arXiv subjects

Tian-Cheng Yi

Publications and source records attributed to Tian-Cheng Yi.

At least 19 recordsLinked to original sources

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, $ν\simeq 1$, 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

Many-body mobility edges in one dimension revealed by efficient and interpretable feature-based learning with Kolmogorov-Arnold Networks

We study the many-body localization (MBL) transition in interacting fermionic systems on disordered one-dimensional lattices using a physics-informed machine-learning framework. Instead of feeding full many-body wave functions into the model, we construct a compact feature representation based on four physically motivated observables: the inverse participation ratio, the Shannon entropy, the many-body hybridization parameter, and the mean level-spacing ratio. These quantities capture complementary aspects of localization, entanglement, and spectral correlations, and are used to train a Kolmogorov--Arnold Network (KAN) classifier on eigenstates deep in the weak and strong disorder regimes. The resulting KAN achieves a validation accuracy exceeding $99.9\%$, comparable to that of convolutional neural networks trained directly on high-dimensional wave-function data, while requiring substantially reduced input dimensionality and significantly shorter training time. Applying the trained classifier across the full energy spectrum yields energy-resolved phase diagrams that reveal a clear many-body mobility edge and provide a consistent estimate of the critical disorder strength. The approach is inherently extensible: additional physically relevant observables can be incorporated into the feature space in a systematic manner without altering the overall architecture. Our results demonstrate that feature-based learning with KAN provides an efficient, scalable, and interpretable methodology for identifying many-body localization transitions, offering a practical alternative to raw-data-based neural network approaches.

cond-mat.dis-nn↗

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

Non-Hermitian Haldane-Hubbard model: Effective description of an open system with balanced gain and loss

We study the correlated Haldane-Hubbard model with single-particle gain and loss, focusing on its non-Hermitian phase diagram and the ensuing non-unitary dynamic properties. The interplay of interactions and non-hermiticity results in insulating behavior with a phase diagram divided into three distinct regions, exhibiting either topologically gapped or (real) gapless regimes and a trivial phase. The latter is mapped by the emergence of a local order parameter associated with a charge density wave. A ${\cal PT}$-symmetry breaking at the low-lying spectrum occurs when increasing the gain-loss magnitude at a fixed interaction strength, marking the transition from gapped to gapless topological behavior. Further increase leads to the onset of charge ordering in a first-order phase transition in which level crossing takes place in the spectrum's imaginary part. The support that the staggered gain and loss display to robust charge density wave in equilibrium is confirmed in the real-time dynamics in the presence of non-hermiticity, suggesting that engineered gain and loss can be used to tailor an ordered many-body state in experiments.

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↗

arXiv2024

Bound states in one-dimensional systems with colored noise

We investigate the phase transitions in a one-dimensional system with colored noise. Previous studies indicated that the phase diagram of this system included extended and disorder-induced localized phases. However, by studying the properties of wave functions, we find that this phase diagram can be further refined, revealing the existence of a bound phase for the large potential amplitude $W$ and noise control parameter $α$. In the bound phase, the wave function cannot extend throughout the entire chain, tails decay faster than exponentially and its distribution expands as the system size increases. By adjusting the potential amplitude to induce a transition from the extended phase to the bound phase, we find that bound states coexist with extended states in the spectrum. In contrast, when the system transitions from the Anderson localized phase to the bound phase, we do not observe the obvious coexistence of Anderson localized and bound states. Finally, by performing the time evolution, we find that the dynamic transition point of the bound phase is inconsistent with the static one for large $α$.

cond-mat.dis-nn↗

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

Two-dimensional polarized superfluids under the prism of the fermion sign problem

Understanding if attractive fermions in an unbalanced occupation of its flavors can give rise to a superfluid state in two dimensions (2D), realizing the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state, presents a long-standing question. A limitation on its solution by numerics is posed by the sign problem, which constrains the applicability of quantum Monte Carlo techniques at sufficiently low temperatures and large lattice sizes, where a potential signature of polarized superfluidity would be unambiguous. By using a recently explored argument that the sign problem may be used instead to infer quantum critical behavior, we explore the regime where partial polarization occurs in the phase diagram, further showing that the average sign $\langle {\cal S}\rangle$ of quantum Monte Carlo weights tracks the criticality between balanced (or fully polarized) and polarized phases. Using the attractive Hubbard model with an unbalanced population, our investigation expands the scope of problems in which $\langle {\cal S}\rangle$ can be used for monitoring critical behavior, providing compelling albeit indirect evidence for the robustness of an FFLO phase in 2D.

cond-mat.str-el↗

arXiv2023

Non-Hermitian Haldane-Hubbard model: Effective description of one- and two-body dissipation

Using numerically exact diagonalization, we study the correlated Haldane-Hubbard model in the presence of dissipation. Such dissipation can be modeled at short times by the dynamics governed by an effective non-Hermitian Hamiltonian, of which we present a full characterization. If the dissipation corresponds to a two-body loss, the repulsive interaction of the effective Hamiltonian acquires an imaginary component. A competition between the formation of a charge-ordered Mott insulator state and a topological insulator ensues, but with the non-Hermitian contribution aiding in stabilizing the topologically non-trivial regime, delaying the onset of the formation of a local order parameter. Lastly, we analyze the robustness of the ordered phase by following the full dissipative many-body real-time dynamics. An exponentially fast melting of the charge order occurs, whose characteristic rate is roughly independent of the interaction strength, for the case of one-body dissipation.

cond-mat.str-el↗

arXiv2023

Dimensional crossover on multileg attractive-$U$ Hubbard ladders

We study the ground state properties of a polarized two-component Fermi gas on multileg attractive-$U$ Hubbard ladders. Using exact diagonalization and density matrix renormalization group method simulations, we construct grand canonical phase diagrams for ladder widths of up to $W=5$ and varying perpendicular geometries, characterizing the quasi-one-dimensional regime of the dimensional crossover. We unveil a multicritical point marking the onset of partial polarization in those phase diagrams, a candidate regime of finite-momentum pairing. We compare our findings with recent experimental and theoretical studies of quasi-one-dimensional polarized Fermi gases.

cond-mat.quant-gas↗

arXiv2022

Higher-order topological insulator in a modified Haldane-Hubbard model

We investigate the ground-state phase diagram of a modified spinless Haldane-Hubbard model with broken threefold rotational symmetry, employing exact diagonalization calculations. The interplay of asymmetry, interactions, and topology gives rise to a rich phase diagram. The non-interacting limit of the Hamiltonian exhibits a higher-order topological insulator characterized by the existence of corner modes, in contrast to known chiral edge metallic states of the standard Haldane model. Our investigation demonstrates that these symmetry-protected states are robust to the presence of finite interactions. Furthermore, in certain regimes of parameters, we show that a topological Mott insulator exists in this model, where a non-trivial topological bulk coexists with an interaction-driven charge-density-wave, whose emergence is characterized by a $Z_2$-symmetry breaking within the 3$d$-Ising universality class.

cond-mat.str-el↗

arXiv2022

Exploring unconventional quantum criticality in the p-wave-paired Aubry-André-Harper model

We have investigated scaling properties near the quantum critical point between the extended phase and the critical phase in the Aubry-André-Harper model with p-wave pairing, which have rarely been exploited as most investigations focus on the localization transition from the critical phase to the localized phase. We find that the spectrum averaged entanglement entropy and the generalized fidelity susceptibility act as eminent universal order parameters of the corresponding critical point without gap closing. We introduce a Widom scaling ansatz for these criticality probes to develop a unified theory of critical exponents and scaling functions. We thus extract the correlation-length critical exponent $ν$ and the dynamical exponent $z$ through the finite-size scaling given the system sizes increase in the Fibonacci sequence. The retrieved values of $ν\simeq 1.000$ and $z \simeq 3.610$ indicate that the transition from the extended phase to the critical phase belongs to a different universality class from the localization transition. Our approach sets the stage for exploring the unconventional quantum criticality and the associated universal information of quasiperiodic systems in state-of-the-art quantum simulation experiments.

cond-mat.dis-nn↗

arXiv2022

Characterizing quantum criticality and steered coherence in the XY-Gamma chain

In this paper, we show that an effective spin Hamiltonian with various types of couplings can be engineered using quantum simulators in atomic-molecular-optical laboratories, dubbed the \emph{XY}-Gamma model. We analytically solve the one-dimensional short-range interacting case with the Jordan-Wigner transformation and establish the phase diagram. In the gapless phase, an incommensurate spiral order is manifested by the vector-chiral correlations. Between distinct gapped phases, a logarithmic scaling behavior of local measures, including spin correlations and the steered quantum coherence, is identified for the quantum critical points, yielding a compelling value of the correlation-length critical exponent. We derive explicit scaling forms of the excitation gap near the quantum critical points. The extracted critical exponents reveal the quantum phase transition on the boundary of Tomonaga-Luttinger liquid belongs to Lifshitz universality class.Our results may provide useful insights into the underlying mechanism in quantum criticality for state-of-the-art experiments of quantum simulation.

quant-ph↗

arXiv2022

Exploration of the computational model and the focusing process with a Flat Multi-channel Plate and a Curved Multi-channel Plate in the MATLAB

By simulating the X-ray paths and the Chapman Model of a flat multi-channel plate and a curved multi-channel plate in the MATLAB, the field of view, local reflection efficiency, spherical aberration, point-spread function, collection efficiency of incident X-ray and peak-to-background ratio on the focal plane of the two devices were compared. At the same time, the advantages and disadvantages of the flat multi-channel plate and the curved multi-channel plate were compared.

physics.optics↗

arXiv2022

Theoretical Simulation and Experiment Investigation of X-ray transmission characteristics though Square Polycapillary Slice Lens with quadratic curve

The x-ray polycapillary lens is an optical device with good optic performance. Similar to the traditional X-ray polycapillary lens, square polycapillary slice lens was regulated on X-ray based on the full reflection principle of X-ray in the capillaries surfaces. According to its geometrical structure model and the X-ray tracing principle, a set of X-ray transmission procedures was established. A complete square polycapillary slice lens with quadratic curve was produced and the optical performance was tested

physics.optics↗

arXiv2022

Recent neutron focusing experiments using polycapillary lens in CSNS

Higher neutron current densities can provide convenience for neutron experiments. Using neutron optical focusing elements, large flux beams transported to sample can be achieved. As one kind of focusing elements, polycapillary lens is very suitable for neutron absorption experiments such as PGAA and NDP technology. At present, a Neutron Physics and Application Spectrometer was in construction in CSNS, which is the first pulsed neutron source in China. To provide some suggestions and ideas for the following design of enhanced PGAA or NDP instrument with polycapillary lens in CSNS, a first neutron focusing experiment using polycapillary lens in CSNS was conducted. For 0.5-12.6 polychromatic beam, a focal spot with FWHM of 800 was obtained. As the value of wavelength increased, the beam size, transmission efficiency and gain increased. For cold neutron, the gain maintained in a level of 7.

physics.ins-det↗

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↗

arXiv2021

Hamming Distance and the onset of quantum criticality

Simulating models for quantum correlated matter unveils the inherent limitations of deterministic classical computations. In particular, in the case of quantum Monte Carlo methods, this is manifested by the emergence of negative weight configurations in the sampling, that is, the sign problem (SP). There have been several recent calculations which exploit the SP to locate underlying critical behavior. Here, utilizing a metric that quantifies phase-space ergodicity in such sampling, the Hamming distance, we suggest a significant advance on these ideas to extract the location of quantum critical points in various fermionic models, in spite of the presence of a severe SP. Combined with other methods, exact diagonalization in our case, it elucidates both the nature of the different phases as well as their location, as we demonstrate explicitly for the honeycomb and triangular Hubbard models, in both their U(1) and SU(2) forms. Our approach charts a path to circumvent inherent limitations imposed by the SP, allowing the exploration of the phase diagram of a variety of fermionic quantum models hitherto considered to be impractical via quantum Monte Carlo simulations.

cond-mat.str-el↗