Papers

We prove the absence of nontrivial local conserved quantities in a class of $U(1)$-symmetric spin-$1$ chains with nearest-neighbor interactions in which some of the quadrupolar couplings vanish, a class that is not covered by previous studies. Applying the technique of Shiraishi to these systems, we show that, for every model in this class on a periodic chain of $N$ sites, there is no $k$-local conserved quantity for any $3\le k\le N/2$. In particular, for a frustration-free spin-$1$ chain that exhibits spontaneous $U(1)$ symmetry breaking at zero temperature in one spatial dimension, we prove that every local conserved quantity with support up to half of the system size is a linear combination of the identity, the total magnetization $S^z$, and the Hamiltonian itself. This rigorously establishes that, unlike the Heisenberg ferromagnet, the model admits no local order parameter commuting with the Hamiltonian, so that its continuous symmetry breaking is enabled by the frustration-free structure rather than by a conserved order parameter. We also prove the absence of $k$-local conserved quantities for $3\le k\le N/2$ in the periodic Motzkin chain, a frustration-free spin-$1$ chain closely related to the original Motzkin chain, for which spontaneous $U(1)$ symmetry breaking at zero temperature has also been reported.

We employ the hybrid Monte Carlo method to efficiently compute the many-anyon non-Abelian braiding matrices associated with different braiding schemes of the Moore-Read quasiholes. A novel proposal in this work is that anyon braiding schemes based on a global rotation are robust against finite-size effects, as demonstrated by benchmarking their errors in the braiding matrix against those of a simple two-anyon exchange. Moreover, we investigate how electron-electron interactions and local electrostatic trapping potentials influence the energetic preference of different fusion channels. Their effect on the non-Abelian braiding matrices has been verified, a surprising phenomenon that demonstrates long-range entanglement of non-Abelian states. Our results are relevant to the experimental realization of non-Abelian physics in fractional quantum Hall and other analogous systems, including the fast-growing field of fractional quantum anomalous Hall states in moiré materials.

Using temperature-dependent rotational anisotropy second harmonic generation (RA-SHG), we identify a charge density wave (CDW) instability on the CoSi (001) face with an onset temperature at $90.0 \pm 0.8$ K. The SHG response tracks the order parameter amplitude, dominated by two nonlinear tensor elements, whose background-subtracted intensity evolves with temperature as a power law. The extracted critical exponent $\beta = 0.30 \pm 0.03$ is consistent with the 3D XY universality class, an unexpected result for a nominally two-dimensional surface layer. No corresponding anomaly is observed in the bulk response, establishing the transition as a purely surface-driven phase transition. We attribute this unexpected scaling to the coupling between surface Fermi-arc states and the bulk topology they are tied to, grounded in a previously observed intra-unit-cell phase relationship between surface sublayers that gives the order parameter intrinsic three-dimensional structure.

Gutzwiller-projected Bardeen–Cooper–Schrieffer (BCS) wave functions of Abrikosov fermions are widely used to describe quantum many-body states. Taking the one-dimensional transverse-field Ising model as an example, we exactly embed any even-parity spinless fermionic Gaussian state representable as a paired exponential in the chosen particle basis into a projected BCS state of spinful Abrikosov fermions. The construction provides controlled initial states for variational Monte Carlo studies of nonintegrable models.

The magnetic structure of a magnetic topological semimetal EuMnSb$_2$ is investigated in fields up to 30 T using polarized and unpolarized neutron diffraction, pulsed-field x-ray magnetic circular dichroism and pulsed-field magnetometry. We determine the zero-field magnetic structures of the Eu and Mn sublattices, and find that magnetic transitions induced by applied fields below 2 T correspond to changes in the magnetic order of the Eu spins alone without detectable perturbation to the order of the Mn spins. An additional magnetic transition is observed at fields close to the saturation field for the Eu spins. We present a mean-field model which describes key features of the magnetic behavior and allows us to estimate the dominant Eu–Eu and Eu–Mn exchange interactions responsible for the coupling between magnetism and electronic topology.

We investigate the emergence of a scarred discrete time crystal (SDTC) phase in a periodically driven dimerized spin chain. While generic interacting Floquet systems are expected to thermalize according to the eigenstate thermalization hypothesis (ETH), we demonstrate that this system hosts quantum many-body scars (QMBS) that induce a regime of weak ergodicity breaking. Through an analysis of Floquet level statistics, entanglement entropy, and eigenstate fidelity, we identify a manifold of low-entanglement states characterized by semi-Poisson statistics embedded within an otherwise thermal spectrum. These scarred states support robust subharmonic oscillations with period doubling, signaling the spontaneous breaking of discrete time-translation symmetry. We show that the SDTC response is robust against a variety of initial state configurations, demonstrating its stability beyond fine-tuned conditions. A finite-size scaling analysis reveals that the time-crystalline lifetime grows with system size within the range accessible to our exact-diagonalization calculations. However, drawing on the general phenomenology of approximate many-body scars, we expect that hybridization between Floquet scars and the thermal continuum will eventually curtail this growth, causing the lifetime to saturate at system sizes beyond our current numerical reach. This characterizes the SDTC as a long-lived metastable dynamical regime rather than a strictly stable thermodynamic phase, providing a comprehensive framework for understanding the interplay between periodic driving and constrained many-body dynamics in disorder-free systems.

Experiments have revealed that collective strong coupling in optical cavities can drastically alter the conductivity and dielectric properties of molecular ensembles, or even trigger abrupt phase transitions (in Rayleigh scattering or dispersion force driven conformational equilibrium). Until now, the underlying physical mechanism has remained unknown. A recently proposed theory attributes these collective effects to cavity-induced electron correlations that share properties of the known spherical Sherrington-Kirkpatrick model of a spin glass. As a consequence, entropic effects can trigger a phase transition in the inter-molecular electron correlations that could potentially explain the above experiments. In the following work, we derive analytic expressions for the correlation (free-)energy-induced polarizability changes, which reveal that under certain conditions collective strong coupling can even render our molecular ensemble metallic by entropically ionizing collectively degenerate molecular orbitals. Our results are a first major step towards a holistic theory of cavity-mediated electron correlation effects.

Higher-form symmetries generalize conventional global symmetries and act on lower-dimensional submanifolds of a quantum system. While Abelian topological phases can be organized by 1-form symmetries that form a group, non-Abelian topological phases based on finite groups require 1-form symmetry operators governed by non-invertible fusion algebras. In this work, we make this statement precise in quantum double lattice models $\mathcal D(G)$ for finite non-Abelian groups $G$. We construct the electric, magnetic, and dyonic 1-form operators directly at the lattice fixed point and show that together they form a complete nonlocal diagnostic algebra for the topological Hilbert space. Using these operators, we explicitly determine the cylinder and torus ground-state subspaces for arbitrary finite $G$. Furthermore, we calculate the microscopic fusion and gluing of the 1-form symmetries and show that their topological deformation properties emerge after projection to the defect-free topological subspace. Our results establish ground states of non-Abelian quantum double models as a concrete microscopic realization of spontaneous non-invertible 1-form symmetry breaking and provide an operator language that may be useful for characterizing such states in quantum processors.

Rayleigh-Ritz on a subspace from sample-based quantum diagonalization yields the spectral function of a probe state; we ask what bounds its error. The captured Born weight w does not do so alone: an analytic counterexample forces any bound indexed on it to its trivial value. On Hubbard rings at broadening $\eta=0.18t$, the probe's whole support (w=1) still has relative error 0.35–0.43: Rayleigh-Ritz displaces the poles a subspace keeps. The error is bounded instead by the missed weight and the Hamiltonian coupling across the subspace boundary. Given the exact ground state, we prove for any orthogonal projector that the relative $L_1$ error lies between 1-w and $\min\{1+w,(1+\sqrt{w})(\sqrt{1-w}+\Lambda(\eta)/\eta)\}$, with $\Lambda$, that coupling at resolution $\eta$, computed from the Ritz pairs and the retained probe. We test it on L-site rings with classical Born draws of an exactly time-evolved probe, or their infinite-shot ranking; our device runs are execution records only. On the ranked subspaces the bound is vacuous at every operating fraction of the resource scan, at all five sizes up to a 10306296-determinant sector: its leakage branch exceeds the trivial bound 1+w by factors 1.66–8.61. It is informative only well above those fractions, where it is calibrated: at L=6–12 it first beats the trivial bound at a true error of (1.2–7.3)$\times10^{-3}$, though an unproven fit in 1-w is tighter on 11 of 14 splits. For the Born-ranked $A(k,\omega)$ at 85% of its sector, the bound is 350–900 times the true error. In the determinant basis, zero leakage at full weight needs every symmetry-allowed determinant: the probe's measured Krylov support at L=6–14. Plane-wave orbitals reduce a momentum probe's support to one block, 1/L of an exponentially growing sector. At full weight a second-order certificate follows; below it, where every operating fraction lies, one is open.

We study the dynamical spin response of UTe$_2$ by using a mixed-dimensional periodic Anderson model. Within the BCS-RPA formalism, we examine how the $f$-orbital character of the quasiparticles affects magnetic excitations in both the normal and superconducting (SC) states. In the normal state, finite mixing between localized $f$ electrons and conduction electrons produces a hybridization gap and enhances the spin response at $\mathbf{Q}_{\mathrm{Y}} = (0,\pi,0)$, indicating that the magnetic excitation originates from particle–hole scattering across the hybridization gap. In the SC state, we compare four odd-parity irreducible representations, $A_u$, $B_{1u}$, $B_{2u}$, and $B_{3u}$, for the spin-triplet order parameter. We find that, for the component of the spin susceptibility parallel to the $\mathbf{d}$ vector, a pronounced superconductivity-induced spin resonance appears at $\mathbf{Q}_{\mathrm{Y}}$ only in the $B_{2u}$ state. This behavior arises because the $B_{2u}$ order parameter remains finite and changes its sign between the relevant $f$-electron-dominated Fermi-surface regions connected by $\mathbf{Q}_\mathrm{Y}$ near $k_z=\pi$. The sign-change criterion is applicable to multiband superconductors in three-dimensional heavy-fermion systems, in the presence of (i) low-dimensional portions of the Fermi surface connected by a nesting vector, (ii) the dominance of the $f$-electron character, and (iii) the finite amplitude of SC gap on the portions.

The origin of the proposed bond disproportionated insulating state of the non-centrosymmetric ($Pnn2$) phase of Ag$_{2}$BiO$_{3}$ is explored using first principles electronic structure calculations. The novel insulating state is elucidated by first considering the initially proposed centosymmetric metallic ($Pnna$) phase of Ag$_{2}$BiO$_{3}$. Our calculations reveal that the valence skipping Bi$^{4+}$ ions in this phase are better described as Bi$^{3+}\underline{L}$ with completely filled Bi-(6$s$) states and a ligand hole. However, phonon calculations indicate that the metallic ($Pnna$) state is dynamically unstable. Structural stability is achieved through breathing distortions of the oxygen octahedra, resulting in two inequivalent Bi sites and a reduction of symmetry to the $Pnn2$ phase. Electronic structure calculations further reveal that the $Pnn2$ phase is a bond disproportionated insulator where the nominal charge state of Bi is described by : 2[Bi$^{3+}\underline{L}$ (Bi$^{4+}$)] $\rightarrow$ Bi$^{3+}\underline{L}^{2-\delta}$ (Bi1$^{5+}$) + Bi$^{3+}\underline{L}^{\delta}$ (Bi2$^{3+}$), highlighting the crucial role of ligand holes in driving the insulating state. Next we have investigated the electronic structure of Ag$_{2}$BiO$_{3}$ in the insulating ($Pnn2$) phase including spin-orbit coupling. Our density functional theory (DFT ) calculations complemented by ${\bf k.p}$ model Hamiltonian analysis reveal persistent spin-textures around the $X$ and $Y$ high symmetry points of the orthorhombic Brillouin zone imposed by non-symmorphic symmetry, positioning Ag$_{2}$BiO$_{3}$ as a promising candidate for spintronic applications.

Time- and angle-resolved photoemission spectroscopy provides direct access to pump-induced changes in the electronic structure of correlated materials, but its theoretical description generally requires computationally demanding two-time non-equilibrium calculations. We introduce an instantaneous approximation for pump-driven correlated systems, based on a separation between the rapid decay of the Green's functions in the relative time variable and their slower evolution in the average time. Combined with a one-shot dynamical mean-field construction at the Hubbard I level, the method incorporates the driven dynamics of the local correlated shell into the lattice Green's function while retaining momentum resolution. We also derive an effective coupling for nominally dipole-forbidden d-d excitations. It arises from a dipole-allowed d-p transition followed by p-d hybridization; beyond the instantaneous limit, the same process produces an energy-dependent vertex correction to the optical response. As a proof of principle, we apply the framework to paramagnetic and antiferromagnetic FePS3, using a density-functional theory derived tight-binding model together with a supercell unfolding procedure. The calculated momentum-resolved spectra reproduce the main qualitative features observed after excitation of the first and second d-d transitions in recent time-resolved photoemission experiments.

Fractionalizing a quantum two-level system is usually associated with encodings based on pairs of Majorana fermions—an operational fractionalization. We show an alternative algebraic fractionalization by embedding Székely's classical “half-coin” into a non-Hermitian Krein space. The coefficients of $(q+pz)^{1/2}$ define a signed sequence and a normalized, non-Hermitian biorthogonal operator describing a biorthogonal half-qubit. We prove that two such objects fuse into an arbitrary pure qubit through the signed Vandermonde convolution that the collective $N\ge2$ vectors are null in Krein space. $L_1$ norm of the half-qubit follows in closed form, $\lVert p\rVert_1 = 2\sqrt{q}-\sqrt{q-p}$. Its $L_1$ norm increases monotonically with the bias and attains its supremum $\sqrt{2}$ precisely at the unbiased point $p=q=1/2$. Interestingly, we identify two structural results as follows. First, number parity and the $\eta$-metric generate a distinguished commuting $\mathbb Z_2\times\mathbb Z_2$ subgroup. Second, we find the $\eta$-metric obstructs any local $\eta$-self-adjoint partner of the parity, so a half-qubit carries a $\mathbb{Z}_2$ observable but no local $SU(2)$. The full Pauli algebra emerges only upon fusion. We then show that the construction survives truncation of the Fock basis: the fused qubit is exact at every cutoff, and the Vandermonde cancellation is visible in sign-weighted photon-number statistics, and can be tested using existing cavity and trapped-ion state-synthesis methods. Finally, we generalize this algebraic fractionalization to a $1/n$-qubit, which can be achieved by replacing the square root with an $n$th root.

Entanglement among particles is a defining feature of strongly correlated quantum materials, distinguishing them from conventional metals and semiconductors. The ability to certify intrinsic entanglement among interacting electrons in solid-state materials is important not only for classifying quantum states of matter, but also for developing material-based quantum technologies. Here, we introduce a transport-based protocol for witnessing multipartite entangled electronic states, based on the equilibrium noise spectrum as an experimentally accessible observable. The appropriately integrated, symmetrized, and projected current noise obeys an upper bound that can be derived from microscopic model parameters and is invariant with respect to the choice of electronic basis. We benchmark this framework in several paradigmatic systems, including twisted bilayer graphene, twisted bilayer MoTe$_2$, and Hubbard models, certifying entanglement in the fractional Chern insulating state. The method extends recently developed scattering-based entanglement witnesses to ultralow-temperature materials, where conventional spectroscopic probes are inaccessible but candidate entangled states are expected to arise.

We present a framework for topological learning based on exceptional point (EP) braiding in a non-Hermitian Bogoliubov-de Gennes Hamiltonian. A closed algebraic equation for the EP super-surface is derived; through momentum quantisation in finite systems, it predicts the exact number and parameter positions of all EPs in real space, irrespective of system size. The EP topology is characterised by two quantised invariants the state-swap fidelity and the normalised Berry phase which cannot both be zero for a topological EP. A complete topological map shows that all EPs lie within a specefic region. Adiabatic encirclements confirm robust state swapping and yield a universal set of braid gates, including Pauli-X, Pauli-Y, Pauli-Z, a Hadamard-like gate, the T-gate, and a SWAP operation, with the special case where a is 0, providing additional phase gates. Building on these generators, we reformulate learning as braid programming a discrete search over the braid group that replaces gradient descent on continuous weights with combinatorial optimisation. A proof-of-concept genetic search successfully discovers short braid words that reproduce the standard Hadamard gate and the H.Z gate with perfect fidelity. This paradigm offers inherent noise immunity, catastrophic-forgetting prevention through compositional concatenation, and guaranteed generalisation by mathematical construction, establishing EP braiding as a promising substrate for robust, interpretable, and topologically protected neuromorphic computation.

We study the emergence of altermagnetic topological phases stabilized by Ising spin-orbit coupling in a prototypical Lieb lattice model of a correlated altermagnet. Treating the electron interactions within the Hartree-Fock and the exact diagonalization techniques, we establish the co-existence of a quantum spin Hall effect with altermagnetic spin order over a wide region of the parameter space for average electron densities of 2 and 4 per unit cell. We explore how the magnetic structure along edges influences the electronic behavior of the associated topological edge modes, demonstrating their robustness against inversion-symmetry breaking terms.

We investigate the ground-state properties and quantum critical behavior of a non-Hermitian transverse-field Ising chain subjected to longitudinal and complex transverse magnetic fields. To address this interacting many-body problem, we employ real-valued neural quantum states based on Restricted Boltzmann Machines (RBMs), optimized using Variational Monte Carlo (VMC) sampling. Spectral analysis of finite chains reveals exceptional points associated with spontaneous parity-time (PT) symmetry breaking. A real-valued RBM framework is developed to reconstruct the ground-state eigenstates of the non-Hermitian Hamiltonian. Benchmark comparisons with exact diagonalization demonstrate that the RBM approach accurately reproduces the ground-state energy, magnetization, and spin-spin correlations. Extending the analysis to larger system sizes, we identify a non-Hermitian quantum phase transition characterized by PT-symmetry breaking and the emergence of magnetic order. Our results establish real-valued neural quantum states as an efficient and scalable framework for investigating critical phenomena in interacting non-Hermitian quantum systems.

We present a method for calculating static lattice susceptibilities with inhomogeneous dynamical mean-field theory. The method utilizes the response of the system to an external field and thereby circumvents two-particle vertex functions. We demonstrate the success of our approach for the magnetic susceptibility of the square-lattice Hubbard model using the numerical renormalization group as an impurity solver and show that it compares well with the results obtained using the standard vertex approach. As it avoids vertex functions and is compatible with virtually any impurity solver, our method is able to reach low temperatures that are hard to access with other methods.

We show that the Hodge-de Rham decomposition of the Berry curvature organises the transport of a Bloch band and its fluctuations within a single geometric structure. Splitting the curvature into $L^2$-orthogonal harmonic, exact, and co-exact sectors yields a dictionary for both moments of the current. In the mean response the harmonic sector carries the topological anomalous-Hall conductivity, the exact sector the Fermi-surface geometry and the antisymmetric Berry-curvature dipole of polar metals, and, in three dimensions, the co-exact sector the chiral anomaly, quantised by the Weyl-node charges. In the fluctuations, described by a particle-conserving stochastic Boltzmann equation constrained by the fluctuation-dissipation theorem (FDT), the harmonic sector is silent, so topological transport is noiseless, while the field-driven noise is sourced by the geometric sectors (solely the exact sector in two dimensions); current-noise spectroscopy therefore separates global band topology from local band geometry. We prove that the harmonic null-space protection is dimension-independent, and we settle the remaining sector: the co-exact (monopole) sector carries no conservation law and, under the thermal sampling measure, mixes with the exact sector at $\mathcal{O}(1)$, so it furnishes no clean noise observable. The separation the noise provides is therefore two-way, topology versus geometry, in both two and three dimensions.

The discovery of altermagnetism has initiated intensive research and opened new avenues for spin- tronic and transport applications. While current efforts are mostly focused on bulk materials which are typically insulating, here we propose design strategies to achieve a combination of altermag- netism and metallicity in oxide superlattices by exploiting symmetry breaking, electrostatic doping and confinement. While bulk SrCrO3 does not exhibit altermagnetism due to compensating effects between adjacent layers our density functional theory calculations with a Hubbard U parameter re- veal, that a single SrCrO3 layer confined in a (SrCrO3)1/(SrTiO3)1(001) superlattice (SL) exhibits a sizable non-relativistic spin splitting (NRSS) up to 350 meV with bulk d-wave nature due to the coexistence of orbital ordering and octahedral rotations (OORs). Since this system is insulating, we extend to SrCrO3/LaCrO3(001) SLs. In the (SrCrO3)4/(LaCrO3)4(001) SL the combination of a polar discontinuity at the interface and stronger OORs promotes metallic d-wave altermagnetism. The NRSS of up to 120 meV is contributed by the interfacial Cr d bands at the Fermi level with indications for a spin-selective Fermi surface nesting. These findings establish oxide superlattices as a promising platform to realize and explore altermagnetism for quantum transport and spintronic functionalities

A nuclear Fermi liquid exhibits competing pairing instabilities in different spin, isospin, and orbital channels. In a Fermi-surface renormalization group (RG) treatment, the channel that develops a pole first is determined not only by its tree-level attraction but also by its one-loop RG coefficient. We illustrate this mechanism in a minimal $S/P$-wave model. A spherical Fermi surface establishes the reference competition between the lowest even- and odd-parity interactions. Axial deformation changes the relevant Fermi-surface integrals and lifts the degeneracy between longitudinal and transverse $P$-wave components. In isospin-asymmetric matter, neutron–proton Fermi-momentum splitting restricts the simultaneous low-energy contribution of the two species and can terminate the $np$ running at finite threshold scales. Our calculations are intended as controlled one-loop RG illustrations rather than as quantitative nuclear-matter calculations. We show how the Fermi-surface geometry and composition can change the ordering of competing pairing instabilities.

Although tremendous progress has been made in recent years in the field of polyhydride superconductors, the realization of high critical temperature superconductivity still relies on formidable high pressures. Searching for superconducting hydrides at lower pressures is of particular importance. Here we report the first experimental synthesis of the Mg2RhH6, which achieves superconductivity under a significantly reduced pressure of 30 GPa. The synthesis of Mg2RhH6 proceeds via a two step process (1) preparation of the Mg2RhH5 precursor containing hydrogen atoms stabilized by covalent bonds, followed by (2) hydrogen supplementation resulting in the filling of electrons into anti bonding orbitals above 30 GPa, which was accompanied by the structural transition from RhH5 square pyramid to RhH6 octahedron. Superconductivity is achieved at 30 GPa with a Tc of 24 K, which is further enhanced to 29 K at 53 GPa, evidenced by a sharp drop of resistivity to zero and characteristic suppression of Tc under applied magnetic fields. Our experiments prove the Mg2RhH6 superconductor to be thermodynamically stable above 30 GPa, making it the first case exhibiting a Tc of approximately 30 K at a readily accessible pressure. This study pioneers a highly promising pathway for the rational design and discovery of high temperature superconductors within phonon mediated BCS framework.

Gapped chiral phases pose an intrinsic obstruction to projected entangled pair state (PEPS) representations with finite bond dimension $D$, which generically develop spurious long-range correlations despite the gapped nature of the target state. To address this long-standing problem, we take a qualitatively different route by considering the target chiral system together with a completely decoupled time-reversed auxiliary copy. Constraining the finite-$D$ PEPS to the factorized form would simply reduce the problem to representing each chiral layer independently, leaving the original finite-$D$ obstruction unchanged. Unexpectedly, however, we find that finite-$D$ variational optimization generates an emergent residual interlayer entanglement, despite the absence of any explicit interlayer coupling in the Hamiltonian. This emergent entanglement is the key mechanism that bypasses the obstruction, qualitatively changing the PEPS from an effectively gapless representation with long-range correlation tails to one with a finite correlation length. We demonstrate this mechanism for both a free-fermion Chern insulator and an interacting chiral spin liquid. The residual entanglement is systematically suppressed with increasing $D$, approaching the decoupled limit, while the chiral topological information remains accessible through layer-resolved entanglement spectra. Our results thus uncover a previously unrecognized mechanism for bypassing the chiral obstruction through variationally generated auxiliary entanglement.

We bound the error in ground-state expectations of local observables caused by truncating the spatial tails of a gapped quantum lattice Hamiltonian. We show that the error is controlled by the interaction strength discarded near each site, rather than by the extensive norm of the omitted Hamiltonian. If the gap remains open along a path that removes the interaction tail, the resulting bounds are uniform in system size and extend, under suitable assumptions, to thermodynamic-limit ground states. The convergence rate reflects the decay of the interaction tail: it is algebraic for power-law interactions, superpolynomial for superpolynomial interactions, and exponential at any strictly smaller rate for exponentially decaying interactions. For superpolynomial interactions, we also derive a direct infinite-volume estimate using automorphic equivalence. The results extend to isolated low-energy sectors and parity-even fermionic systems. For two-body interactions decaying as $r^{-p}$ in $d$ dimensions, we prove an error bound $O(R^{-(p-d)})$ for $p>2d$, where $R$ is the truncation range. We construct a gapped non-translation-invariant example that saturates this scaling, showing that the bound is optimal for the general class considered. Our results quantify when finite-range truncations faithfully reproduce the local physics of gapped long-range systems.

Downfolding ab initio material band structure into a low-energy subspace spanned by orbitals of specified atomic character, a procedure known as Wannier downfolding, is a common task in the simulation of complex materials. We introduce the Intrinsic Wannier Function (IWF) method to Wannierize bands with given atomic character. The method is non-iterative and requires only a single dimensionless parameter to disentangle bands. In benchmarks on silicon, graphene, and the three-band model of a mercury cuprate, we show that Intrinsic Wannier Functions provide high quality downfolded band structures compared to those from standard approaches such as Maximally Localized Wannier Functions and the Selected Columns of the Density Matrix method. Further, their straightforward implementation and robustness positions Intrinsic Wannier Functions as a general and useful tool for Wannier downfolding in materials electronic structure and in high-throughput applications.

We propose several zero-point type arguments based on the inevitable zero point(s) of a spectral gap in the quantum spin system phase diagrams in various dimensions. We consider multi-parameter families of Hamiltonian extending the conventional zero-point theorem that includes only one parameter. Analogously to the zero-point theorem, we only impose model-independent transformation relations along the parameter boundary, rather than specifying any low-energy dynamics or response. We further give a series of conjectures, which generalize our statements in a uniform way. Our results give powerful and universal model-independent constraints on the possible relevant operators for critical phenomena in quantum spin models in arbitrary high dimensions.

A class of monitored topological invariants compares ordinary and symmetry-twisted quantum trajectories with identical stochastic records, so direct estimation requires exponentially costly matched-record postselection. We replace the twisted quantum experiment by uniformly randomized symmetry eigenstates with known charges, ordinary-boundary monitoring, and an offline twist decoder. Their correlation yields an exact finite-time response identity and removes this experimental sampling bottleneck. When the ordinary charge sharpens and the ordinary-to-flux deformation has trivial net readout-character flow, the response converges to the projective commutator of the symmetry-protected-topological phase; generator-pair responses then determine its finite-Abelian cohomology class. Spectator-sector crossings may close the global Lyapunov gap without changing this character-valued response. In monitored cluster circuits, the decoder is exact and polynomial in the Gaussian limit, while Gaussian-drop reconstruction treats interacting records; independent joint-sector spectroscopy and effect-state diagnostics validate the topological deformation.

Local measurements transform a many body wavefunction into a statistical ensemble of conditional quantum states. In chaotic systems, the higher moments of such ensembles diagnose the emergence of quantum state randomness, but their structure at equilibrium quantum criticality is largely unknown. Here we show that the projected ensemble of a Tomonaga-Luttinger liquid exhibits a universal nonlinear hierarchy of state overlap moments. Remarkably, the leading scaling exponents are independent of the continuously varying Luttinger parameter. Replica boundary conformal field theory reveals a geometric origin: outcome locking combines the active replica swaps into a single collective rotated sector, while intersecting compact replica branes eliminate the leading interaction dependent zero mode contribution. Matrix product state calculations across the interacting XXZ critical phase and direct free fermion calculations independently confirm the interaction independence and nonlinear hierarchy.

We investigate a spin-$1/2$ anisotropic Heisenberg model on a lattice consisting of two identical bipartite sublattices. A family of exact eigenstates generated by the restricted spectrum generating algebra (RSGA) constitutes quantum many-body scar states, characterized by subextensive entanglement entropy and supporting. These scar states are magnon-pair condensates exhibiting off-diagonal long-range order (ODLRO). At the resonance point of the inter-sublattice interaction, the model exactly maps onto a mixed spin-$1$ and spin-$0$ XY model on a bipartite lattice, which decomposes into independent sub-Hamiltonians labeled by all possible spin configurations. Each spin-$0$ particle is dynamically isolated from its neighbors and acts as a kinetic constraint, giving rise to emergent Hilbert space fragmentation (HSF). Our work establishes an exactly solvable platform in which quantum many-body scars, magnon-pair condensation exhibiting off-diagonal long-range order, and Hilbert space fragmentation naturally coexist.

We investigated the structural and magnetic properties of single-crystalline SmCuAs$_2$ using high-resolution synchrotron X-ray diffraction and X-ray resonant magnetic scattering (XRMS) at the Sm $L_2$ and $L_3$ edges. Temperature-dependent diffraction measurements confirm that SmCuAs$_2$ maintains its tetragonal symmetry from room temperature down to 8 K, with lattice parameters showing anomalous behavior below the resistivity minimum ($T \approx$ 30 K). Notably, the c-axis lattice parameter exhibits a plateau and subsequent increase near the Néel temperature, indicating magnetoelastic coupling. XRMS measurements reveal a commensurate antiferromagnetic structure with a propagation vector \textbf{q} = (0, 0, 0.5). Our measurement shows that the Sm moments are aligned within the \textbf{ab} plane and arranged in a $++--$ stacking along the \textbf{c}-axis. Comparison with related RECuAs$_2$ compounds (RE = Pr, Nd, and Gd) suggests that in-plane moment orientation and associated magnetic frustration play a key role in the emergence of the resistivity minimum. Differences in spin-orbit and magnetoelastic coupling across the series highlight their importance in governing low-temperature transport behavior.