arXiv subjects

Z. Song

Publications and source records attributed to Z. Song.

At least 19 recordsLinked to original sources

arXiv2026

String Order in Quench Dynamics as a Probe of Quantum Phase Transitions

We study the anisotropic XY chain in a transverse field by introducing a global string order parameter and examining its equilibrium behavior and its quench dynamics from a fully polarized initial state. The corresponding string operator is defined as the product of local projected spin operators over the entire chain. The nonequilibrium order parameter is the long-time average of the logarithm of the string-operator expectation value per site after the quench. For the ground state, its field derivative is singular on the Ising critical lines; after the quench, the steady-state response also records the field boundaries and the anisotropy transition. We derive analytically the nonanalytic behavior of the order parameter at the quantum critical lines. Our results reveal a hidden nonlocal order underlying this paradigmatic model of conventional quantum phase transitions. They also connect measurable spin populations with equilibrium and dynamical topological structure.

cond-mat.str-el↗

arXiv2026

Boundary-dependent topological degeneracy in an Ising chain

The influence of boundary conditions on bulk properties is generally expected to vanish in the thermodynamic limit. Here we show that this expectation can fail in an open transverse field Ising chain with modified boundary fields. By removing only the transverse fields acting on the two edge spins while leaving the bulk Hamiltonian unchanged, we uncover a boundary-induced switching of the topological spectral degeneracy. In contrast to the conventional open chain, where the topological degeneracy occurs in the ferromagnetic phase ($\left\vert g\right\vert <1$), the modified boundary condition shifts it to the paramagnetic phase ($\left\vert g\right\vert >1$). We demonstrate that the underlying mechanism originates from two exact local conserved quantities associated with the edge spins, which partition the Hilbert space into invariant sectors. Based on this structure, we establish an exact description in terms of domain-wall excitations, under which the Hamiltonian decomposes into two independent Kitaev chains. Complementarily, the Majorana representation reveals that the spectral switching originates from different unit-cell conventions and boundary terminations of the corresponding effective SSH lattice, leading to distinct boundary zero-mode structures without altering the bulk Hamiltonian. Furthermore, we show that the boundary-induced topological degeneracy remains observable at finite temperatures through non-Hermitian quench dynamics, providing a dynamical manifestation of the bulk-boundary correspondence. These results demonstrate that boundary engineering, through the introduction of local conserved boundary degrees of freedom, provides an effective route for controlling topological degeneracy in quantum spin chains without modifying bulk interactions.

cond-mat.str-el↗

arXiv2026

Emergent one-dimensional Bloch oscillations in coupled Ising layers

Bloch oscillations typically arise in periodic systems subjected to a constant force generated by a potential gradient. Here, we study domain-wall dynamics in coupled Ising layers under asymmetric longitudinal fields. The interlayer coupling is of Heisenberg type and acts as an effective transverse coupling in the emergent pseudospin representation. We show that the rung pseudospin structure gives rise to kinetic constraints, restricting the many-body dynamics to an emergent one-dimensional quasiparticle subspace within the original two-dimensional system. Furthermore, the imbalance between the longitudinal fields of the two layers induces an effective linear potential for the emergent domain-wall excitations, leading to their confinement between two oppositely polarized ferromagnetic domains. Remarkably, the resulting Wannier--Stark ladder of domain-wall excitations gives rise to Bloch oscillations in the absence of a conventional tilted potential, revealing a distinct mechanism for coherent quantum dynamics. Numerical simulations of time-dependent observables confirm the analytical predictions.

cond-mat.str-el↗

arXiv2026

Generalized η-pairing eigenstates in three-component Hubbard models under a transverse field

We investigate three-component Hubbard models on a bipartite lattice in the presence of a trans?verse field. Unlike the two-component Hubbard model, where the η-pairing symmetry survives the transverse field, the three-component model possesses neither η-pairing symmetry nor conservation of the particle number of each component. We introduce a generalized η-pairing operator, formed as a hybridization of three types of two-component pairing operators, and employ the restricted spectrum-generating algebra to construct a family of exact eigenstates. These eigenstates exhibit off-diagonal long-range order. Furthermore, we construct an exact tensor-product state whose co?herent periodic dynamics provide an exact realization of quantum many-body scar dynamics while simultaneously exhibiting long-range magnetic order. We also propose three protocols for preparing this state via quench dynamics, and verify their effectiveness through numerical simulations.

cond-mat.str-el↗

arXiv2026

Exact phase diagram of the XXZ Heisenberg chain in a staggered magnetic field

We study the phase diagram of the spin-1/2 XXZ Heisenberg chain in a staggered magnetic field. An exact solution is obtained along the phase boundary, where the exchange anisotropy and the staggered-field strength satisfy an exact analytical relation, yielding a highly degenerate manifold of ground states with off-diagonal long-range order. We demonstrate that these exact ground states lie on the boundary between the ferromagnetic phase and a gapless Luttinger liquid phase. Upon further decreasing the anisotropy, the gapless phase eventually gives way to a gapped quantum-disordered phase. Large-scale density-matrix renormalization group calculations confirm this phase structure and indicate that the transition across the exact boundary is of first order. Our results provide an exact benchmark for understanding quantum phase transitions driven by staggered magnetic fields in one-dimensional quantum spin systems.

cond-mat.str-el↗

arXiv2026

Quantum Many-Body Scars, Magnon-Pair Condensation, and Hilbert Space Fragmentation in an Anisotropic Heisenberg Model

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.

cond-mat.str-el↗

arXiv2026

Exact interlayer triplet-pairing eigenstates in the extended Hubbard model

$η$-pairing symmetry generalizes the pairing mechanisms in superconductivity but is broken in the presence of interlayer interactions. In this work, we extend this approach to triplet pairs. We propose interlayer triplet-pairing operators for the multi-layer extended Hubbard model. We find that a set of exact condensate-pair eigenstates can be constructed, which exhibit off-diagonal long-range order. In contrast to the $η$-pairing mechanism, this originates from restricted spectrum generating algebra and is only available for bilayer and trilayer systems in the presence of interlayer Hubbard interactions. Nevertheless, the system also retains the original on-site $η$-pairing symmetry in the absence of interlayer interactions. Consequently, both singlet and triplet pairs coexist in the eigenstates of the multi-layer Hubbard model. We employ quench dynamics to demonstrate the results through numerical simulations. Our findings open avenues for the study of exact condensate-pair states in strongly correlated systems.

cond-mat.str-el↗

arXiv2026

Pairing-induced Bloch oscillations in an interacting Kitaev chain

We study the peculiar dynamics of the Kitaev chain induced by nearest-neighbor (NN) interaction. We show that a strong NN interaction suppresses single-particle hopping but enhances pairing, resulting in a Wannier-Stark ladder. Based on the spin-fermion correspondence at the symmetry point, the model maps to a transverse field Ising model on a zigzag lattice, providing a clear physical picture and guiding experimental verification. The Wannier-Stark state corresponds to a localized domain wall between ferromagnetic and antiferromagnetic phases. It exhibits Bloch oscillation even in the absence of a longitudinal field, in contrast to previous works. Numerical simulations of time-dependent observables verify these conclusions. Our findings provide an example demonstrating emergent Stark many-body localization.

cond-mat.str-el↗

arXiv2026

Condensate states in Fermi and Bose-Hubbard ladders

Although neither hardcore bosons nor fermions can occupy the same single-site state, they still obey different statistics, resulting in distinct many-particle quantum states, such as condensate states versus Fermi-liquid states. However, when only pair states are considered, the two can take the same form, since a local hardcore Bose pair and a Fermi pair obey the same statistics. In this work we demonstrate this by studying both Fermi and Bose extended Hubbard ladders, which can be realized experimentally in synthetic atomic ladders. A set of exact condensate-pair eigenstates for the Fermi ladder is constructed under SU(2) symmetry and can then be obtained by the spectrum generating algebra. The corresponding hardcore boson counterpart can be simply obtained by replacing fermionic operators with hardcore bosonic ones. Nevertheless, the boson-pair eigenstates are associated not with symmetry but with the restricted spectrum generating algebra. We also investigate the effect of next-nearest-neighbor hopping on the condensate states through numerical simulations of the dynamic response. The conclusions can be extended to a two-layer system. Our result reveals not only the resemblance of fermions to hardcore bosons, but also a possible mechanism of Hilbert-space fragmentation.

cond-mat.str-el↗

arXiv2026

Periodic dynamics in an Ising chain with a quadratic transverse field

A quadratic well plays a central role in a wide variety of modern physical theories and applications. In this work, we investigate many-body dynamics in a quadratic well, using an Ising chain as a paradigmatic example. In contrast to a uniform Ising chain, where the quantum phase transition is driven by the field strength, the present system exhibits spatially varying quantum phases along the chain. Through analysis of the Majorana representation, we obtain exact solutions for localized modes, revealing a topologically degenerate spectrum in the thermodynamic limit. In the case of a finite-size quantum phase region, the Kramers-like degeneracy is lifted by a constant shift, leading to periodic oscillations for a finite-temperature thermal initial state. Numerical simulations of the magnetization, local density of state, and quench fidelity support our conclusions. Our findings enrich the understanding of many-body dynamics in a trapping field.

quant-ph↗

arXiv2026

Hilbert space fragmentation in quantum Ising systems induced by side coupling

We study Hilbert space fragmentation and quantum scars in quantum spin systems with Ising interactions. The system consists of two sets of quantum spins, A and B. As the parent system, set A is an Ising model on arbitrary lattices with a transverse field, while set B comprises free spins that are coupled to set A. We show that the Hilbert space is fragmented into exponentially many decoupled sectors when the transverse field and the side coupling strength are at resonance. As examples, several typical systems with quantum scars are studied analytically. Numerical simulations of probability distribution of entanglement entropy for finite-size chains, square and triangular lattices are performed using the Monte Carlo method. The results show that Hilbert space fragmentation and the corresponding quantum scars become pronounced when the system approaches resonance.

cond-mat.str-el↗

arXiv2026

Reduced-Order Variational Deterministic-Particle-Based Scheme for Fokker-Planck Equations in Microscopic Polymer Dynamics

This study proposes an acceleration technique for the computational challenges in extending the variational deterministic-particle-based scheme (VDS) [Bao et al., Journal of Computational Physics 522 (2025) 113589] to 3D complex fluid simulations with multi-bead polymers. While the original VDS effectively captures configuration space dynamics for 2D dumbbell polymers, its direct extensions reveal critical scalability limitations. The growing configuration space dimensionality necessitates prohibitively large particle ensembles to maintain distributional accuracy, so its quadratic computational cost scaling impedes practical applications. In this paper, we develop a model reduction framework integrating proper orthogonal decomposition (POD) to speed up the computation of the VDS for microscopic Fokker-Planck equations. Numerical validation using bead-spring chain models in simple shear flow demonstrates that the computational efficiency of the reduced model increases systematically with molecular complexity. The reduced-order model introduces about $6\%$ relative error in predicting the dynamics while requiring only about $6\%$ of the original computational time for $4$-bead chain polymers, where the relative numerical error of the reference dynamics is about $5\% \sim 10\%$, and the degrees of freedom can be reduced significantly to about $0.1\%$ of the original model, which means the low-dimensional structure is found by POD. This establishes a practical pathway for multiscale and complex fluid simulations.

physics.comp-ph↗

arXiv2026

Exceptional nodal rings emerging in spinful Rice-Mele chains

The Weyl exceptional nodal lines usually occur in 3D topological semimetals, but also emerge in the parameter space of 1D systems. In this work, we study the impact of dissipation on the nodal ring in a 3D topological semimetal. We find that the energy spectrum becomes fully complex in the presence of dissipation, and the original nodal ring is split into two exceptional rings. We introduce a vortex field in the momentum space, which is generated from the spectrum, to characterize the topology of the exceptional rings. This provides a clear physical picture of the topological structure. The two exceptional rings act as two vortex filaments of a free vortex flow with opposite circulations. In this context, the 3D topological semimetal is the boundary separating two quantum phases identified by two configurations of exceptional rings. We also propose a 1D model that has the same topological feature in the parameter space. It provides a simple way to measure the topological invariant in a low-dimensional system. Numerical simulations indicate that the topological invariant is robust under the random perturbations of the system parameters.

cond-mat.str-el↗

arXiv2026

Hierarchic superradiant phases in anisotropic Dicke model

We revisit the phase diagram of an anisotropic Dicke model by revealing the non-analyticity induced by underlying exceptional points. We find that, from a dynamical perspective, the conventional superradiant phase can be further separated into three regions, in which the systems are characterized by different effective Hamiltonians, including the harmonic oscillator, the inverted harmonic oscillator, and their respective counterparts. We employ the Loschmidt echo to characterize different quantum phases by analyzing the quench dynamics of a trivial initial state. Numerical simulations for finite systems confirm our predictions about the existence of hierarchic superradiant phases.

quant-ph↗

arXiv2025

Hilbert Space Fragmentation in Hardcore Bose and Fermi Hubbard Models on Generalized Lieb Lattices

We study the Hilbert space fragmentation (HSF) in hardcore Bose and Fermi Hubbard models in the framework of the restricted spectrum generating algebra (RSGA). We present a family of hardcore Bose-Hubbard models with repulsive density-density interactions on a generalized Lieb lattice. We show that this system possesses the RSGA structure in the large interaction strength limit, exhibiting quantum HSF. It allows us to construct a set of exact condensate eigenstates, possessing off diagonal long-range order. Based on numerical simulations conducted on several representative lattices, we demonstrate the existence of weak fragmentations when the constraints are not exact. As applications, we also studied the connection between HSF and RSGA in modified fermionic Hubbard models, where the η-pairing states are shown to be energy towers, acting as quantum scars.

cond-mat.str-el↗

arXiv2025

Dynamic destruction of magnetic order in a quantum Ising chain with oscillating transverse field

We study the dynamic response of magnetic domain walls in low-lying excited states of an Ising chain to an oscillating transverse field. Based on the exact instantaneous eigenstates, we find that when the frequency of the external field is in off-resonant regions, the domain wall exhibits Bloch oscillation, maintaining the magnetic order. However, the magnetic order is destroyed when the field is at resonant frequency. Numerical simulations of the dynamics of magnetization and entanglement entropy for initial states with single and double domain walls accord with the predictions. These findings reveal the nontrivial effect of a monochromatic electromagnetic field on quantum spin dynamics.

cond-mat.str-el↗

arXiv2025

Critical dynamics and superconducting state preparation in the quenched Kitaev chain with pairing imbalance

The dynamical balance of the pairing term plays a crucial role in the emergence of topological superconductivity in the p-wave spinless Kitaev chain, particularly in the non-Hermitian regime. In this work, we systematically investigate the effects of non-Hermitian pairing terms on both equilibrium and nonequilibrium phenomena in the Kitaev chain. Our analysis focuses on two representative forms of pairing imbalance: uniform and staggered. We demonstrate that a uniform imbalance induces only minor perturbations to the spectrum and dynamical properties, without significantly affecting its equilibrium phase or nonequilibrium steady behavior. In contrast, even a slight staggered imbalance leads to drastic changes. At the symmetry point, it enables the resonant generation of two distinct superconducting states through critical dynamics, with the realized state determined by the direction of the bias. Both states exhibit exact off-diagonal long-range order (ODLRO) in the thermodynamic limit. Our results emphasize the fragility of coherent dynamics in non-Hermitian topological systems and elucidate the interplay among non-Hermiticity, topology, and dynamical criticality in quench processes.

cond-mat.supr-con↗

arXiv2025

Exceptional-point-induced dynamic sensitivity to particle-number parity

As an exclusive feature of a non-Hermitian system, the existence of exceptional points (EPs) depends not only on the details of the Hamiltonian but also on the particle-number filling and the particle statistics. In this paper, we study many-particle EPs in a Bose Hubbard chain with two end-site resonant imaginary potentials. Starting from a single-particle coalescing eigenstate, we construct $n$-particle condensate eigenstates for the cases with zero and infinite $U$. Compared with the free bosonic case, where the $ n $-particle condensate eigenstate is an $(n+1)$-th-order coalescing state, the hardcore-boson counterpart is a second-order coalescing state for odd $n$ , while it is not for even $n$. The difference in particle-number parity results in distinct quenching dynamics of the condensate states, highlighting the role of parity in system behavior. Our finding may stimulate research on the dynamic sensitivity to particle-number parity.

cond-mat.str-el↗