We explore how the quantum geometric properties of the Bloch wave function, characterized by the Hilbert-Schmidt quantum distance, impact magnetic phases in solid-state systems. To this end, we investigate the spin susceptibility within the random phase approximation, considering the onsite Coulomb interaction. We demonstrate that spin susceptibility can be decomposed into a trivial part, dependent solely on the band dispersion, and a geometric part, where the quantum distance plays a crucial role. Focusing on a model of a quadratic band-touching semimetal, we show that a magnetic phase transition between ferromagnetic and antiferromagnetic order can be induced solely by tuning the wavefunction geometry, even while the energy spectrum is held constant. This highlights the versatility of quantum geometry as a mechanism for tuning magnetic properties independent of the energy spectrum. Applying our framework to the Fe-pnictide and kagome lattice models, we further show that the geometric contribution is decisive in stabilizing their known antiferromagnetic and ferromagnetic states, respectively. Our work sheds light on the hidden quantum geometric aspects necessary for understanding and engineering magnetic order in quantum materials.

Recent advances in quantum technology have enabled the simulation of quantum many-body systems on real quantum devices. However, such quantum simulators are inherently subject to decoherence, and its impact on system dynamics - particularly near quantum phase transitions - remains insufficiently understood. In this work, we experimentally investigate how decoherence in quantum devices affects the dynamics of quantum time crystals, using a 156-qubit IBM Quantum system. We find that decoherence shifts the location of critical behavior associated with the phase transition, suggesting that noisy simulations can lead to inaccurate identification of phase boundaries. Our results underscore the importance of understanding and mitigating decoherence to reliably simulate quantum many-body systems on near-term quantum hardware.

The superconducting diode effect (SDE) is characterized by the nonreciprocity of Cooper-pair motion with respect to current direction. In three-dimensional (3D) materials, SDE results in a critical current that varies with direction, making the effect distinctly observable: the material exhibits superconductivity in one direction while behaving as a resistive metal in the opposite direction. However, in genuinely two-dimensional (2D) materials, the critical current density is theoretically zero, leaving the manifestation of SDE in the 2D limit an intriguing challenge. Here, we present the observation of SDE in a heterostructure composed of the topological insulator Bi$_2$Te$_3$ and the iron based superconductor Fe(Se,Te) $-$a candidate for topological superconductor$-$ where superconductivity is confined to the 2D limit. The observed I-V characteristics reveal nonreciprocity in the vortex-creep regime, where finite voltages arise due to the two-dimensional nature of superconductivity. Furthermore, our 2D film demonstrates abrupt voltage jumps, influenced by both the current flow direction and the transverse magnetic field direction. This behavior resembles that of 3D materials but, in this case, is driven by the vortex-flow instability, as illustrated by voltage controlled S-shaped I-V curves. These results underscore the pivotal role of vortex dynamics in SDE and provide new insights into the interplay between symmetry breaking and two-dimensionality in topological insulator/superconductor systems.

Counterdiabatic (CD) protocols enable fast driving of quantum states by invoking an auxiliary adiabatic gauge potential (AGP) that suppresses transitions to excited states throughout the driving process. Usually, the full spectrum of the original unassisted Hamiltonian is a prerequisite for constructing the exact AGP, which implies that CD protocols are extremely difficult for many-body systems. Here, we apply a variational CD protocol recently proposed by P. W. Claeys et al. [Phys. Rev. Lett. 123, 090602 (2019)] to a two-component fermionic Hubbard model in one spatial dimension. This protocol engages an approximated AGP expressed as a series of nested commutators. We show that the optimal variational parameters in the approximated AGP satisfy a set of linear equations whose coefficients are given by the squared Frobenius norms of these commutators. We devise an exact algorithm that escapes the formidable iterative matrix-vector multiplications and evaluates the nested commutators and the CD Hamiltonian in analytic representations. We then examine the CD driving of the one-dimensional Hubbard model up to $L = 14$ sites with driving order $l \leqslant 3$. Our results demonstrate the usefulness of the variational CD protocol to the Hubbard model and permit a possible route towards fast ground-state preparation for many-body systems.

Topological spin textures exhibit a hierarchical nature. For instance, magnetic skyrmions, which possess a particle-like nature, can aggregate to form superstructures such as skyrmion strings and skyrmion lattices. Magnetic hopfions are also regarded as superstructures constructed from closed loops of twisted skyrmion strings, which behave as another independent particles. However, it remains elusive whether such magnetic hopfions can also aggregate to form higher-level superstructures. Here, we report a stable superstructure with three-dimensional periodic arrangement of magnetic hopfions in a frustrated spin model with easy-plane anisotropy. By comprehensively examining effective interactions between two hopfions, we construct the hopfion superstructure by a staggered arrangement of one-dimensional hopfion chains with Hopf number $H=+1$ and $H=-1$ running perpendicular to the easy plane. Each hopfion chain is threaded by a magnetic meron string, resulting in a nontrivial topological texture with skyrmion number $N_{\rm sk}=2$ per magnetic unit cell on any two-dimensional cut parallel to the easy plane. We show that the hopfion superstructure remains robust as a metastable state across a range of the hopfion density. Furthermore, we demonstrate that superstructures with higher Hopf number can also be stabilized. Our findings extend the existing hierarchy of topological magnets and pave the way for exploring new quantum phenomena and spin dynamics.

We develop a first-principles framework for finite-temperature structural optimization that incorporates vibrational contributions to the free energy through anharmonic phonon theory. We extend and further improve the efficiency of the recent approach, enabling its application to systems in which the size of the primitive cell changes across structural phase transitions. Applying this framework to La$_3$Ni$_2$O$_7$, we establish its pressure-temperature phase diagram and find that the slope of the phase boundary between the high-symmetry and low-symmetry phases is negative, with a magnitude of approximately -60 K / GPa. The present results provide a theoretical foundation for discussing how changes in crystal symmetry influence the emergence of superconductivity.

Quantum geometry, which describes the geometry of Bloch wavefunctions in solids, has become a cornerstone of modern quantum condensed matter physics. The quantum geometrical tensor encodes this geometry through two fundamental components: the quantum metric (real part) and the Berry curvature (imaginary part). While the Berry curvature gained prominence through its manifestation in the intrinsic anomalous Hall effect, recent advances have revealed equally significant effects arising from the quantum metric. This includes its signatures in nonlinear transport, superfluid density of flat-band superconductors, and nonlinear optical responses. These advances underscore how quantum geometry is reshaping our understanding of condensed matter systems, with far-reaching implications for future technologies. In this review, we survey recent progress in the field, focusing on both foundational concepts and emergent phenomena in transport and optics-with particular emphasis on the pivotal role of the quantum metric.

We present a first-principles method based on density functional theory and many-body perturbation theory for computing spin excitations in magnetic systems with noncollinear spin textures. Traditionally, the study of magnetic excitations has relied on spin models that assume magnetic moments to be localized. Beyond this restriction, recent $ab~initio$ methods based on Green's functions within the local spin-density approximation have emerged as a general framework for calculating magnetic susceptibilities. However, their application has so far been largely limited to collinear ferromagnetic and antiferromagnetic systems. In this work, we extend this framework and enable the treatment of large-scale noncollinear magnetic systems by leveraging a Wannier-basis representation and implementing an ansatz potential method to reduce computational cost. We apply our method to the spin-spiral state of LiCu$_2$O$_2$, successfully capturing its steady-state spin-rotation pitch in agreement with the experimental measurement and resolving the characteristic magnon dispersion. We further analyze the interplay between the spiral spin structure and the on-site spin-exchange splitting, and elucidate the crucial role of magnetic dipoles on ligand ions in mediating effective ferromagnetic interaction among the primary spins on Cu$^{2+}$ ions. Finally, we provide a theoretical prediction of the magnon dispersion on top of the helical spin background in high agreement with the experimental measurement. Overall, this work establishes a general and computationally efficient framework for simulating collective spin dynamics in noncollinear magnetic systems from first principles, exemplified by -- but not limited to -- spin-spiral states.

Unconventional magnetic orders usually interplay with superconductivity in intriguing ways. Here we propose that a conventional superconductor in proximity to a compensated $p$-wave magnet exhibits behaviors analogous to those of Ising superconductivity found in transition-metal dichalcogenides, which we refer to as pseudo-Ising superconductivity. The pseudo-Ising superconductivity is characterized by several distinctive features: (i) it stays much more robust under strong $p$-wave magnetism than usual ferromagnetism or $d$-wave altermagnetism, thanks to the apparent time-reversal symmetry in $p$-wave spin splitting; (ii) in the low-temperature regime, a second-order superconducting phase transition occurs at a significantly enhanced in-plane upper critical magnetic field $B_{c2}$; (iii) the supercurrent-carrying state establishes non-vanishing out-of-plane spin magnetization, which is forbidden by symmetry in Rahsba and Ising superconductors. We further propose a spin-orbit-free scheme to realize Majorana zero modes by placing superconducting quantum wires on a $p$-wave magnet. Our work establishes a new form of unconventional superconductivity generated by $p$-wave magnetism.

Periodically driven (Floquet) systems typically evolve toward an infinite-temperature thermal state due to continuous energy absorption. Before reaching equilibrium, however, they can transiently exhibit long-lived prethermal states that host exotic nonequilibrium phenomena, such as discrete time crystals (DTCs). In this study, we investigate the relaxation dynamics of periodically driven product states in a kicked Ising model implemented on the IBM Quantum Eagle and Heron processors. By using ancilla qubits to mediate interactions, we construct Kagome and Lieb lattices on superconducting qubits with heavy-hex connectivity. We identify two distinct types of noise-induced DTCs on Kagome and Lieb lattices, both arising from quantum noise in ancilla qubits. Type-I DTCs originate from robust boundary-mode period-doubling oscillations, stabilized by symmetry charge pumping, that are redistributed into the bulk due to ancilla noise. Type-II DTCs, in contrast, emerge in systems without charge-pumped qubits, where quantum noise unexpectedly stabilizes period-doubling oscillations that would otherwise rapidly decay. On the noisier Eagle device (ibm_kyiv), we observe both type-I and type-II DTCs on 53-qubit Kagome lattices with and without charge-pumped qubits, respectively. In contrast, on the lower-noise Heron device (ibm_marrakesh), period-doubling oscillations are confined to boundary-localized oscillations on 82-qubit Kagome and 40-qubit Lieb lattices, as redistribution into the bulk is suppressed. These experimental findings are supported by noisy matrix-product-state simulations, in which ancilla noise is modeled as random sign flips in the two-qubit gate rotation angles. Our results demonstrate that quantum noise in ancilla qubits can give rise to novel classes of prethermal dynamical phases, including boundary-protected and noise-induced DTCs.

Quantum systems driven by a time-periodic field are a platform of condensed matter physics where effective (quasi)stationary states, termed "Floquet states", can emerge with external-field-dressed quasiparticles during driving. They appear, for example, as a prethermal intermediate state in isolated driven quantum systems or as a nonequilibrium steady state in driven open quantum systems coupled to environment. Floquet states may have various intriguing physical properties, some of which can be drastically different from those of the original undriven systems in equilibrium. In this article, we review fundamental aspects of Floquet states, and discuss recent topics and applications of Floquet states in condensed matter physics.

Stimulated by recent interest in altermagnets, a novel class of antiferromagnets with macroscopic time-reversal symmetry breaking, we investigate the coexistence of altermagnetism and superconductivity. By developing a Ginzburg--Landau theory based on microscopic models, we show that a phase-modulated Fulde--Ferrell superconducting state is stabilized via altermagnetic spin splitting, in contrast to the typical amplitude-modulated states that occur under the uniform Zeeman field. We apply our framework to different models to compare the resulting phase diagrams: a two-sublattice model with altermagnetic order, a continuum model with an anisotropic Zeeman field mimicking altermagnetic spin splitting, and a conventional square-lattice model with two kinds of anisotropic Zeeman fields. We show that the multi-sublattice structure is crucial for realizing the phase-modulated superconductivity, and highlight spin-split altermagnets as a promising platform for exploring this exotic superconductivity without external magnetic fields.

Magneto-conductance in thin wires often exhibits complicated patterns due to the quantum interference of conduction electrons. These patterns reflect microscopic structures in the wires, such as defects or potential distributions. In this study, we propose an inverse design method to automatically generate a microscopic structure that exhibits desired magneto-conductance patterns. We numerically demonstrate that our method accurately generates defect positions in wires and can be effectively applied to various complicated patterns. We also discuss techniques for designing structures that facilitate experimental investigation.

We propose an extended version of the symmetry-adapted variational-quantum-eigensolver (VQE) and apply it to a two-component Fermi-Hubbard model on a bipartite lattice. In the extended symmetry-adapted VQE method, the Rayleigh quotient for the Hamiltonian and a parametrized quantum state in a properly chosen subspace is minimized within the subspace and is optimized among the variational parameters implemented on a quantum circuit to obtain variationally the ground state and the ground-state energy. The corresponding energy derivative with respect to a variational parameter is expressed as a Hellmann-Feynman-type formula of a generalized eigenvalue problem in the subspace, which thus allows us to use the parameter-shift rules for its evaluation. The natural-gradient-descent method is also generalized to optimize variational parameters in a quantum-subspace-expansion approach. As a subspace for approximating the ground state of the Hamiltonian, we consider a Krylov subspace generated by the Hamiltonian and a symmetry-projected variational state, and therefore the approximated ground state can restore the Hamiltonian symmetry that is broken in the parametrized variational state prepared on a quantum circuit. We show that spatial symmetry operations for fermions in an occupation basis can be expressed as a product of the nearest-neighbor fermionic swap operations on a quantum circuit. We also describe how the spin and charge symmetry operations, i.e., rotations, can be implemented on a quantum circuit. By numerical simulations, we demonstrate that the spatial, spin, and charge symmetry projections can improve the accuracy of the parametrized variational state, which can be further improved systematically by expanding the Krylov subspace without increasing the number of variational parameters.