arXiv subjects

Wen-Long You

Publications and source records attributed to Wen-Long You.

At least 19 recordsLinked to original sources

arXiv2026

Analytical diagonalization of the open-boundary bosonic Kitaev chain: An asymmetric plane-wave ansatz approach

The bosonic Kitaev chain under open boundary conditions has attracted recent attention due to its realization in driven-dissipative systems and its intriguing non-Hermitian boundary physics. The model is known to be solvable via local squeezing transformations in the position-momentum representation. In this paper, we present an alternative, purely algebraic solution that relies entirely on the standard bosonic Bogoliubov transformation. For an $N$-site chain, we propose an asymmetric plane-wave ansatz with unequal left- and right-moving momenta to analytically solve the associated $2N\times 2N$ non-Hermitian ``associated matrix". The left eigenvalue problem yields $N$ distinct eigenvalues, each of which is twofold degenerate. By carefully resolving these degeneracies using the bosonic commutation relations, we construct the $N$ physical Bogoliubov quasiparticle operators. The construction reveals non-uniquenesses that in special cases exactly mirror the freedom in the local squeezing transformations of the original approach. The diagonal form of the Hamiltonian is obtained explicitly and is shown to be equivalent to the original Hamiltonian. The proposed asymmetric plane-wave ansatz and degeneracy-resolution technique are not limited to the present model and can be generalized to other bosonic pairing systems, including those with inhomogeneous pairing or hopping terms.

quant-ph↗

arXiv2026

Arithmetic Tuning of Dynamical Critical Exponents in Quasiperiodic Localization Transitions

The critical exponents and universality classes of localization transitions in quasiperiodic systems are of fundamental importance for understanding critical phenomena in aperiodic systems. Here we show that the dynamical critical behavior can be tuned without adding new terms or changing the form of the Hamiltonian, but solely by varying the incommensurate frequency of the quasiperiodic onsite potential. We construct a family of incommensurate frequencies from the limiting ratios of generalized Fibonacci sequences controlled by the parameters $(m,n)$, and use them to define the quasiperiodic onsite potential. By combining generalized fidelity susceptibility, localization-length scaling, and finite-size gap analysis, we find that the correlation-length exponent is insensitive to the choice of the incommensurate frequency and remains consistent with the correlation-length critical exponent, $\nu \simeq 1$, in the localization transition of the standard Aubry--Andr'e--Harper model. In contrast, the dynamical exponent extracted from the low-energy gap scaling varies systematically with the incommensurate frequency. Our results show that changing the incommensurate frequency provides a simple way to tune dynamical critical scaling in deterministic aperiodic systems. Our results suggest instead that the arithmetic structure of an irrational number can serve as a control parameter for nonequilibrium quantum dynamics, enabling the tuning of dynamical critical behavior without changing the microscopic Hamiltonian or the physical spatial dimension.

cond-mat.dis-nn↗

arXiv2026

Krylov complexity of anyons

Anyons obey fractional statistics that lie between bosonic and fermionic statistics, giving rise to a broad range of intriguing phenomena. However, how anyonic statistics govern quantum-state complexity is still largely unexplored. In this work, we investigate the interplay between the statistical phase and on-site interactions in the anyon-Hubbard model, identifying exact quantum many-body scar eigenstates and novel quench dynamics. The Krylov complexity exhibits perfect periodic revivals independent of the statistical phase in the scarred dynamics, whereas after a quench it depends on both the statistical phase and the interaction strength. In the strong-interaction regime, we find approximate scarred dynamics, while in the weak-interaction regime the state spreads over Krylov space and the complexity ultimately saturates. Moreover, for the bosonic initial state, the complexity of fermions exhibits the lowest saturation value, and vice versa. For fractional statistics, the saturation plateau is minimized when the post-quench statistical phase is close to that of the initial state. Our results demonstrate the central role of the statistical phase in governing many-body dynamics and provide new insights into Krylov complexity and quantum many-body scars.

quant-ph↗

arXiv2026

Quantum criticality and factorization in a constrained Rydberg spin chain

We investigate the zero-temperature phase diagram of a one-dimensional constrained quantum spin chain realized in coherently driven Rydberg-atom arrays with competing local Rabi driving and dipole-dipole exchange interactions. Projecting onto the blockade-constrained Hilbert space yields an effective model in which local and nonlocal quantum fluctuations compete on equal footing. Combining exact diagonalization, the density-matrix renormalization group, and variational uniform matrix-product-state calculations, we establish a complete phase diagram comprising a Luttinger liquid, an antiferromagnetic ordered phase, and a polarized paramagnet. We identify two distinct mechanisms for the destruction of antiferromagnetic order: a conventional Ising transition at strong driving and a continuous quantum melting into the Luttinger liquid at weak driving, characterized using entanglement-based diagnostics and finite-entanglement scaling. In addition, we uncover an exact ground-state factorization line embedded within the ordered phase, providing an analytically tractable zero-entanglement reference point for experiments with programmable Rydberg quantum simulators.

cond-mat.str-el↗

arXiv2026

Tighter thermalization bounds for perturbed quantum many-body scars

Quantum many-body scars (QMBS) are exceptional eigenstates that defy thermalization, enabling long-lived coherent dynamics in strongly interacting systems. However, their stability under perturbations remains inadequately understood. In this work, we derive improved lower bounds on the thermalization time of QMBS under local perturbations with strength $\lambda$. Using both numerical simulations and analytical reasoning, we show that exact QMBS exhibit slow thermalization, with a timescale scaling as $\tau \sim \mathcal{O}(\lambda^{-1/d})$ owing to the stabilizing restricted spectrum-generating algebra (RSGA), which is a significant improvement over previous bounds (e.g., $\tau \sim \mathcal{O}(\lambda^{-1/(d+1)})$). Counterintuitively, approximate QMBS can thermalize even more slowly under generic perturbations, exhibiting $\tau \sim \mathcal{O}(\lambda^{-2})$ scaling due to second-order perturbative effects in the absence of such protective structure. These distinct thermalization behaviors clarify how exact and approximate scars maintain coherence. Our work advances previous findings by establishing a tighter bound on the thermalization time, clarifying when scarred dynamics remain long-lived under weak but generic perturbations.

cond-mat.str-el↗

arXiv2025

Generalized Aubry-Andr\'{e}-Harper model with power-law quasiperiodic potentials

We investigate a generalized Aubry-Andr\'{e}-Harper (AAH) model with non-reciprocal hopping and power-law quasiperiodic potentials $V(i) = V\left[ \cos(2\pi \beta i) \right]^p$. Our study reveals that the interplay between nonreciprocity, quasiperiodicity, and the power-law exponent $p$ gives rise to a variety of phase transitions and localization phenomena. In the Hermitian case, the system undergoes a direct transition from extended to localized phases for $p=1, 2$, while for $p \geq 3$, an intermediate mixed phase emerges, characterized by the coexistence of extended and localized states and the presence of mobility edges. Importantly, we find that prominent high-IPR states associated with well-resolved spectral gaps appear at specific energy levels, whose positions are captured by the relation $x_n = n\beta - \lfloor n\beta \rfloor$, for low-order $n$. In the non-Hermitian regime, the energy spectrum becomes complex and the $\mathcal{PT}$ transition coincides with the extended-to-localized phase boundary for $p = 1, 2$, whereas for $p \geq 3$, $\mathcal{PT}$-symmetry breaking occurs at the mixed-to-localized phase transition. This work reveals how power-law quasiperiodic potentials and non-reciprocal hopping govern phase transitions, providing new insight into localization phenomena of quasiperiodic systems.

cond-mat.dis-nn↗

arXiv2025

Yang-Lee edge singularity and quantum criticality in non-Hermitian PXP model

We present a comprehensive theoretical framework for quantum criticality in the non-Hermitian detuned PXP model, and establish the complete phase diagram, which had remained elusive in previous studies. Starting from a numerically identified phase transition point, we construct an exact second-order phase transition boundary through a similarity transformation in the real-energy regime. By introducing the biorthogonal entanglement entropy and biorthogonal Loschmidt echo, we demonstrate from both equilibrium and nonequilibrium perspectives that this transition belongs to the Ising universality class. Using the correlation function, we further distinguish between confined and deconfined phases within the $\mathcal{PT}$-symmetric region. In the complex-energy regime, we identify both a full $\mathcal{PT}$ transition and a first-excited-state $\mathcal{PT}$ transition, respectively. Moreover, we identify the location of the Yang-Lee edge singularity (YLES) using both the associated-biorthogonal and self-normal Loschmidt echoes, and extract the corresponding critical exponent, which agrees with the predictions of non-unitary conformal field theory. Finally, we propose an experimental scheme to observe the YLES in Rydberg atomic arrays, which offers a promising route to exploring non-Hermitian critical phenomena and singularities in future experimental settings.

quant-ph↗

arXiv2025

Quantum criticality and emergent orders in the spin-1 bilinear-biquadratic-Kitaev chain

Higher-spin quantum magnets with competing interactions offer a rich platform for exploring quantum phases that transcend the paradigms of spin-1/2 systems, owing to their enlarged local Hilbert spaces and the emergence of multipolar correlations. We investigate a one-dimensional spin-1 chain where quadrupolar order is promoted by two distinct mechanisms: conventional bilinear-biquadratic exchange and bond-directional antiferromagnetic Kitaev frustration. Using density matrix renormalization group calculations, we determine the complete ground-state phase diagram and uncover two emergent phases induced by the Kitaev interaction: a Kitaev nematic phase and a Kitaev-dimer phase. The Kitaev nematic phase emerges from a fragile biquadratic dimer state via a continuous quantum phase transition in the Ising universality class. The Kitaev dimer phase spontaneously breaks a screw symmetry to favor either $x$- or $y$-spin bonding, forming a gapped state that coexists with a crystalline order of alternating $\mathbb{Z}_2$ fluxes.

cond-mat.str-el↗

arXiv2025

Unveiling quantum criticality of disordered Aubry-André-Harper models via typical fidelity susceptibility

In this study, we investigate the localization transition and quantum criticality {in the ground state of the} disordered Aubry-André-Harper (AAH) model, where a quasiperiodic potential is hybridized with a disordered potential. In the clean limit, the AAH model undergoes a localization transition from an extended phase to a localized phase via an intermediate critical phase as the strength of the quasiperiodic potential is varied. While the staggered potential merely shifts the critical point to a lower value, Fibonacci and Thue-Morse potentials induce immediate localization. This contrast reveals the sensitivity of localization behavior to the structural complexity of the potential, with the onset of localization correlating with the sequence's complexity. More specifically, the system follows a hierarchy defined by the complexity measures of the applied potentials. In addition, the typical fidelity susceptibility exhibits a power-law scaling behavior at the localization transition, enabling reliable extraction of the critical exponent. We focus on the AAH model with the Fibonacci potential due to its minimal finite-size effects compared to other cases. For the disordered AAH model with the Fibonacci potential, we determine critical exponents that differ from those of the AAH model without disorder and the Anderson model. Moreover, despite differences in localization behavior, we find that the disordered AAH models with the staggered potential and the Fibonacci potential share the same correlation-length critical exponent. These findings provide a unified framework for understanding localization transitions in quasiperiodic systems and are amenable to experimental validation using emerging techniques.

cond-mat.dis-nn↗

arXiv2025

Quantum anomaly triggers the violation of scaling laws in gravitational system

Scaling laws for critical phenomena take pivotal status in almost all branches of physics. However, as scaling laws are commonly guaranteed by the renormalization group theory, systems that violate them have rarely been found. In this letter, we demonstrate that gravitational system can break scaling laws. We derive this result through investigating phase transition and critical phenomenon in a gravitational system with quantum anomaly. For the first time, we outline the key conditions to violate the scaling laws in generic gravitational system viewed from the equation of state $P=P(T,V)$. Our results indicate that quantum effects can magnify the distinctiveness of gravity, which may be significant to understand the microscopic structure of spacetime.

gr-qc↗

arXiv2025

Krylov complexity in quantum many-body scars of spin-1 models

Weak ergodicity breaking, particularly through quantum many-body scars (QMBS), has become a significant focus in many-body physics. Krylov state complexity quantifies the spread of quantum states within the Krylov basis and serves as a powerful diagnostic for analyzing nonergodic dynamics. In this work, we study spin-one XXZ magnets and reveal nonergodic behavior tied to QMBS. For the XY model, the nematic Néel state exhibits periodic revivals in Krylov complexity. In the generic XXZ model, we identify spin helix states as weakly ergodicity-breaking states, characterized by low entanglement and nonthermal dynamics. Across different scenarios, the Lanczos coefficients for scarred states display an elliptical pattern, reflecting a hidden SU(2) algebra that enables analytical results for Krylov complexity and fidelity. These findings, which exemplify the rare capability to characterize QMBS analytically, are feasible with current experimental techniques and offer deep insights into the nonergodic dynamics of interacting quantum systems.

cond-mat.str-el↗

arXiv2025

Deconfined quantum criticality of frustrated hard-core dipolar bosons

Deconfined quantum critical points (DQCPs) are proposed as unconventional second-order phase transitions beyond the Landau-Ginzburg-Wilson paradigm. The nature and experimental realizations of DQCPs are crucial issues of importance. We illustrate the potential for DQCPs between the valence bond solid state and the antiferromagnetic phase to arise in optical lattices containing frustrated dipolar bosons subject to hard-core constraints. The emergence of DQCPs is comprehended through the fusion of two Berezinskii-Kosterlitz-Thouless (BKT) transitions. The DQCPs and the BKTs are confirmed by the scaling of ground-state fidelity susceptibilities in finite systems and the analysis of order parameters obtained from infinite systems. The numerical analysis reveals varying critical exponents of the correlation length in DQCPs and the logarithmic scaling in BKTs, respectively. This work offers a promising platform for realizing DQCPs and provides valuable insights into their nature within the framework of topological phase transitions.

cond-mat.str-el↗

arXiv2025

Continuously varying critical exponents in an exactly solvable long-range cluster XY mode

We investigate a generalized antiferromagnetic cluster XY model in a transverse magnetic field, where long-range interactions decay algebraically with distance. This model can be exactly solvable within a free fermion framework. By analyzing the gap, we explicitly derive the critical exponents $ν$ and $z$, finding that the relationship $νz = 1$ still holds. However, the values of $ν$ and $z$ depend on the decaying exponent $α$, in contrast to those for the quantum long-range antiferromagnetic Ising chain. To optimize scaling behavior, we verify these critical exponents using correlation functions and fidelity susceptibility, achieving excellent data collapse across various system sizes by adjusting fitting parameters. Finally, we compute the entanglement entropy at the critical point to determine the central charge $c$, and find it also varies with $α$. This study provides insights into the unique effect of long-range cluster interactions on the critical properties of quantum spin systems.

cond-mat.str-el↗

arXiv2025

Spin-polarized scanning tunneling microscopy measurement scheme for determining the quantum geometric tensor

The quantum geometric tensor (QGT) embodies the geometry of the eigenstates of a system's Hamiltonian, and its full characterization across diverse quantum systems is essential. However, it is challenging to characterize the QGT of solid-state systems. Here we present an electric scheme to measure the complete QGT of two-dimensional solid-state systems by using spin-polarized scanning tunneling microscopy (STM), in which the spin texture is extracted from geometric amplitudes of Friedel oscillations induced by the intentionally introduced magnetic impurity, and then the QGT is derived from the momentum differential of spin texture. As a canonical spin model, the surface states of a topological insulator offer a promising way to demonstrate the scheme. In a slab of topological insulator, the gapped surface states host complete QGT, i.e., nonvanishing quantum metric and Berry curvature as its symmetric real part and the antisymmetric imaginary part. Thus, a detailed derivation guides the use of the developed scheme to measure the QGT of gapped surface states, even with an external magnetic field. This study opens a new avenue to directly measure the complete QGT of two-dimensional solid-state systems by using spin-polarized STM.

cond-mat.mes-hall↗

arXiv2024

Exploring quantum criticality and ergodicity-breaking dynamics in spin-1 Kitaev chains via single-ion anisotropies

We investigate topological gauge-theory terms and quantum criticality in a spin-1 Kitaev chain with general single-ion anisotropies (SIAs). The ground-state phase diagram, including the Kitaev spin liquid (KSL) and gapless dimer phases, is determined by the infinite time evolving block decimation (iTEBD) method. A quantum phase transition between the KSL and dimer phases occurs by varying uniaxial SIA, analogous to the confinement-deconfinement transition in the lattice Schwinger model with a topological $θ$ angle of $π$. Introducing rhombic SIA shifts this angle from $π$, resulting in $y$- and $x$-ferroquadrupole phases. The transition between these phases can occur through a crossover in the KSL phase or a genuine phase transition along a deconfined line. We map the spin-1 Hamiltonian to an effective spin-1/2 PXP Hamiltonian, with uniaxial SIA corresponding to uniform detuning and rhombic SIA to staggered detuning. We explore the hierarchical fragmentation of the Hilbert space, revealing that quantum many-body scars (QMBSs) emerge under weak uniform detuning, while slow dynamics under large staggered detuning is accurately captured by a second-order effective Hamiltonian via the Schrieffer-Wolff transformation. Our work establishes a framework for simulating topological $θ$ angles and ergodicity-breaking dynamics, bridging higher-spin generalizations of scarred models with lattice gauge theories, potentially realizable using state-of-the-art cold-atom quantum simulators.

cond-mat.str-el↗

arXiv2024

Quantum criticality of generalized Aubry-André models with exact mobility edges using fidelity susceptibility

In this study, we explore the quantum critical phenomena in generalized Aubry-André models, with a particular focus on the scaling behavior at various filling states. Our approach involves using quantum fidelity susceptibility to precisely identify the mobility edges in these systems. Through a finite-size scaling analysis of the fidelity susceptibility, we are able to determine both the correlation-length critical exponent and the dynamical critical exponent at the critical point of the generalized Aubry-André model. Based on the Diophantine equation conjecture, we can determines the number of subsequences of the Fibonacci sequence and the corresponding scaling functions for a specific filling fraction, as well as the universality class. Our findings demonstrate the effectiveness of employing the generalized fidelity susceptibility for the analysis of unconventional quantum criticality and the associated universal information of quasiperiodic systems in cutting-edge quantum simulation experiments.

quant-ph↗

arXiv2024

Machine-learning-inspired quantum control in many-body dynamics

Achieving precise preparation of quantum many-body states is crucial for the practical implementation of quantum computation and quantum simulation. However, the inherent challenges posed by unavoidable excitations at critical points during quench processes necessitate careful design of control fields. In this work, we introduce a promising and versatile dynamic control neural network tailored to optimize control fields. We address the problem of suppressing defect density and enhancing cat-state fidelity during the passage across the critical point in the quantum Ising model. Our method facilitates seamless transitions between different objective functions by adjusting the {optimization strategy}. In comparison to gradient-based power-law quench methods, our approach demonstrates significant advantages for both small system sizes and long-term evolutions. We provide a detailed analysis of the specific forms of control fields and summarize common features for experimental implementation. Furthermore, numerical simulations demonstrate the robustness of our proposal against random noise and spin number fluctuations. The optimized defect density and cat-state fidelity exhibit a transition at a critical ratio of the quench duration to the system size, coinciding with the quantum speed limit for quantum evolution.

quant-ph↗

arXiv2024

Optimal Dynamical Gauge in the Quantum Rabi Model

In this paper, we investigate the gauge dependence of various physical observables in the quantum Rabi model (QRM) under different potential fields, arising from the Hilbert-space truncation of the atomic degree of freedom. We discover that in both the square-well potential and oscillator potential,the optimal gauges for the ground-state energy of the QRM vary with respect to the cavity frequency, with the dipole gauge being optimal in the low-frequency limit and the Coulomb gauge in the high-frequency limit of the cavity frequency. Additionally, for higher energy levels, the optimal gauge asymptotically approaches the dipole gauge. However, for the dynamical quantity out-time-order correlator (OTOC), we find the necessity to introduce an optimal dynamical gauge. We determine the optimal dynamical gauge by minimizing the mean error between the two-level OTOC and the full Hamiltonian one. We expect that this study will contribute to a more profound understanding of the subtle relation between gauge choice and the dynamics of QED systems.

quant-ph↗