arXiv subjects

D. C. Liu

Publications and source records attributed to D. C. Liu.

5 recordsLinked to original sources

arXiv2026

Exact Matching-Polynomial Solution of the Periodic Baxter-Fendley $Z_N$ Clock Chain

The periodic non-Hermitian Baxter-Fendley $Z_N$ clock chain has lacked a complete finite-size spectral solution, whereas its open-chain counterpart admits a solution in terms of independent quasienergies. For the periodic model we show that the operator-valued matching polynomial associated with its cyclic Weyl algebra simultaneously generates a set of conserved quantities, including the Hamiltonian, and realizes a cyclic $\tau^{(2)}$ Yang-Baxter transfer matrix. Root-of-unity closure yields a finite system of polynomial spectral equations in each charge sector, which reproduces the complete finite-size energy spectrum counted with algebraic multiplicity. As a first application of this result, we show that Newton continuation of these equations provides a practical numerical route to the periodic ground-state energy without enumerating the full spectrum. For homogeneous chains the thermodynamic seam response yields a criterion for boundary-induced criticality; for $N=3$ it predicts two reciprocal critical couplings with singular ground-state curvature, in contrast to the single self-dual open boundary critical point.

quant-ph↗

arXiv2026

Exact Solution for Non-Hermitian Free Fermions: A Case Study of the XY Chain

We consider the non-Hermitian XY spin chain with open boundary conditions when the anisotropy parameter is extended to complex values. By analyzing the quasi-Hamiltonian matrix, we demonstrate that the free-fermion structure of the quasi-energy spectrum coincides with that of the Hermitian model and construct the corresponding biorthogonal fermionic basis away from exceptional points (EPs). We make use of an explicit Chebyshev-polynomial representation of the open-boundary eigenvectors in which the quasi-energy $\varepsilon$ is the natural spectral variable. This quasi-energy polynomial form is particularly useful at EPs, because EPs correspond to repeated roots of the same boundary polynomial, making the construction of generalized eigenvectors by $\varepsilon$-differentiation transparent. At EPs, where the quasi-Hamiltonian becomes defective, we derive the Jordan normal form and construct the associated generalized eigenvectors, which yields the correct counting of independent many-body eigenstates. We further show that EPs act as branch points in the complex anisotropy plane, leading to the characteristic permutation of eigenenergies and eigenstates upon encirclement. The branch-cut structure of the biorthogonal eigenstates provides direct evidence for the exchange of eigenstates when an EP is encircled. These results provide an analytically controlled many-body platform for studying EP physics and non-Hermitian topology beyond momentum-space descriptions.

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arXiv2025

Exceptional point rings and $PT$-symmetry in the non-Hermitian XY model

The XY spin chain is a paradigmatic example of a model solved by free fermions, in which the energy eigenspectrum is built from combinations of quasi-energies. In this article we show that by extending the XY model's anisotropy parameter $λ$ to complex values, it is possible for two of the quasi-energies to become degenerate. In the non-Hermitian XY model these quasi-energy degeneracies give rise to exceptional points (EPs) where two of the eigenvalues and their corresponding eigenvectors coalesce. The distinct $λ$ values at which EPs appear form concentric rings in the complex plane which are shown in the infinite system size limit to converge to the unit circle coinciding with the boundary between distinct topological phases. The non-Hermitian model is also seen to possess a line of broken $PT$ symmetry along the pure imaginary $λ$-axis. For finite systems, there are four EP values on this broken $PT$-symmetric line if the system size is a multiple of 4.

quant-ph↗

arXiv2025

Characterizing phase transitions and criticality in non-Hermitian extensions of the XY model

In this work we study non-Hermitian extensions of the paradigmatic spin-1/2 XY chain in a magnetic field. Using the mapping of the model to free fermion form, we provide analytical insights into the energy spectrum of the non-Hermitian model and establish an intrinsic connection between the quasienergies and topological invariants. We also use exact diagonalization as a supplementary method to examine the performance of biorthogonal-based expectation values. Our results confirm that the theoretical analysis is consistent with the numerical results, with the extended phase diagram determined via the analytical solution and the critical behavior of the fidelity and entanglement. The entanglement transition goes hand in hand with the non-Hermitian topological phase transition. Like the Hermitian case, we analyze the critical behavior using finite-size scaling. Our results show that non-Hermiticity can induce the system into a new universality class with unusual critical exponent. We also emphasize the ability of the Loschmidt echo to characterize potential phase transitions and introduce the average of the Loschmidt echo to describe phase transitions in non-Hermitian systems.

quant-ph↗

arXiv2024

Improved scaling of the scrape-off layer particle flux width by the Bayes theorem on EAST

The scaling of scrape-off layer (SOL) power width (λq) is essential for advancing the understanding of particle and heat transport in the SOL. Due to the sparse layout of divertor Langmuir probes (Div-LPs) and probe erosion during long-pulse, high-performance operations on EAST, estimating SOL particle flux width (λjs, used to approximate λq) from the ion saturation current density profile (js) often incurs substantial uncertainty. This study presents a maximum a posteriori (MAP) estimation method based on Bayes' theorem, achieving approximately 30% improvement in fitting accuracy over traditional ordinary least squares. Using this method and the FreeGS equilibrium code, we updated databases from Liu et al., Nucl. Fusion 64 (2024). Revised λjs scalings for L-mode and H-mode in deuterium and helium plasmas demonstrate better regression quality and slightly altered regression results. Unified L-mode and H-mode scalings in deuterium and helium are: λ_js^L = 0.11 L_c^1.06 n_e^0.35 Z^0.32 P_SOL^0.25 p^(-0.26) and λ_js^H = 0.11 L_c^1.28 n_e^0.56 Z^0.36 P_SOL^0.30, where L_c is the average SOL connection length, n_e the line-averaged electron density, Z the charge number, PSOL the power crossing the last closed flux surface, and p the core-averaged plasma pressure. Key findings include: (i) λjs strongly depends on SOL connection length, indicating a machine size dependence absent in the Eich scaling, and (ii) helium λjs is slightly larger than deuterium λjs. Extrapolated scalings suggest λq ~ 6 mm for ITER L-mode (Ip = 12 MA) and ~13 mm for H-mode (Ip = 15 MA).

physics.plasm-ph↗