arXiv subjects

Han-Chuan Kou

Publications and source records attributed to Han-Chuan Kou.

9 recordsLinked to original sources

arXiv2026

Interference of critical dynamics associated with zero modes

We study the interference of critical dynamics associated with zero modes (ICDZM) in the generalized Creutz ladders using closed quench paths that pass through two critical points successively. By reading out the final zero-mode transfer probability, we find rich ICDZM interference patterns dependent on the quench path. In particular, when the closed path links two topologically nontrivial phases, the ICDZM pattern may either vanish or exhibit period doubling. Within the framework of WKB analysis, this phenomenon is well clarified by the interference phase accumulated in the quench procedure. We also demonstrate that the zero-mode transfer probability can be detected by the deviation of the boundary particle number from its initial fractional value, which arises from the blending of bulk modes in the critical dynamics. As an edge defect, the zero-mode transfer probability captures both the ICDZM oscillation and the known anomalous defect production in a non-closed quench path. These results identify ICDZM and the corresponding edge defect as probes for critical dynamics associated with topological zero modes.

quant-ph↗

arXiv2026

Optimized adiabatic-impulse protocol preserving Kibble-Zurek scaling with attenuated anti-Kibble-Zurek behavior

We propose an optimized adiabatic-impulse (OAI) protocol that substantially reduces the evolution time for crossing a quantum phase transition while preserving Kibble-Zurek (KZ) scaling. Near criticality, the control parameter is ramped linearly across the critical point at a rate characterized by a quench time $\tau_Q$. Away from criticality, the evolution remains adiabatic and is tuned close to the threshold of adiabatic breakdown, as quantified by an adiabatic coefficient $\zeta$ that scales as $\tau_Q^\alpha$. As a consequence, the total evolution time exhibits a sublinear power-law dependence on $\tau_Q$, and the conventional linear quench is recovered in the limit $\alpha\rightarrow\infty$. We apply the OAI protocol to the transverse Ising chain and numerically determine the minimal $\zeta$ required for KZ scaling. We further investigate the nonequilibrium dynamics in the presence of a noisy field that can induce anti-Kibble-Zurek (AKZ) behavior. Within the OAI protocol, noise-induced defects is significantly attenuated due to the shorter evolution time. The optimal quench time at which the defect density is minimized obeys an altered universal power-law scaling with the noise strength. Finally, we generalize the OAI protocol to the nonlinear quenches and numerically demonstrate a marked reduction in noise-induced defects.

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arXiv2025

Critical dynamics and its interferometry in the one-dimensional p-wave-paired Aubry-André-Harper model

In this work, we focus on the critical dynamics of the one-dimensional quasiperiodic p-wave-paired Aubry-André-Harper model, which exhibits a transition point between the gapped critical and the gapless localized phases. First, we disclose that the dynamical exponent features two distinct plateaus in the gapless localized phase. Besides the plateau with dynamical exponent $z=1.388$ near the transition point, there is a second one with $z=1$ away from the transition point. Then we demonstrate that these two plateaus intrinsically affect the critical dynamics with moderate quench rate by employing both one-way and round-trip quench protocols. In the one-way quench protocol, we clarify that the Kibble-Zurek (KZ) regime consists of two sub-regimes with different KZ exponents, which is a direct consequence of the two-plateau structure of the dynamical exponent. We also diagnose the KZ, pre-saturated, and saturated regimes by varying the quench rate from slow to fast limits. While, in the round-trip quench protocol, we confirm the interference effect of two critical dynamics and show a narrow neck in the oscillatory density of defects. It turns out that the position of the neck depends on the ratio of to-and-fro quench rates and the p-wave superconductivity pairing amplitude. We show how the position of the neck can be used to quantitatively determine the turning point of the two KZ sub-regimes.

quant-ph↗

arXiv2025

Kibble-Zurek scaling immune to anti-Kibble-Zurek behavior in driven open systems at the limit of loss difference

We investigate the dissipative quench dynamics in a family of two-band fermionic systems by linearly ramping the staggered on-site energy. In the Lindblad formalism, we present an analytical solution in the presence of uniform loss or loss difference on bipartite lattices, which tells that dissipation exponentially suppresses the Kibble-Zurek (KZ) scaling behavior and the quantum jump term of the dissipation is responsible for the anti-KZ (AKZ) behavior. Interestingly, we find two different scaling behaviors at the limit of loss difference. Both scaling behaviors arise from the gapless Liouvillian. But one is accompanied by impulse stage rendered by the criticality of the system, so that it is ascribed to the universal KZ scaling law. Another depends on the dissipation strength and there is no impulse stage in it. We also point out a convenient way to observe the two new scaling behaviors by counting the number of residual particles in the end, since it is immune to the influence of AKZ behavior. We illustrate our findings through the prototypical one-dimensional Rice-Mele model first. Then, in the one-dimensional Shockley model and the two-dimensional Haldane model for Chern insulators, we show that the two scaling behaviors can appear together or separately with appropriate quench protocols.

quant-ph↗

arXiv2023

Varying quench dynamics in the transverse Ising chain: the Kibble-Zurek, saturated, and pre-saturated regimes

According to the Kibble-Zurek mechanism, there is a universal power-law relationship between the defect density and the quench rate during a slow linear quench through a critical point. It is generally accepted that a fast quench results in a deviation from the Kibble-Zurek scaling law and leads to the formation of a saturated plateau in the defect density. By adjusting the quench rate from slow to very fast limits, we observe the varying quench dynamics and identify a pre-saturated regime that lies between the saturated and Kibble-Zurek regimes. This significant result is elucidated through the adiabatic-impulse approximation first, then verified by a rigorous analysis on the transverse Ising chain as well. As we approach the turning point from the saturated to pre-saturated regimes, we notice a change in scaling laws and, with an increase in the initial transverse field, a shrinking of the saturated regime until it disappears. During another turning point from the Kibble-Zurek to pre-saturated regimes, we observe an attenuation of the dephasing effect and a change in the behavior of the kink-kink correlation function from a Gaussian decay to an exponential decay. Finally, the coherent many-body oscillation after quench exhibits different behaviors in the three regimes and shows a significant change of scaling behavior between the S and PS regimes.

quant-ph↗

arXiv2022

Interferometry based on quantum Kibble-Zurek mechanism

We propose an interferometry within the framework of quantum Kibble-Zurek mechanism by exemplifying two prototypical quench protocols, namely the round-trip and quarter-turn ones, on the transverse Ising and quantum $XY$ chains. Each protocol contains two linear ramps that drive the system across quantum critical point twice. The two linear ramps arouse two respective nonadiabatic critical dynamics that are well described by the quantum Kibble-Zurek mechanism. However, in combination, the two critical dynamics can interfere with each other deeply. As an effect of the interference, the dynamical phase is exposed in the final excitation probability, which leads to a quantum coherent many-body oscillation in the density of defects with predictable characteristic period. Thus such an interference is available for direct experimental observations. In the quantum $XY$ model, we show that an interference can also arise from the interplay between two different critical dynamics derived from a critical point and a tricritical point. Furthermore, we demonstrate that the interference influences the dephasing of the excited quasiparticle modes intricately by disclosing a phenomenon of multiple length scales, diagonal and off-diagonal ones, in the defect-defect correlators. It turns out that the dephased result relies on how the diagonal and off-diagonal lengths are modulated by the controllable parameter in a quench protocol.

quant-ph↗

arXiv2021

Quantum cluster kink and ring frustration

In this paper, we work on the pure and mixed cluster models with periodic boundary condition. The first purpose is to establish the concept of quantum cluster kink. We clarify that there are two types of cluster kinks since there are two types of ground states depending on the choice of cluster length, of which the first type exhibits symmetry breaking order and the second one string order. Simple pictures are constructed according to the pure cluster model, which facilitates us to introduce the quantity, cluster kink number. As we demonstrate, cluster kinks deriving from different sources can coexist, compete with each other, and lead to quantum phase transition in a mixed cluster model. The second purpose is to elucidate that the effect of ring frustration can be realized in the cluster model with symmetry breaking order, instead of the one with string order. The reason lies in that ring frustration can induce a huge ground-state degeneracy or a special extended-kink phase with gapless excitations in the former case. And, although ring frustration does not change the phase transition point, it can produce unusual ground state in the extended-kink phase, whose special properties are uncovered by the nonlocal scaling factor in the correlation function and the doubled degeneracies of the eigenvalues of the entanglement spectrum.

cond-mat.str-el↗

arXiv2020

Impurity-driven transitions in frustrated quantum Ising ring

We study the quantum phase transitions driven by a point impurity in a chain seamed with ring frustration. Rich phases and quantum phase transitions are uncovered and characterized by both bulk and impurity correlation functions. Nonlocality of the correlation functions are emphasized in manifesting the novel features in the system. We demonstrate that the long-range correlation function can be factorized into local and nonlocal factors in the thermodynamic limit. The gapless topological extended-kink (TEK) phase is disclosed to exhibit long-range correlation but without long-range order, because its ground state is nondegenerate and thus immune to spontaneous symmetry breaking. This conclusion is also true in the classical impurity limit, which is significantly different from that for the open boundary chain without ring frustration. However, spontaneous symmetry breaking does occur in the gapped kink zero mode (KZM) phase and leads to the antiferromagnetic zero mode (AFZM), in which antiferromagnetic order develops in the bulk while entangled states persists locally around the impurity. And as a new feature of quantum phase transition induced by impurity, the transition from the TEK phase to the KZM-AFZM phase is reflected by a steplike nonlocal factor of the correlation function.

cond-mat.str-el↗

arXiv2019

Quaternary Jordan-Wigner mapping and topological extended-kink phase in the interacting Kitaev ring

On a ring, a single Jordan-Wigner transformation between the Kitaev model and the spin model suffers redundant degrees of freedom. However, we can establish an exact quaternary Jordan-Wigner mapping involving two Kitaev rings and two spin rings with periodic or antiperiodic boundary conditions. This mapping facilitates us to demonstrate exactly how a topological extended-kink (TEK) phase develops in the interacting Kitaev ring with odd number of lattice sites. The emergence of this new phase is attributed to the effect of geometrical ring frustration. Unlike the usual topological phases protected by energy gap in noninteracting systems, the TEK phase is gapless. And because the spectra of low energy excitations are quadratic, the specific heat per site approaches a half of Boltzmann constant near absolute zero temperature. More interestingly, the ground state is unique, immune to spontaneous symmetry breaking. It exhibits a long-range correlation function with a nonlocal factor, but no local order parameter can be defined. As a concomitant effect, a special kind of localized kink zero mode (KZM) takes place if we introduce a type of bond defect. We also show that the KZM is robust against moderate disorders.

cond-mat.str-el↗