arXiv subjects

Z. Song

Publications and source records attributed to Z. Song.

At least 37 records · Page 2Linked to original sources

arXiv2025

$η$-pairing states in the Hubbard model with non-uniform Hubbard interaction

The existence of $η$-pairing eigenstates in the fermionic Hubbard model is fundamentally rooted in the $η$-pairing symmetry, which may hold for systems with non-uniform Hubbard interaction $U$. In this work, we present a generalized Hubbard model containing a variety of pseudo-spin terms that break the SO$_{4}$ symmetry but retain the $η$-pairing symmetry. This allows us to construct a variety of correlated systems possessing $η$% -pairing eigenstates.\ We exemplify our findings by considering a modified Hubbard model associated with alternative magnetic fields and on-site repulsion. We find that the same quasi-$η$-pairing eigenstate exhibits two distinct dynamic behaviors in the two models. Numerical results of the time evolution driven by several typical Hamiltonians accord with the analytic predictions and provide a way of the control of an $η$-pairing wavepacket with the aid of a time-dependent Hamiltonian.

cond-mat.str-el↗

arXiv2025

Condensate ground states of hardcore bosons induced by an array of impurities

Neither hardcore bosons nor fermions can occupy the same lattice site-state. However, a nearest neighbour interaction may counteract the hardcore effect, resulting in condensate states in a bosonic system. In this work, we unveil the underlying mechanism by developing a general method to construct the condensate eigenstates from those of sub-Hamiltonians. As an application, we find that a local on-site potential can induce an evanescent condensate mode. Based on this, exact condensate ground states of hardcore bosons, possessing off-diagonal long-range order, can be constructed when an array of impurities is applied. The effect of the off-resonance impurity on the condensate ground states is also investigated using numerical simulations of the dynamic response.

cond-mat.quant-gas↗

arXiv2025

Bloch oscillations in interacting systems driven by a time-dependent magnetic field

According to Faraday's law in classical physics, a varying magnetic field stimulates an electric eddy field. Intuitively, when a classical field is constant and imposed on a lattice, the Wannier-Stark ladders (WSL) can be established, resulting in Bloch oscillations. In this work, we investigate the dynamics of an interacting system on a (generalized) ring lattice threaded by a varying magnetic flux. Based on the rigorious results, we demonstrate that there exist many invariant subspaces in which the dynamics is periodic when the flux varies linearly over time. Nevertheless, for a given initial state, the evolved state differs from that driven by a linear field. However, the probability distributions of the two states are identical, referred to as the quantum analogue of Faraday's law. Our results are ubiquitous for a wide variety of interacting systems. We demonstrate these results through numerical simulations in an extended fermi-Hubbard model.

cond-mat.str-el↗

arXiv2025

Higher order coherence as witness of exceptional point in Hermitian bosonic Kitaev dimer

The non-analyticity induced by exceptional points (EPs) has manifestations not only in non-Hermitian but also in Hermitian systems. In this work, we focus on a minimal Hermitian bosonic Kitaev model to reveal the dynamical demonstration of EPs in a Hermitian system. It is shown that the EPs separate the parameter space into four regions, in which the systems are characterized by different equivalent Hamiltonians, including the harmonic oscillator, the inverted harmonic oscillator, and their respective counterparts. We employ the second-order intensity correlation to characterize a nonequilibrium quantum phase transition by calculating the time evolution of a trivial initial state. The results indicate that the concept of the EP can be detected in a small Hermitian bosonic system.

quant-ph↗

arXiv2025

Coalescing hardcore-boson condensate states with nonzero momentum

Exceptional points (EPs), as an exclusive feature of a non-Hermitian system, support coalescing states to be alternative stable state beyond the ground state. In this work, we explore the influence of non-Hermitian impurities on the dynamic formation of condensate states in one-, two-, and three-dimensional extended Bose-Hubbard systems with strong on-site interaction. Based on the solution for the hardcore limit, we show exactly that condensate modes with off-diagonal long-range order (ODLRO) can exist when certain system parameters satisfy specific matching conditions. Under open boundary conditions, the condensate states become coalescing states when the non-Hermitian $\mathcal{PT}$-symmetric boundary gives rise to the EPs. The fundamental mechanism behind this phenomenon is uncovered through analyzing the scattering dynamics of many-particle wavepackets at the non-Hermitian boundaries. The EP dynamics facilitate the dynamic generation of condensate states with non-zero momentum. To further substantiate the theoretical findings, numerical simulations are conducted. This study not only unveils the potential condensation of interacting bosons but also offers an approach for the engineering of condensate states.

quant-ph↗

arXiv2025

Exact eigenstates with off-diagonal long-range order for interacting bosonic systems

Fermions and hardcore bosons share the same restriction: no more than one particle can occupy a single site in a lattice system. Specifically, in one dimension, two systems can share the same matrix representation. In this work, we investigate both the fermion and hardcore-boson models with nearest-neighbor (NN) interaction in a ring lattice. We construct the exact eigenstates of the hardcore-boson model with resonant NN interaction and show that they possess off-diagonal long-range order (ODLRO) in the thermodynamic limit. In comparison, the fermionic counterpart does not support such a feature due to the different particle statistics, although they share an identical energy spectrum. In addition, we examine the effect of the periodic boundary condition on the dynamics of the condensate states through numerical simulations.

cond-mat.str-el↗

arXiv2025

Formations of generalized Wannier-Stark ladders: Theorem and applications

The Wannier-Stark ladder (WSL) is a basic concept, supporting periodic oscillation, widely used in many areas of physics. In this paper, we investigate the formations of WSL in generalized systems, including strongly correlated and non-Hermitian systems. We present a theorem on the existence of WSL for a set of general systems that are translationally symmetric before the addition of a linear potential. For a non-Hermitian system, the WSL becomes complex but maintains a real energy level spacing. We illustrate the theorem using 1D extended Bose-Hubbard models with both real and imaginary hopping strengths. It is shown that the Bloch-Zener oscillations of correlated bosons are particularly remarkable under resonant conditions. Numerical simulations for cases with boson numbers $n=2$, $3$, and $4$ are presented. Analytical and numerical results for the time evolution of the $n$-boson-occupied initial state indicate that all evolved states exhibit quasi periodic oscillations, but with different profiles, depending on the Hermiticity and interaction strength.

cond-mat.str-el↗

arXiv2025

Topological quantized edge-pumping-spin flip in Rice-Mele model with spin-orbit coupling

The quantized Thouless pumping charge in a spinless Rice-Mele (RM) model originates from a degeneracy point in the parameter space and cannot be detected when open boundary conditions are applied. In this work, we investigate the topological features of a spinful Rice-Mele (RM) model. We demonstrate that spin-orbit coupling facilitates the transition of a single degenerate point into a degenerate loop, which is anticipated to be the source of the topological characteristics. When periodic boundary conditions are considered, we find that the pumping spin is zero for an adiabatic loop within the nodal loop and is 2 (in units of $\hbar /2$) for an adiabatic passage enclosing the nodal loop. When open boundary conditions are considered, the boundary-bulk correspondence is demonstrated by quantized pumping-spin flips at the edges, which can be obtained by completing double periods of a closed passage, rather than a single cycle. Our findings reveal an alternative dynamic manifestation of the boundary-bulk correspondence.

cond-mat.mes-hall↗

arXiv2024

Dynamic Moiré-like pattern in non-Hermitian Wannier-Stark ladder system

We study the dynamical behavior of the non-Hermitian Wannier-Stark ladder system, which is a non-Hermitian Su-Schrieffer-Heeger chain with a position-dependent real potential. In the presence of a linear external field, we employ the non-Hermitian Floquet method and find that the energy levels are sensitive to the field. The system exhibits two distinct dynamic behaviors separated by an exceptional point: one in the $\mathcal{PT}$ symmetrical region associated with two real Wannier-Stark ladders, and another in the $\mathcal{PT}$\ symmetry-breaking region associated with complex conjugate ladders. As the boundary between the two regions, two ladders coalesce into a single ladder. In the case of a non-linear field, these two distinct regions appear alternately along the chain, exhibiting dynamic Moiré-like patterns.

quant-ph↗

arXiv2024

Dynamics of non-Hermitian Floquet Wannier-Stark system

We study the dynamics of the non-Hermitian Floquet Wannier-Stark system in the framework of the tight-binding approximation, where the hopping strength is a periodic function of time with Floquet frequency $ω$. It is shown that the energy level of the instantaneous Hamiltonian is still equally spaced and independent of time $t$ and the Hermiticity of the hopping term. In the case of off resonance, the dynamics are still periodic, while the occupied energy levels spread out at the resonance, exhibiting $t^z$ behavior. Analytic analysis and numerical simulation show that the level-spreading dynamics for real and complex hopping strengths exhibit distinct behaviors and are well described by the dynamical exponents $z=1$ and $z=1/2$, respectively.

quant-ph↗

arXiv2024

Extended Wannier-Stark ladder and particle-pair Bloch oscillations in dimerized non-Hermitian systems

In the Hermitian regime, the Wannier-Stark ladder characterizes the eigenstates of an electron in a periodic potential with an applied static electric field. In this work, we extend this concept to the complex regime for a periodic non-Hermitian system under a linear potential. We show that although the energy levels can be complex, they are still equally spaced by a real Bloch frequency. This ensures single-particle Bloch oscillations with a damping (or growing) rate. The system can also support standard two-particle Bloch oscillations under certain conditions. We propose two types of dimerized non-Hermitian systems to demonstrate our results. In addition, we also propose a scheme to demonstrate the results of electron-pair dynamics in a single-particle 2D $\mathcal{PT}$-symmetric square lattice.

quant-ph↗

arXiv2024

Emerging topological characterization in non-equilibrium states of quenched Kitaev chains

Topological characteristics of quantum systems are typically determined by the closing of a gap, while the dynamical quantum phase transition (DQPT) during quantum real-time evolution has emerged as a nonequilibrium analog to the quantum phase transition (QPT). In this paper, we illustrate that the system dynamics can be elucidated by considering the precession of a collection of free-pseudo spins under a magnetic field based on the exact results of extended Kitaev chains. The topology of the driven Hamiltonian is determined by the average winding number of the nonequilibrium state. Furthermore, we establish that the singularity of the DQPT arises from two perpendicular pseudo-spin vectors associated with the pre- and post-quenched Hamiltonians. Moreover, we investigate the distinct behaviors of the dynamic pairing order parameter in both topological and non-topological regions. These findings offer valuable insights into the non-equilibrium behavior of topological superconductors, contributing to the understanding of the resilience of topological properties in driven quantum systems.

cond-mat.str-el↗

arXiv2024

Detecting the Chern number via quench dynamics in two independent chains

The Chern number, as a topological invariant, characterizes the topological features of a 2D system and can be experimentally detected through Hall conductivity. In this work, we investigate the connection between the Chern number and the features of two independent chains. It is shown that there exists a class of 2D systems that can be mapped into two independent chains. We demonstrate that the Chern number is identical to the linking number of two loops, which are abstracted from each chain individually. This allows for the detection of the Chern number via quench dynamics in two independent chains. As an example, the Qi-Wu-Zhang (QWZ) model is employed to illustrate the scheme. Our finding provides a way to measure the phase diagram of a 2D system from the 1D systems.

quant-ph↗

arXiv2024

Hidden exceptional point, localization-delocalization phase transition in Hermitian bosonic Kitaev model

Exceptional points (EPs), a unique feature of non-Hermitian systems, represent degeneracies in non-Hermitian operators that likely do not occur in Hermitian systems. Nevertheless, unlike its fermionic counterpart, a Hermitian bosonic Kitaev model supports a non-Hermitian core matrix, involving a quantum phase transition (QPT) when an exceptional point appears. In this study, we examine QPTs by mapping the Hamiltonian onto a set of equivalent single-particle systems using a Bardeen-Cooper-Schrieffer (BCS)-like pairing basis. We demonstrate the connection between the hidden EP and the localization-delocalization transition in the equivalent systems. The result is applicable to a Dicke model, which allows the experimental detection of the transition based on the measurement of the average number of photons for the quench dynamics stating from the empty state. Numerical simulations of the time evolution reveal a clear transition point at the EP.

quant-ph↗

arXiv2024

Topological quantum slinky motion in resonant extended Bose-Hubbard model

We study the one-dimensional Bose-Hubbard model under the resonant condition, where a series of quantum slinky oscillations occur in a two-site system for boson numbers $n\in \lbrack 2,\infty )$. In the strong interaction limit, it can be shown that the quantum slinky motions become the dominant channels for boson propagation, which are described by a set of effective non-interacting Hamiltonians. They are sets of generalized Su-Schrieffer-Heeger chains with an $n$-site unit cell, referred to as trimerization, tetramerization, and pentamerization, etc., possessing non-trivial Zak phases. The corresponding edge states are demonstrated by the $n$-boson bound states at the ends of the chains. We also investigate the dynamic detection of edge boson clusters through an analysis of quench dynamics. Numerical results indicate that stable edge oscillations clearly manifest the interaction-induced topological features within the extended Bose-Hubbard model.

quant-ph↗

arXiv2024

Non-Hermitian dynamics of Cooper pair splitter

We propose a non-Hermitian model for Cooper pair splitters, in which the process of electron tunneling into electrodes is characterized by non-Hermitian terms. We find that across a broad range of parameters, the energy levels consistently remain real, and coalescing states are always present. The Coulomb repulsion between electrons in a quantum dot affects the order of the coalescing states. This gives rise to two distinct dynamic behaviors: (i) when the initial state is an empty state, the final state supports a nonzero electron-escaping rate; (ii) the electron-escaping rate is zero for a single-electron initial state. In the former case, our exact solutions reveal that the average electron-escaping rate vanishes along a set of hyperbolic curves in the plane of the chemical potentials of the two quantum dots. The stability of the results in the presence of disordered perturbation is also investigated. Our findings pave the way for investigating Cooper pair splitters within the framework of non-Hermitian quantum mechanics.

cond-mat.str-el↗

arXiv2024

Insulating-to-conducting state transition in the bilayer Hubbard model induced by a perpendicular quench field

A many-body quantum system with varying parameters can exhibit two distinct quantum states within the same energy shell. This allows for a dynamic transition from the ground state of the pre-quench Hamiltonian to a steady state of the post-quench Hamiltonian. We investigate the dynamic response of the ground states in a two-layer half-filled Hubbard model to a perpendicular electric field. We demonstrate that the steady state exhibits conductivity when the field is in resonance with the on-site repulsion, while the initial state is a Mott-insulating state. Additionally, the two layers exhibit identical conducting behavior due to the formation of long-lived dopings, as evidenced by the charge fluctuation. The key factor in achieving this dynamic transition is the cooperative interplay between on-site interactions and the resonant field, rather than the individual roles they play. Our findings offer an alternative mechanism for field-induced conductivity in strongly correlated systems.

cond-mat.str-el↗

arXiv2024

Coherent Transfer of Lattice Entropy via Extreme Nonlinear Phononics in Metal Halide Perovskites

Entropy transfer in metal halide perovskites, characterized by significant lattice anharmonicity and low stiffness, underlies the remarkable properties observed in their optoelectronic applications, ranging from solar cells to lasers. The conventional view of this transfer involves stochastic processes occurring within a thermal bath of phonons, where lattice arrangement and energy flow from higher to lower frequency modes. Here we unveil a comprehensive chronological sequence detailing a conceptually distinct, coherent transfer of entropy in a prototypical perovskite CH$_3$NH$_3$Pbl$_3$. The terahertz periodic modulation imposes vibrational coherence into electronic states, leading to the emergence of mixed (vibronic) quantum beat between approximately 3 THz and 0.3 THz. We highlight a well-structured, bi-directional time-frequency transfer of these diverse phonon modes, each developing at different times and transitioning from high to low frequencies from 3 to 0.3 THz, before reversing direction and ascending to around 0.8 THz. First-principles molecular dynamics simulations disentangle a complex web of coherent phononic coupling pathways and identify the salient roles of the initial modes in shaping entropy evolution at later stages. Capitalizing on coherent entropy transfer and dynamic anharmonicity presents a compelling opportunity to exceed the fundamental thermodynamic (Shockley-Queisser) limit of photoconversion efficiency and to pioneer novel optoelectronic functionalities.

cond-mat.mtrl-sci↗