arXiv subjects

Gaoyong Sun

Publications and source records attributed to Gaoyong Sun.

At least 19 recordsLinked to original sources

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

Decoding Equilibrium and Dynamical Criticality in the 2D Topological Order

Analytically connecting equilibrium criticality and dynamical quantum phase transitions (DQPTs) under complex driving fields remains a significant challenge, primarily due to the combinatorial complexity of non-local long-range entanglement. Here, we decode this connection in the 2D strongly interacting Wen-plaquette model. By mapping its anyonic excitations to 1D effective dissipative channels, we reveal that microscopic single-particle fidelity zeros exactly reconstruct the macroscopic equilibrium topological phase boundaries. Beyond equilibrium, we demonstrate that during non-unitary quench dynamics, these very same static singularities enforce a momentumspace exclusion against dynamical Fisher zeros. Furthermore, a newly identified dissipation-phase racing mechanism prematurely depletes the decaying mode, suppressing DQPTs and generating topologically trivial steady states. Our results establish exact microscopic static singularities as an analytical decoder for macroscopic non-unitary topological dynamics involving discrete symmetry breaking.

cond-mat.str-el↗

arXiv2025

Non-Hermitian symmetry breaking and Lee-Yang theory for quantum XYZ and clock models

Lee-Yang theory offers a unifying framework for understanding classical phase transitions and dynamical quantum phase transitions through the analysis of partition functions and Loschmidt echoes. Recently, this framework is extended to characterize quantum phase transitions of quantum Ising models by introducing the concepts of non-Hermitian parity-symmetry breaking and fidelity zeros. Here, we generalize the theory by studying a broad class of quantum models, including the XY, the XXZ, the XYZ, and the $\mathbb{Z}_p$ clock models in one dimension, subject to a complex magnetic field. For the XY, XXZ and XYZ models, we find that the complex field breaks parity symmetry and induces oscillations of the ground state between the two parity sectors, giving rise to fidelity zeros within the ordered phases. For the $\mathbb{Z}_3$ clock model, the complex field splits the real part of the ground-state energy between the neutral sector ($q=0$) and the charged sectors ($q=1,2$), while preserving the degeneracy within the charged sector. Fidelity zeros arise only after projecting out one of the charged sectors. For the $\mathbb{Z}_4$ and $\mathbb{Z}_5$ clock models, the ground states are instead projected to oscillate between the neutral sector ($q=0$) and the charged sectors $q=2$ and $q=1$, respectively, giving rise to fidelity zeros. Finite-size scaling of these zeros yields critical exponents in full agreement with analytical predictions, demonstrating that this approach is applicable not only to the Ising model with $\mathbb{Z}_2$ symmetry, but also to more general Heisenberg-type models and systems with higher discrete symmetries.

quant-ph↗

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

Fidelity zeros and Lee-Yang theory of quantum phase transitions

Lee-Yang theory is central to the analysis of thermal phase transitions. However, the underlying mechanism of the theory and the nature of Lee-Yang zeros in quantum many-body systems remains elusive. Here, we develop a unified framework for understanding quantum phase transitions from fidelity zeros induced by symmetry breaking. These zeros, arising from transitions between symmetry sectors, obey the Lee-Yang theorem and give rise to fidelity edges near critical points. Quantum criticality is further characterized through the finite-size scaling of fidelity zeros. As concrete examples, we analytically and numerically investigate fidelity zeros in one- and two-dimensional ferromagnetic Ising models under a complex magnetic field. Our results provide new insights into the mechanism of Lee-Yang theory and open avenues for exploring unexplored landscapes of phase transitions in quantum many-body systems.

quant-ph↗

arXiv2024

Dynamical signatures of the Yang-Lee edge singularity in non-Hermitian systems

The Yang-Lee edge singularity is an intriguing critical phenomenon characterized by nonunitary field theory. However, its experimental realization for interacting many-body systems remains elusive. We show that Yang-Lee edge singularities, regarded as many-body exceptional points, can be observed using both the self-normal and the associated-biorthogonal Loschmidt echoes, leveraging the advantages of nonunitary dynamics in non-Hermitian systems. The Loschmidt echoes are demonstrated to display unitary dynamics in the $\mathcal{PT}$-symmetric regime but exhibit nonunitary dynamics in the $\mathcal{PT}$ symmetry-broken regime, leading to a sharp change near an exceptional point. We hereby identify exceptional points in both the non-Hermitian transverse field Ising model and the Yang-Lee model, and determine the critical exponent that is consistent with nonunitary conformal field theory. This work provides a direct observation of Yang-Lee edge singularities in non-Hermitian many-body systems arising from nonunitary dynamics.

cond-mat.quant-gas↗

arXiv2024

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↗

arXiv2024

Fidelity and criticality in the nonreciprocal Aubry-Andr{\'e}-Harper model

We study the critical behaviors of the ground and first excited states in the one-dimensional nonreciprocal Aubry-Andr{\'e}-Harper model using both the self-normal and biorthogonal fidelity susceptibilities. We demonstrate that fidelity susceptibility serves as a probe for the phase transition in the nonreciprocal AAH model. For ground states, characterized by real eigenenergies across the entire regime, both fidelity susceptibilities near the critical points scale as $N^{2}$, akin to the Hermitian AAH model. However, for the first-excited states, the fidelity susceptibilities exhibit distinct scaling laws, contingent upon whether the lattice consists of even or odd sites. For even lattices, both the self-normal and biorthogonal fidelity susceptibilities near the critical points continue to scale as $N^{2}$. In contrast, for odd lattices, the biorthogonal fidelity susceptibilities diverge, while the self-normal fidelity susceptibilities exhibit linear behavior, indicating a novel scaling law.

cond-mat.dis-nn↗

arXiv2024

Many-body entanglement and spectral clusters in the extended hard-core bosonic Hatano-Nelson model

We study many-body entanglements and spectra of the extended bosonic Hatano-Nelson model in the hard-core limit. We show that the system undergoes a phase transition from a gapless phase to a charge density wave phase accompanied by a $\mathcal{PT}$ transition in the first excited state. The phase transition is characterized by the crossing of the ground-state biorthogonal order parameter and the sudden change of the first excited-state entanglement entropy. The gapless phase is verified by the logarithmic scaling of the ground-state entanglement entropy with the central charge $c=1$. Furthermore, we show that all energy spectral clusters would form ellipses in strong nearest-neighbor interactions, for which we establish a universal scaling law. The lengths of the major and minor axes are shown to obey power laws with respect to the nearest-neighbor interaction. The exact expressions are derived for the numbers of energy levels on the outermost elliptic ring of each clusters.

cond-mat.str-el↗

arXiv2023

Many-body phase transitions in a non-Hermitian Ising chain

We study many-body phase transitions in a one-dimensional ferromagnetic transversed field Ising model with an imaginary field and show that the system exhibits three phase transitions: one second-order phase transition and two $\mathcal{PT}$ phase transitions. The second-order phase transition occurring in the ground state is investigated via biorthogonal and self-normal entanglement entropy, for which we develop an approach to perform finite-size scaling theory to extract the central charge for small systems. Compared with the second-order phase transition, the first $\mathcal{PT}$ transition is characterized by the appearance of an exceptional point in the full energy spectrum, while the second $\mathcal{PT}$ transition only occurs in specific excited states. Furthermore, we interestingly show that both of exceptional points are second-order in terms of scalings of imaginary parts of the energy. This work provides an exact solution for many-body phase transitions in non-Hermitian systems.

cond-mat.str-el↗

arXiv2023

Aufbau Principle for Non-Hermitian Systems

We develop a generalized Aufbau principle for non-Hermitian systems that allows for building up the configurations of indistinguishable particles. The Aufbau rule of non-Hermitian systems is unexpectedly shown to be identical to that developed in Hermitian systems when the real parts of the complex energy levels are considered. We derive full many-body energy spectra of the fermionic and bosonic Hatano-Nelson models as examples by filling single-particle energy levels in the momentum space. For open boundary conditions, we show that many-body non-Hermitian skin effects persist in all many-body eigenstates for both fermions and bosons. Furthermore, we find surprisingly that the ground state of bosons is an anomalous Bose-Einstein condensation with all of the particles simultaneously localizing in both the real and momentum space beyond the Heisenberg uncertainty principle. For periodic boundary conditions, we show that hard-core bosons cannot be mapped to fermions. This work establishes a general framework for understanding the many-body physics of non-Hermitian systems, revealing rich unique non-Hermitian many-body physics.

quant-ph↗

arXiv2023

Dynamical scaling laws in the quantum $q$-state clock chain

We show that phase transitions in the quantum $q$-state clock model for $q \leq 4$ can be characterized by an enhanced decay behavior of the Loschmidt echo via a small quench. The quantum criticality of the quantum $q$-state clock model is numerically investigated by the finite-size scaling of the first minimum of the Loschmidt echo and the short-time average of the rate function. The equilibrium correlation-length critical exponents are obtained from the scaling laws which are consistent with previous results. Furthermore, we study dynamical quantum phase transitions by analyzing the Loschmidt echo and the order parameter for any $q$ upon a big quench. For $q \leq 4$, we show that dynamical quantum phase transitions can be described by the Loschmidt echo and the zeros of the order parameter. In particular, we find the rate function increases logarithmically with $q$ at the first critical time. However, for $q > 4$, we find that the correspondence between the singularities of the Loschmidt echo and the zeros of the order parameter no longer exists. Instead, we find that the Loschmidt echo near its first minimum converges, while the order parameter at its first zero increases linearly with $q$.

cond-mat.str-el↗

arXiv2023

Biorthogonal quantum criticality in non-Hermitian many-body systems

We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.

cond-mat.str-el↗

arXiv2023

Dynamical scaling of Loschmidt echo in non-Hermitian systems

We show that non-Hermitian biorthogonal many-body phase transitions can be characterized by the enhanced decay of Loschmidt echo. The quantum criticality is numerically investigated in a non-Hermitian transverse field Ising model by performing the finite-size dynamical scaling of Loschmidt echo. We determine the equilibrium correlation length critical exponents that are consistent with previous results from the exact diagonalization. More importantly, we introduce a simple method to detect quantum phase transitions with the short-time average of rate function motivated by the critically enhanced decay behavior of Loschmidt echo. Our studies show how to detect equilibrium many-body phase transitions with biorthogonal Loschmidt echo that can be observed in future experiments via quantum dynamics after a quench.

cond-mat.str-el↗

arXiv2022

Quantum criticality in interacting bosonic Kitaev-Hubbard models

Motivated by recent work on the non-Hermitian skin effect in the bosonic Kitaev-Majorana model, we study the quantum criticality of interacting bosonic Kitaev-Hubbard models on a chain and a two-leg ladder. In the hard-core limit, we show exactly that the non-Hermitian skin effect disappears via a transformation from hard-core bosonic models to spin-1/2 models. We also show that hard-core bosons can engineer the Kitaev interaction, the Dzyaloshinskii-Moriya interaction and the compass interaction in the presence of the complex hopping and pairing terms. Importantly, quantum criticalities of the chain with a three-body constraint and unconstrained soft-core bosons are investigated by the density matrix renormalization group method. This work reveals the effect of many-body interactions on the non-Hermitian skin effect and highlights the power of bosons with pairing terms as a probe for the engineering of interesting models and quantum phase transitions.

cond-mat.quant-gas↗

arXiv2022

Quantum Many-Body Scars in Spin-1 Kitaev Chains

To provide a physical example of quantum scars, we study the many-body scars in the spin-1 Kitaev chain where the so-called PXP Hamiltonian is exactly embedded in the spectra. Regarding the conserved quantities, the Hilbert space is fragmented into disconnected subspaces and we explore the associated constrained dynamics. The continuous revivals of the fidelity and the entanglement entropy when the initial state is prepared in $\vert\mathbb{Z}_k\rangle$ ($k=2,3$) state illustrate the essential physics of the PXP model. We study the quantum phase transitions in the one-dimensional spin-1 Kitaev-Heisenberg model using the density-matrix renormalization group and Lanczos exact diagonalization methods, and determine the phase diagram. We parametrize the two terms in the Hamiltonian by the angle $ϕ$, where the Kitaev term is $K\equiv\sin(ϕ)$ and competes with the Heisenberg $J\equiv\cos(ϕ)$ term. One finds a rich ground state phase diagram as a function of the angle $ϕ$. Depending on the ratio $K/J\equiv\tan(ϕ)$, the system either breaks the symmetry to one of distinct symmetry broken phases, or preserves the symmetry in a quantum spin liquid phase with frustrated interactions. We find that the scarred state is stable for perturbations which obey $\mathbb{Z}_2$-symmetry, while it becomes unstable against Heisenberg-type perturbations.\\ \textit{Accepted for publication in Physical Review Research}

cond-mat.str-el↗

arXiv2022

Quantum criticality and universality in the $p$-wave paired Aubry-André-Harper model

We investigate the quantum criticality and universality in Aubry-André-Harper (AAH) model with $p$-wave superconducting pairing $Δ$ in terms of the generalized fidelity susceptibility (GFS). We show that the higher-order GFS is more efficient in spotlighting the critical points than lower-order ones, and thus the enhanced sensitivity is propitious for extracting the associated universal information from the finite-size scaling in quasiperiodic systems. The GFS obeys power-law scaling for localization transitions and thus scaling properties of the GFS provide compelling values of critical exponents. Specifically, we demonstrate that the fixed modulation phase $ϕ=π$ alleviates the odd-even effect of scaling functions across the Aubry-André transition with $Δ=0$, while the scaling functions for odd and even numbers of system sizes with a finite $Δ$ cannot coincide irrespective of the value of $ϕ$. A thorough numerical analysis with odd number of system sizes reveals the correlation-length exponent $ν\simeq 1.000$ and the dynamical exponent $z$ $\simeq$ 1.388 for transitions from the critical phase to the localized phase,suggesting the unusual universality class of localization transitions in the AAH model with a finite $p$-wave superconducting pairing lies in a different universality class from the Aubry-André transition. The results may be testified in near term state-of-the-art experimental settings.

cond-mat.dis-nn↗