Understanding how frustration and disorder shape relaxation in complex systems is a central problem in statistical physics and quantum annealing. Spin glass models provide a natural framework to explore this connection, as their energy landscapes are governed by competing interactions and constrained topologies. We investigate the nonexponential relaxation behavior of spin glasses on network architectures relevant to quantum annealing hardware—such as finite size Chimera, Pegasus, and Zephyr graphs—where embedding constraints and finite connectivity strongly modulate the distribution of barriers and metastable states. This slow relaxation arises from the combined effects of frustration and disorder, which persist even beyond the conventional spin glass transition. Within the Fortuin-Kasteleyn-Coniglio-Klein cluster formalism, the appearance of unfrustrated cluster regions gives rise to multiple relaxation scales, as distinct domains follow different dynamical pathways across a rugged energy landscape. This framework enables a broader characterization of spin glass energy landscapes and provides physical insight into how topological constraints, frustration, and disorder jointly govern relaxation dynamics in complex networks relevant to quantum annealing architectures.

We investigate the electronic structure of ${\mathrm{AgF}}_2, {\mathrm{AgFBF}}_4$, AgF, and ${\mathrm{Ag}}_2\mathrm{O}$ using x-ray absorption spectroscopy (XAS) and resonant inelastic x-ray scattering (RIXS) at the Ag $L_3$ edge. XAS results were compared with density functional theory computations of the spectra, allowing an identification of main features and an assessment of the theoretical approximations. Our RIXS measurements reveal that ${\mathrm{AgF}}_2$ exhibits charge-transfer (CT) excitations and $dd$ excitations, analogous to those observed in ${\mathrm{La}}_2{\mathrm{CuO}}_4$. We propose to use the ratio of $dd$ to CT spectral weight as a measure of the covalence of the compounds and provide explicit equations for the weights as a function of the scattering geometry for crystals and powders. The measurements at the metal site $L_3$ edge and previous measurement in the ligand $K$ edge reveal a striking similarity between the fluoride and cuprate materials, with fluorides somewhat more covalent than cuprates. These findings support the hypothesis that silver fluorides are an excellent platform to mimic the physics of cuprates, providing a promising avenue for exploring high-$T_c$ superconductivity and exotic magnetism in quasi-two-dimensional (${\mathrm{AgF}}_2$) and quasi-one-dimensional (${\mathrm{AgFBF}}_4$) materials.

By means of cellular dynamical mean-field theory (CDMFT), we study how short-range correlations drive the breakdown of the self-consistent perturbation theory in two-dimensional systems and the most relevant physical consequences associated with it, such as the CDMFT Mott transition. To this aim, we first derive in a structured and consistent way the Bethe-Salpeter equation (BSE) formalism at the CDMFT level in all physical channels, explicitly addressing the important aspect of the related Ward identities. In this context, we perform systematic calculations of the BSE for the two-dimensional Hubbard model at half filling at intermediate coupling. Our study illustrates how the divergence of a fundamental building block of the BSE in the charge channel, the two-particle irreducible vertex, systematically occurs at lower interactions than in the (purely local) DMFT case. We establish that these divergences are a prerequisite for the CDMFT Mott instability in two dimensions, which occurs at larger interaction values, and explicitly demonstrate that both are driven by short-ranged antiferromagnetic spin fluctuations.

We develop an analytical approach for steady-state normal-ordered magnon moments (NOMMs) in a driven-dissipative magnon-qubit system with coherent and dissipative couplings, and further benchmark it against the full quantum master-equation simulations of mean magnon number and second-order intensity correlation function, $g^{\left(2\right)}\left(0\right)$. Specifically, we first show that strong coherent coupling alone can produce an intermediate-pump magnon-lasing-like emission window, identified by a small-signal stability criterion and characterized by near-Poissonian statistics $[g^{\left(2\right)}\left(0\right)\simeq 1]$ and pronounced linewidth narrowing. For dissipative coupling alone, the magnon emission exhibits nonclassical antibunching $[g^{\left(2\right)}\left(0\right)<1]$ at the optimal mean magnon number and features a large pump-tunable spectral linewidth. In the hybrid dissipative and weak-coherent-coupling regime, the dissipative channel can substantially enhance the steady-state mean magnon number while simultaneously inducing strong magnon antibunching, with $g^{\left(2\right)}\left(0\right)\ll 1$. The results obtained here may find potential applications in microwave-magnonic and related hybrid quantum platforms, and the analytical NOMM method could also provide a route to treating other driven open boson-fermion systems.

We present a rigorous derivation of the matrix elements of the orbital magnetic moment (OMM) of Bloch states. Our calculations include the Berry connection term in the $k$-derivatives of Bloch states, which was omitted in previous works. The resulting formula for the OMM matrix elements applies to any nondegenerate Bloch states within Hilbert space. We identify two new contributions: The first restores gauge covariance for nondegenerate states, while the second, being itself gauge covariant, can provide significant quantitative corrections depending on the system under study. We examine their impact on the orbital Hall effect in two bilayer systems: a 2H transition metal dichalcogenide bilayer and a biased bilayer graphene. In both cases, these new terms reduce the orbital Hall conductivity plateau compared with results that neglect them, suggesting that multilayered van der Waals materials may be particularly susceptible to the derived OMM corrections. Our findings may contribute to the formal understanding of electronic OMM transport and to the conceptual foundations of the emerging field of orbitronics.

We compare three complementary diagnostics for mixed Gaussian states at nonzero temperature, focusing on the Su-Schrieffer-Heeger (SSH) chain and its inversion-symmetric extension. While the ensemble geometric phase, a mixed-state generalization of the Zak phase, remains well defined at nonzero temperature, the modulus of the corresponding expectation value vanishes in the thermodynamic limit, limiting its practical use. To develop diagnostics suitable for large systems, we introduce local twist operators acting on neighboring sites, whose expectation values provide local indicators of the underlying topological phase. The topological phase is identified from the relative magnitude of these expectation values, which only requires measuring two local expectation values at nonzero temperature, together with one additional nonlocal expectation value when next-nearest-neighbor hopping is included. In addition, we generalize the local chiral marker to mixed Gaussian states, fully determined by its single-particle correlation matrix, with a nonzero purity gap in their effective single-particle Hamiltonian. The presence of a purity gap ensures that the correlation matrix can be flattened to an effective projector. Evaluating the chiral marker with respect to the band-flattened correlation matrix yields a real-space topological invariant that coincides with the winding number in the zero-temperature limit. The ensemble geometric phase, the local twist operators, and the local chiral marker provide complementary methods to characterize topology in the SSH chain beyond pure states.

We investigate two coupled one-dimensional Aubry-André-Harper rings with $N$ sites, where a site-dependent angular twist in the second ring generates a spatially varying mosaic of distance-modulated couplings. By varying the quasiperiodic potential strength $V$ and twist periodicity $k$, we find multiple closely spaced mobility edges separating localized, extended, and critical eigenstates within narrow energy intervals. Fractal dimension analysis shows that $k$ strongly controls the spectral distribution of these states, with larger $k$ enhancing the coexistence of different localization characters. In addition, we find that for $k=2$, most eigenstates remain nearly equally distributed between the two rings, whereas larger $k$ drives pronounced layer polarization. We further examine real-time wave-packet dynamics and show that increasing $k$ accelerates the crossover from nearly ballistic spreading to subdiffusive motion and lowers the long-time saturation of the normalized mean-square displacement. At the same time, an initially layer-balanced wave packet remains strongly hybridized for $k=2$, whereas the interlayer overlap is reduced for $k=3$ and $k=4$. Thus, the site-dependent twist provides a tunable mechanism to control spectral localization, wave-packet transport, and interlayer mixing in quasiperiodic bilayer lattices.

Tripartite interactions are fundamental for realizing quantum phenomena beyond pairwise physics, yet their native implementation—particularly among distinct quantum systems—remains challenging. Here, we propose a hybrid quantum architecture comprising a magnonic mode [in a yttrium iron garnet (YIG) sphere], an Andreev spin qubit, and a superconducting qubit, to realize a native and strong interaction rather than relying on synthesis from two-body processes, leveraging the coupling between the spin-dependent supercurrent and the magnetic field of YIG sphere. Through analytical and numerical studies, we demonstrate that this interaction induces synchronized collapse and revival in qubit populations when the magnon is initially prepared in a coherent state. Notably, during the collapse region—where populations remain static—the entanglement structure undergoes a dramatic and continuous reorganization. We show that the genuine tripartite entanglement is redistributed into bipartite entanglement between the two qubits, and vice versa, with the total entanglement conserved. These phenomena, unattainable via bipartite couplings, underscore the potential of tripartite interactions for exploring intrinsically new quantum effects and advancing hybrid quantum information platforms.

Quantum embedding methods, such as dynamical mean-field theory (DMFT), provide a powerful framework for investigating strongly correlated materials. A central computational bottleneck in DMFT is in solving the Anderson impurity model (AIM), whose exact solution is classically intractable for large bath sizes. In this work, we benchmark a quantum-classical hybrid solver tailored for particle-hole symmetric AIMs, using the variational quantum eigensolver to prepare the ground state of the model with shallow quantum circuits. The solver uses shallow quantum ansätze and one set of variational parameters to prepare the ground state and its particle and hole excitations, enabling the construction of the impurity Green’s function through a continued-fraction expansion. We evaluate the performance of this approach across a few bath sizes and interaction strengths under noisy, shot-limited conditions. We compare three optimization routines (COBYLA, Adam, and L-BFGS-B) in terms of convergence and fidelity, assess the benefits of estimating a quantum-computed moment correction to the variational energies, and benchmark the approach by comparing the density of states computed from the impurity Green’s function against that obtained using a classical pipeline. Our results demonstrate the feasibility of Green’s function construction on near-term devices and establish practical benchmarks for quantum impurity solvers embedded within self-consistent DMFT loops.

Due to its localized nature and controllability, the negatively charged boron vacancy centers (${\mathrm{V}}_{\text{B}}^{-}$) in hexagonal boron nitride (hBN) are a promising spin platform for accessing its neighboring nuclei with potential for performing quantum computational tasks. However, the methods of utilizing and manipulating the nuclear spins are still lacking. In this work, we propose a protocol for the preparation of single- and multiqubit gates on the nuclear spins, utilizing the electron spin as an auxiliary qubit. By applying a background magnetic field and a multitone continuous drive, we show that the electron spin coupling to the nuclei can be efficiently engineered. This allows for suppressing the undesired electron-nuclear interactions through the Hahn-echo pulse sequence. The target gates are then implemented by employing proper rf drives. Our numerical results for realistic parameters show gate fidelities as high as $99\%$ for single-qubit and $95\%$ for multiqubit gates. With the gate execution durations being less than 300 ns, our protocol evades electron spin decoherence effects. Therefore, our scheme sets the stage for the practical application of ${\mathrm{V}}_{\text{B}}^{-}$ in hBN for quantum computation purposes.

We derive the full spectrum of decorated Cayley trees that constitute tree analogs of selected two-dimensional Euclidean lattices, namely, the Lieb, the double-Lieb, the kagome, and the star lattice. The common feature of these Euclidean lattices is that their nearest-neighbor models give rise to flat energy bands interpretable through compact localized states. We find that the tree analogs exhibit similar flat or nearly flat energy bands at the corresponding energies. Interestingly, such flat bands in the decorated Cayley trees acquire an interpretation that is absent in their Euclidean counterparts: as edge states localized to the inner or the outer boundary of the tree branches. In particular, we establish an exact correspondence between the Lieb-Cayley tree and an ensemble of one-dimensional Su-Schrieffer-Heeger chains, which maps topological edge states on one side of the chains to flat-band states localized in the bulk of the tree, furnishing the flat energy band with a topological stability. Similar mapping to topological edge states or to states bound to edge defects in one-dimensional chains is shown for flat-band states in all the considered tree decorations. We finally show that the persistence of exact flat bands on infinite decorated trees (i.e., Bethe lattices) arises naturally from a covering interpretation of tree graphs. Our findings reveal a rich landscape of flat-band and topological phenomena in non-Euclidean systems, where geometry alone can generate and stabilize unconventional quantum states.

Non-Hermitian systems exhibit spectral and topological phenomena absent in Hermitian physics; however, their geometric characterization remains subtle due to the intrinsic ambiguity of biorthogonal eigenspaces. Since left and right eigenvectors are not related by Hermitian conjugation, the associated Berry connection is generally nonunique, leading to complex geometric phases and ambiguously defined holonomies. Here, we formulate a covariant geometric framework for non-Hermitian quantum systems based on the metric structure of the underlying Hilbert space. We show that, in the quantum regime with continuous state evolution, the conventional Berry connection and the associated Berry holonomy over closed parameter-space loops can be consistently defined only in the pseudo-Hermitian limit, where the spectrum is real. For generic non-Hermitian Hamiltonians with complex spectra, the relevant geometric object is instead the Aharonov-Anandan holonomy associated with cyclic evolution in projective Hilbert space. Within the pseudo-Hermitian regime, we construct a unique Hermitian Berry connection that is covariant under arbitrary $\mathrm{GL}(N,\mathbb{C})$ frame transformations and reduces to the standard Berry connection in the Hermitian limit. The resulting formalism separates the intrinsic geometry of the Hamiltonian eigenspace from contributions arising from the parameter dependence of the Hilbert-space metric, revealing that the conventional biorthogonal formulation generally mixes these distinct geometric effects. Consequently, geometric phases, synthetic gauge fields, and topological characteristics commonly attributed to non-Hermitian eigenspace geometry may, in part, originate from the underlying metric structure. Our framework therefore provides a consistent geometric foundation for Berry phases, non-Abelian holonomies, and topological invariants in non-Hermitian quantum systems.

Within a circuit quantum electrodynamics architecture, we theoretically investigate the detection of a single propagating microwave photon traveling through a resonant microwave cavity dispersively interacting with a double quantum dot tunnel coupled to a lead. Under suitable conditions, a single photon in the cavity can induce a measurable change in the electronic occupation of the charge states. We develop a quantum cascade approach that enables a time-resolved description of a single-photon wave packet impinging on the cavity. We make use of a simple model of charge detector to assess the efficiency of our photo-detection configuration as functions of key parameters such as coupling strength, tunneling rate, temperature, and photon resonance linewidth. We finally highlight a measurement-induced backaction effect on the cavity mode associated with the dispersive, nonabsorptive detection process.

Efficient charge separation in van der Waals (vdW) heterostructures is crucial for optimizing light harvesting and detection applications. However, precise control over the microscopic pathways governing ultrafast charge transfer remains an open challenge. These pathways are intrinsically linked to charge transfer states with strongly delocalized wave functions that appear at various momenta in the Brillouin zone. Here, we use time- and angle-resolved photoemission spectroscopy to investigate the possibility of steering carriers through specific charge transfer states in a prototypical ${\mathrm{WS}}_2$-graphene heterostructure. By selectively exciting electron-hole pairs at the K point (A-exciton resonance) and close to the Q point (C-exciton resonance) of ${\mathrm{WS}}_2$ with different pump photon energies, we find that charge separation is faster at higher excitation energies. This behavior is attributed to the fact that absorption at the C-exciton resonance generates electron-hole populations at energies well above the direct band gap. The resulting elevated carrier temperatures open an additional, highly efficient charge-transfer channel for holes in the ${\mathrm{WS}}_2$ valence band, leading to an overall acceleration of interlayer hole transfer for C-exciton excitation. The microscopic insights gained in this work can be leveraged to optimize the performance of vdW heterostructures in optoelectronic devices.

We investigate how fermionic anticommutation shapes transport in a noninteracting resonant-level model where a single central site is coupled to an environment. To this end, we compare a fermionic reservoir with a bath of spin-$\frac{1}{2}$ modes using exact diagonalization and a perturbative expansion of the master equation to identify the differences. Notably, we find different reduced dynamics for the spin and fermionic baths even though both models restrict each local mode to at most one excitation; unlike the fermionic bath, however, the spin bath consists of commuting two-level modes and therefore lacks the global exchange antisymmetry of true fermions. These differences originate from higher-order terms in the system-bath coupling, where fermionic anticommutation introduces exchange signs in higher-order correlations. In contrast, all second-order contributions, set solely by two-point correlators, coincide. Deviations are largest for small to intermediate bath sizes, fading in the effectively Markovian regime where higher-order corrections are negligible. These results identify when spin baths can be a substitute for fermionic reservoirs and vice versa.

We analyze the metastability of Bose-Hubbard condensates for finite-size one-dimensional ring lattices and open chains, using a semiclassical tomographic perspective that emphasizes the relation of the many-body spectrum to the underlying classical phase-space structures. In order to address quantum ergodicity in far-from-equilibrium scenarios of experimental interest, we inspect both local aspects (via Bogoliubov analysis) and global aspects (mixed regular-chaotic dynamics). In particular, we highlight the roles of the two parameters that control metastability, clarify the essential differences between low- and high-dimensional chaos, and show how the dynamical instabilities diminish in the limit of the Gross-Pitaevskii equation. It is somewhat frustrating that with more degrees of freedom, the dynamically metastable islands become better distinct from the ergodic sea, while their borders become ill-defined topologically. This stands in opposition to the very structured phase space of two-degree-of-freedom systems, as reflected in the tomographic quantum spectrum.

Superlattice engineering, the introduction of periodic potentials to a material, can induce selective scattering events that modify the electrical properties of the material in predictable ways. Extending superlattice engineering to three-dimensional (3D) electronic materials can expand the tunability of their transport properties beyond traditional means such as doping. Here, we show that magnetotransport can be modified by superlattices in 3D materials based on the relative symmetry between the Fermi surface and nanostructured superlattice. We demonstrate commensuration oscillations in the ballistic transport regime of a nanostructured 3D material with the Weyl semimetal NbP. The oscillations encode information about the shared properties between the quasiparticles at the Fermi surface—including their momentum, charge, mass, and rotational symmetry—and the structure of the superlattice. These results point toward methods to engineer quantum transport in 3D electronic materials based on the mutual properties of the superlattice and Fermi surface.