Comment on “Quantum phase transitions of Dirac particles in a magnetized rotating curved background: Interplay of geometry, magnetization, and thermodynamics”

Emergent dynamical quantum phase transition in a Z3 symmetric chiral clock model

Classical optical analogues of excited-state quantum phase transitions in a squeezing-enhanced generalized Lipkin–Meshkov–Glick model

Quantum phase transitions lie at the heart of condensed matter physics. Observing these transitions, however, requires the careful engineering of materials to realize specific, finely tuned systems. In this work, we demonstrate a quantum phase transition within artificial molecular spin pairs, where the ground state can be controllably switched between the antiferromagnetic phase and ferromagnetic phase by an external magnetic field. The combination of scanning tunneling microscopy experiments and theoretical calculations not only reveals the microscopic details of this phase transition but also establishes that its critical behavior is tunable through precise modulation of the intermolecular interactions. These results establish a practical platform for exploring quantum phase transitions in molecular systems.

The fractional quantum Hall effect at half-filled Landau levels provides a promising route to unusual topological phases that may host non-Abelian excitations, but these states are often fragile and difficult to control experimentally. Here, we report the observation of a cascade of even-denominator fractional quantum Hall states at fillings ν = -5/2, -7/2, -9/2, -11/2 and -13/2, alongside numerous odd-denominator states in mixed-stacked pentalayer graphene-a system characterized by intertwined quadratic and cubic band dispersions. These even-denominator states emerge from two distinct intra-zeroth Landau levels and exhibit displacement-field tunability. At half fillings, continuous quantum phase transitions between even-denominator states, magnetic Bloch states, and composite Fermi liquids are clearly identified upon tuning external fields. Numerical calculations support possible Moore-Read type pairing for even-denominator states, although direct probes of their exchange statistics remain important for future experiments. These results establish mixed-stacked graphene as a versatile platform for tunable correlated topological phases.

The orbital Fulde-Ferrell-Larkin-Ovchinnikov (orb-FFLO) state has lately emerged as an exotic dissipationless state, but a thermodynamic demonstration, which is key for its establishment, has been lacking. Here, we reveal a first-order quantum phase transition in the tunneling spectroscopy under an in-plane magnetic field on multilayer 2H-NbSe2. The transition manifests itself as a sudden enhancement of the superconducting gap with prominent hysteresis by sweeping the in-plane magnetic field well below the upper critical field. Such a first-order transition quickly disappears once the magnetic field tilts away from the in-plane direction by about one degree, and it depends sensitively on disorder. Furthermore, we obtain a comprehensive phase diagram of the phase transition as a function of magnetic field, temperature, and the sample thickness. These observed behaviors can be reproduced by the theory that considers the energetics between a uniform Ising superconductor and the orb-FFLO state.

The Bogoliubov–Bose–Hubbard Model: Existence of Minimizers and Absence of Quantum Phase Transition

We present analytical results on the exact tensor network representations and correlation functions of the first examples of 2D ground states with quantum phase transitions between area law and extensive entanglement entropy. The tensor networks constructed are one dimension higher than the lattices of the physical systems, allowing entangled physical degrees of freedoms to be paired with one another arbitrarily far away. Contraction rules of the internal legs are specified by a simple translationally invariant set of rules in terms of the tesselation of cubes or prisms in 3D space. The networks directly generalize the previous holographic tensor networks for 1D Fredkin and Motzkin chains. We also analyze the correlation in the spin and color sectors from the scaling of the height function of random surfaces, revealing additional characterizations of the exotic phase transitions.

Abstract Dynamical quantum phase transitions (DQPTs), which serve as a theoretical framework for understanding far-from-equilibrium physics in quantum many-body systems, have recently been observed experimentally. Their topological properties are typically characterized by the winding number, which acts as an order parameter. While DQPTs exhibiting both integer and half-integer jumps in the winding number have been reported, the underlying mechanisms behind these distinct topological behaviors, as well as the potential existence of other topological classes, remain open questions. To address this, we investigate DQPTs in the one-dimensional XY model under a quench protocol. We show that the observed topological diversity originates from the nature of the critical modes, which we classify into two categories: boundary modes and interior modes. Specifically, critical interior modes always lead to DQPTs with an integer winding number, while critical boundary modes always result in DQPTs characterized by a half-integer winding number. By analyzing the number and classification of critical modes, we provide a classification of the topological properties of DQPTs in the one-dimensional XY model. According to their distinct topological features, we categorize DQPTs into six types, three of which have not been previously identified in the literature. We discuss in detail the conditions associated with each type and present the corresponding dynamical phase diagrams. Our framework is not restricted to the XY model; it is applicable to other two-band models in one-dimensional systems, including the SSH model, Kitaev chain, Rice-Mele model, and Creutz model.

Abstract We investigate the spatial and temporal scales of dynamical quantum phase transitions in the one-dimensional Bose-Hubbard model in the strong interaction limit. Using Jordan-Wigner transformation, we obtain the time-dependent wavefunction and therefore the subsystem Loschmidt echo, and systematically investigate how its properties vary with subsystem size. It is found that when the subsystem is sufficiently large, it exhibits logarithmic divergence identical to that of the full system Loschmidt echo, yielding a critical exponent of zero. We also obtain the required subsystem size and temporal resolution for detecting dynamical quantum phase transitions using the subsystem Loschmidt echo. It is expected that the present results provide a reliable foundation for further experimental investigations.

Abstract This work investigates dynamical quantum phase transitions (DQPTs) in a one-dimensional Ising model subjected to a periodically modulated transverse field. In contrast to sudden quenches, we demonstrate that a DQPT can be induced in two distinct ways. First, when the system remains within a given phase--ferromagnetic (FM) or paramagnetic (PM), a resonant periodic drive can trigger a DQPTs when its frequency matches the energy-level transition of the system. This DQPT is intimately connected to the emergence of Floquet topological phases. The timescale for the transition is governed by the perturbation strength $\lambda'$, the critical mode $k_c$, and its energy gap $\Delta_{k_c}$, following the scaling relation $\tau\propto\Delta_{k_c}\lambda'^{-1}\csc k_c$. Second, for drives across the critical point between the FM and PM phases, low frequencies can always induce DQPT, regardless of resonance. This behavior stems from the degeneracy of the energy-level at the critical point, which ensures that any drive with a frequency lower than the system’s intrinsic transition frequency will inevitably excite the system. However, in the high-frequency regime, such excitation will be strongly suppressed, thereby inhibiting the occurrence of DQPTs. This study provides deeper insight into the nonequilibrium dynamics of quantum spin chains.

Abstract The Lottery Ticket Hypothesis (LTH) posits that within overparametrized neural networks, there exist sparse subnetworks that are capable of matching the performance of the original model when trained in isolation from the original initialization. We extend this hypothesis to the unsupervised task of approximating the ground state of quantum many-body Hamiltonians, a problem equivalent to finding a neural-network compression of the lowest-lying eigenvector of an exponentially large matrix. Focusing on two representative quantum Hamiltonians, the transverse field Ising model (TFIM) and the toric code (TC), we demonstrate that sparse neural networks can reach accuracies comparable to their dense counterparts, even when pruned by more than an order of magnitude in parameter count. Crucially, and unlike the original LTH, we find that performance depends only on the structure of the sparse subnetwork, not on the specific initialization, when trained in isolation. Moreover, we identify universal scaling behavior that persists across network sizes and physical models, where the boundaries of scaling regions are determined by the underlying Hamiltonian. At the onset of high-error scaling, we observe signatures of a sparsity-induced quantum phase transition that is first-order in shallow networks. Finally, we demonstrate that pruning enhances interpretability by linking the structure of sparse subnetworks to the underlying physics of the Hamiltonian.

Abstract Recently, scaling behavior in Yang-Lee edge singularities (YLES) has attracted sustained attention. However, the scaling mechanism in the overlapping critical region between classical and quantum YLES remains unclear. In this work, we apply established renormalization group (RG) crossover theory to non-Hermitian YLES system. We demonstrate that, in the overlapping critical region between classical and quantum YLES, the scaling behavior can be described by a hybrid scaling mechanism, which asserts that scaling functions from both critical regimes apply simultaneously and satisfy a constraint relation. The transverse Ising chain in an imaginary longitudinal field is employed as a model to test this hybrid scaling mechanism. This model exhibits zero-dimensional (0D) and one-dimensional (1D) quantum YLES phase transitions at zero temperature, as well as 0D and 1D classical YLES phase transitions at finite temperature. We systematically investigate the scaling functions in the critical regions of 0D and 1D quantum YLES and those of 0D and 1D classical YLES. Furthermore, the hybrid scaling mechanisms in the overlapping critical regions, particularly between classical and quantum YLES, are thoroughly examined. Our results provide a concrete realization of quantum-to-classical crossover in a non-Hermitian YLES system and establish a hybrid scaling framework that captures critical behavior in overlapping regions between classical and quantum phase transitions. This framework enables the extraction of quantum critical information from finite-temperature classical measurements, thereby bridging the two paradigms and offering a pathway to probe quantum criticality experimentally.

Unsupervised framework for identifying diverse quantum phase transitions using classical shadow tomography

The Anderson transition on random graphs is a paradigm for understanding high-dimensional quantum phase transitions driven by disorder and closely mirrors several features of many-body localization. In this Letter, we introduce a unitary Anderson model on small-world graphs, enabling large-scale, long-time simulations of wave-packet dynamics. This allows us to uncover logarithmically slow critical dynamics, two distinct localization times, and a crossover to ergodic diffusion. Finite-time scaling reveals distinct critical exponents, establishing a dynamical universality class for this exotic transition. Our model opens the way to an experimental realization of the Anderson transition on random graphs in quantum simulators. By combining disorder, high dimensionality, and dynamics, our approach provides a general framework for probing universal features of out-of-equilibrium quantum phase transitions, including those relevant to many-body localization.

Chemically realistic quasi-one-dimensional (1D) materials in which Dirac Fermions and highly degenerate flat bands coexist intrinsically at the Fermi level are exceedingly rare, while representing a highly desirable platform for correlated and topological quantum phenomena. Here, using specialized symmetry-adapted first-principles calculations we predict a new class of nanomaterials─phosphorus carbide nanotubes (P2C3NTs)─obtained by rolling monolayer P2C3, a two-dimensional material shown in a previous letter to host "double Kagome bands". Both armchair and zigzag P2C3NTs are stable at room temperature and feature the rare coexistence of Dirac crossings and multiple flat bands at the Fermi level inherited from the underlying honeycomb-Kagome lattice, with the flat bands resilient to elastic deformations. Under large strain, the structure transforms from honeycomb-Kagome to "brick-wall", accompanied by multiple coupled structural and quantum phase transitions. We also uncover localized edge states, spin splitting from vacancies and dopants, and strain-tunable magnetism. Together, these results establish P2C3NTs as a chemically specific and mechanically tunable 1D material platform with potential applications in quantum hardware and spintronics.

Quantum phase diagrams and transitions for Chern topological insulators

Topological quantum phase transitions and multicritical caloric effects in the AI symmetry class

Overdoped cuprate superconductors are strange metals above their superconducting transition temperature. In such materials, the electrical resistivity has a strong linear dependence on temperature (T) and electrical current is not carried by electron quasiparticles as in conventional metals. Here we demonstrate that the strange metal behaviour co-exists with strongly temperature-dependent critical spin fluctuations showing dynamical scaling across the cuprate phase diagram. Our neutron scattering observations and the strange metal behaviour are consistent with a spin density wave quantum phase transition in a metal with spatial disorder in the tuning parameter. Numerical computations using a theory of spin density waves in a disordered metal yield an extended 'Griffiths phase' with scaling properties in agreement with experimental observations. Thus we establish that low-energy spin excitations and spatial disorder are central to the strange metal behaviour.

Metals at the brink of electronic quantum phase transitions display high-temperature superconductivity, competing orders, and unconventional charge transport, revealing strong departures from conventional Fermi liquid behavior. Investigation of these fascinating intertwined phenomena has been at the center of research across a variety of correlated materials over the past many decades. A ubiquitous experimental observation is the emergence of a universal timescale that governs electrical transport and momentum relaxation. In this Letter, we analyze an equally important theoretical question of how the energy contained in the electronic degrees of freedom near a quantum phase transition relaxes to the environment via their coupling to acoustic phonons. Assuming that the bottleneck for energy dissipation is controlled by the coupling between electronic degrees of freedom and acoustic phonons, we present a universal theory of the temperature dependence of the energy relaxation rate in a marginal Fermi liquid. We find that the energy relaxation rate exhibits a complex set of temperature-dependent crossovers controlled by emergent energy scales in the problem. We place these results in the context of recent measurements of the energy relaxation rate via nonlinear optical spectroscopy in the normal state of hole-doped cuprates.