symmetries merging on the multicritical DTAF-TC line leads to a 4-state Potts universality not contained in the microscopic Hamiltonian, which we associate with the Ashkin-Teller model. Our results represent a systematic step in understanding emergent phenomena in quantum magnetic materials including the ``Shastry-Sutherland compound'' SrCu$_2$(BO$_3$)$_2$.

Motivated by the recent discovery of superconductivity in La$_3$Ni$_2$O$_7$ under pressure, we discuss the basic ingredients of a model that captures its microscopic physics under pressure tuning. We anchor our description in terms of the spectroscopic evidence of strong correlations in this system. In a bilayer Hubbard model including the Ni $3d$ $x^2-y^2$ and $z^2$ orbitals, we show the ground state of the model crosses over from a low-spin $S=1/2$ state to a high-spin $S=3/2$ state. In the high-spin state, the two $x^2-y^2$ and the bonding $z^2$ orbitals are all close to half-filling, which promotes a strong orbital selectivity in a broad crossover regime of the phase diagram pertinent to the system. Based on these results, we construct an effective multiorbital $t$-$J$ model to describe the superconductivity of the system, and find the leading pairing channel to be an intraorbital spin singlet with a competition between the extended $s$-wave and $d_{x^2-y^2}$ symmetries. Our results highlight the role of strong multiorbital correlation effects in driving the superconductivity of La$_3$Ni$_2$O$_7$.

Incommensurability plays a critical role in many strongly correlated systems. In some cases, the origin of such exotic order can be theoretically understood in the framework of 1d line-like topological excitations known as “quantum strings”. Here we study an extended transverse field Ising model on a triangular lattice. Using large-scale quantum Monte Carlo simulations, we find that the spatial anisotropy can stabilize an incommensurate phase out of the commensurate clock order. Our results for the structure factor and the string density exhibit a linear relationship between incommensurate ordering wave vector and the density of quantum strings, which is reminiscent of hole density in under-doped cuprate superconductors. When introducing the next-nearest-neighbor interaction, we observe a quantum tricritical point out of the incommensurate phase. After carefully analyzing the ground state energies within different string topological sectors, we conclude that this tricriticality is non-trivially caused by effective long-range inter-string interactions with two competing terms following different decaying behaviors.

Spin-orbit coupling is an important ingredient to regulate the many-body physics, especially for many spin liquid candidate materials such as rare-earth magnets and Kitaev materials. The rare-earth chalcogenides (Ch = O, S, Se) is a congenital frustrating system to exhibit the intrinsic landmark of spin liquid by eliminating both the site disorders between and ions with the big ionic size difference and the Dzyaloshinskii-Moriya interaction with the perfect triangular lattice of the ions. The temperature versus magnetic-field phase diagram is established by the magnetization, specific heat, and neutron-scattering measurements. Notably, the neutron diffraction spectra and the magnetization curve might provide microscopic evidence for a series of spin configuration for in-plane fields, which include the disordered spin liquid state, 120° antiferromagnet, and one-half magnetization state. Furthermore, the ground state is suggested to be a gapless spin liquid from inelastic neutron scattering, and the magnetic field adjusts the spin orbit coupling. Therefore, the strong spin-orbit coupling in the frustrated quantum magnet substantially enriches low-energy spin physics. This rare-earth family could offer a good platform for exploring the quantum spin liquid ground state and quantum magnetic transitions.

Simulating $\mathrm{U(1)}$ quantum gauge theories with spatial dimension greater than one is of great physical significance yet has not been achieved experimentally. Here we propose a simple realization of $\mathrm{U(1)}$ gauge theory on triangular lattice Rydberg atom arrays. Within experimentally accessible range, we find that the effective model well simulates various aspects of the $\mathrm{U(1)}$ gauge theory, such as emergence of topological sectors, incommensurability, and the deconfined Rokhsar-Kivelson point. Our proposal is easy to implement experimentally and exhibits pronounced quantum dynamics compared with previous proposals realizing $\mathrm{U(1)}$ and $\mathbb Z_2$ gauge theories.

Simulating $\mathrm{U(1)}$ quantum gauge theories with spatial dimension greater than one is of great physical significance yet has not been achieved experimentally. Here we propose a simple realization of $\mathrm{U(1)}$ gauge theory on triangular lattice Rydberg atom arrays. Within experimentally accessible range, we find that the effective model well simulates various aspects of the $\mathrm{U(1)}$ gauge theory, such as emergence of topological sectors, incommensurability, and the deconfined Rokhsar-Kivelson point. Our proposal is easy to implement experimentally and exhibits pronounced quantum dynamics compared with previous proposals realizing $\mathrm{U(1)}$ and $\mathbb Z_2$ gauge theories.

We investigate the quantum dynamics of the antiferromagnetic transverse field Ising model on the triangular lattice through large-scale quantum Monte Carlo simulations and stochastic analytic continuation. This model effectively describes a series of triangular rare-earth compounds, for example, TmMgGaO 4 . At weak transverse field, we capture the excitations related to topological quantum strings, which exhibit continuum features described by XY chain along the strings and those in accord with ‘Luttinger string liquid’ in the perpendicular direction. The continuum features can be well understood from the perspective of topological strings. Furthermore, we identify the contribution of strings from the excitation spectrum. Our study provides characteristic features for the experimental search for string-related excitations and proposes a theoretical method to pinpoint topological excitations in the experimental spectra.