Research

Nonequilibrium quantum many-body systems have become a central theme in modern condensed-matter physics, as they can host forms of order and universality that are fundamentally distinct from equilibrium, especially under pulse excitation or periodic driving. At the same time, real-time dynamics typically generate rapid entanglement growth, which restricts the practical reach of classical simulations based on tensor-network methods. This challenge provides a natural motivation for using quantum computers as a new computational resource. However, because today’s devices are noisy intermediate-scale quantum (NISQ) processors, increasing attention has turned to quantum-circuit dynamics themselves—including discrete-time unitary evolution and measurements—as a realistic platform for nonequilibrium physics, rather than waiting for fully error-corrected quantum algorithms.  

In this context, discrete time crystals—defined by the spontaneous breaking of discrete time-translation symmetry in periodically driven (Floquet) systems—represent a prototypical example of nonequilibrium order. Their hallmark is a long-lived subharmonic response relative to the drive period, whose stability relies on mechanisms that suppress heating and stabilize the dynamics. Quantum circuits natively implement discrete-time evolution and are directly realizable on quantum hardware, providing a natural setting for connecting time-crystal physics with the NISQ era.  

In our recent studies, we investigated the conditions for realizing and stabilizing discrete time crystals in quantum-circuit many-body systems, focusing on circuit design, error mitigation, and careful comparisons with classical simulations. These efforts deepen our understanding of nonequilibrium many-body dynamics while articulating a concrete strategy: quantum devices can be most impactful precisely in regimes where entanglement growth makes classical computation difficult. More broadly, our work highlights the potential of quantum circuits not only as computational tools but also as experimental platforms for synthesizing and probing novel nonequilibrium quantum phases.  

In strongly correlated electron systems, electrons interact with each other so strongly that they no longer behave as simple, freely moving particles. As a result, the two fundamental degrees of freedom—charge and spin—become tightly coupled, giving rise to optical responses that differ markedly from those of ordinary metals or semiconductors. In particular, in Mott insulators, which do not conduct electricity under normal conditions, light irradiation can generate doublon–holon pairs. Their motion disturbs the surrounding spin order, producing dynamics characteristic of strong electron correlations.  

In this process, antiferromagnetic spin correlations provide an effective attractive interaction between the photo-generated electron and hole. This leads to a characteristic peak near the absorption edge of the optical spectrum, known as an exciton. Such a feature cannot be explained by simple interband transitions; rather, it is a direct manifestation of the cooperative motion of spin and charge. By examining the optical conductivity in detail, one can probe how electrons interact and move collectively, both in energy and in time.  

In recent years, non-perturbative numerical methods such as the time-dependent density matrix renormalization group (tDMRG) have made it possible to quantitatively compute the optical response of two-dimensional Hubbard models. The resulting spectra agree well with experimental measurements in cuprate Mott insulators and related materials. This agreement provides concrete insight into how the coupling between spin and charge appears in the optical response of strongly correlated systems.  

Thus, the study of optical responses in strongly correlated electron systems offers a direct way to observe and understand new quantum phenomena that emerge from collective electron behavior. It not only deepens our understanding of fundamental electronic states in solids but also opens pathways toward discovering novel optoelectronic materials and quantum functionalities.  

In strongly correlated electron systems, strong electron–electron repulsion invalidates the single-particle picture in which electrons can be treated as independent quasiparticles. Instead, the system exhibits properties of an emergent collective quantum state. A hallmark of such systems is the appearance of novel quantum phases that are not easily characterized by conventional order parameters. Typical examples include quantum spin liquids, which lack local magnetic order yet exhibit long-range entanglement, and quantum liquid-crystal phases, which break only part of the spatial symmetry and display intermediate forms of order, such as stripe-like charge patterns or loop-current structures.  

A paradigmatic example is the Kitaev model, where strong bond-directional exchange interactions generate frustration and enhance quantum fluctuations, stabilizing a spin-liquid phase. However, when additional spin interactions present in real materials are introduced as perturbations, a variety of competing magnetic orders emerge nearby in the phase diagram. Two-dimensional DMRG studies of the extended Kitaev–Heisenberg model have shown that while the spin-liquid phase exhibits characteristic pair degeneracy in the entanglement spectrum, magnetically ordered phases tend to display non-degenerate structures. Moreover, the Schmidt gap changes across phase boundaries adjacent to the spin-liquid phase, demonstrating that the structure of quantum entanglement provides a useful diagnostic for identifying Kitaev spin liquids.  

When charge degrees of freedom are incorporated, the landscape becomes even richer, allowing for stripe-type charge order and superconducting states. In studies focusing on spin loop currents (sLCs), loop currents can be reinterpreted as manifestations of quantum liquid-crystal behavior. Using DMRG combined with pinning fields to visualize spatial patterns of spin currents, we investigate the conditions under which sLC correlations become long ranged. We find that such correlations grow in regimes associated with excitonic condensation or block-type antiferromagnetic order. Furthermore, in the square-lattice  𝑡-𝑡′-𝑈 model (the Hubbard model with next-nearest-neighbor hopping), at parameters relevant to high-Tc superconductors (𝑡′ / 𝑡 = − 0.25), axial sLC order emerges at hole doping  𝛿 = 0.125, coexisting with charge stripes.  

Taken together, the study of novel quantum phases in strongly correlated systems aims to uncover collective quantum states that arise from the competition between strong interactions and quantum fluctuations—states that go beyond conventional “simple” orders and require genuinely quantum-mechanical descriptions.