arXiv subjects

Xu-Yang Hou

Publications and source records attributed to Xu-Yang Hou.

At least 19 recordsLinked to original sources

arXiv2026

Torsion-induced gauge structure in curved quantum waveguides

We investigate the effective dynamics of a particle confined near a space curve. In the strict thin-layer reduction of the nondegenerate transverse ground state, torsion does not enter the local effective Hamiltonian, which contains only the curvature-induced scalar geometric potential. In contrast, for a thin guide with finite transverse width, a leading-order adiabatic projection onto the twofold-degenerate first-excited transverse band renders the rotation of the Frenet normal frame dynamically relevant and generates a matrix-valued Abelian gauge potential. Using a projection-based derivation in a co-rotating Frenet-frame basis, we show that this effective gauge potential is directly determined by the local torsion of the curve. The resulting effective Hamiltonian takes a gauge-covariant form and produces two transverse-mode branches whose parabolic dispersions are shifted in opposite directions in momentum space. For closed curves, the associated holonomy is controlled by the integrated torsion and leads to geometric interference. These results provide a direct realization of a Wilczek--Zee-type connection induced purely by spatial geometry in curved quantum waveguides. We further construct a classical-wave analogue using the degenerate bending modes of an isotropic elastic rod, demonstrating that the same torsion-induced gauge structure appears in continuum wave physics.

quant-ph↗

arXiv2026

Theory of the Uhlmann Phase in Quasi-Hermitian Quantum Systems

Geometric phases play a fundamental role in understanding the geometric structure of quantum states, yet extending the Uhlmann phase to non-Hermitian systems poses significant challenges due to parameter-dependent inner product structures. In this work, we develop a comprehensive theory of the Uhlmann phase for quasi-Hermitian systems, where the physical Hilbert space metric varies with external parameters. By constructing a generalized purification that respects the quasi-Hermitian inner product, we derive the corresponding parallel transport condition and Uhlmann connection. Our analysis reveals that the parameter-dependent metric modifies the Uhlmann connection and leads to a finite-temperature distribution of Uhlmann-phase regions that differs from the standard Hermitian case. Applying this formalism to solvable two-level models, we uncover tunable finite-temperature Uhlmann-phase diagrams, where the parameter-dependent metric shifts and deforms the zeros of the Uhlmann amplitude, thereby reshaping the temperature intervals in which nontrivial Uhlmann phases occur. Furthermore, by extending established interferometric protocols originally developed for Hermitian systems, the geometric amplitude can be recast as a measurable Loschmidt amplitude between purified states, providing a practical and experimentally accessible pathway to investigate quasi-Hermitian mixed-state geometric phases and their finite-temperature transitions. This work establishes a unified framework for understanding mixed-state geometric phases in quasi-Hermitian quantum systems and, through its natural relation to the mixed-state quantum geometric tensor, opens new avenues for exploring local geometry in quasi-Hermitian thermal states.

quant-ph↗

arXiv2026

Thermal Suppression of Dynamical Quantum Phase Transitions in Finite-Dimensional Systems A Quasi-Hermitian Framework

We investigate dynamical quantum phase transitions (DQPTs) in finite-dimensional systems prepared in thermal equilibrium states and subjected to a sudden quench. A mixed-state Loschmidt amplitude is constructed from first principles within a metric-stationary pseudo-Hermitian framework, providing a self-contained derivation of the finite-temperature quench dynamics. Applying this framework to an $N$-level model consisting of a two-level sector coupled to $N-2$ spectator states, we find that temperature controls the DQPTs through the redistribution of thermal weights among the eigenstates. This mechanism leads to a dimensionality-dependent threshold temperature that becomes finite when the Hilbert-space dimension reaches five, above which the Loschmidt amplitude loses all real zeros and the DQPTs are fully suppressed. The thermal suppression mechanism suggests a general principle for controlling dynamical criticality through thermal occupation, while the quasi-Hermitian framework provides the self-consistent foundation for its rigorous derivation.

quant-ph↗

arXiv2026

Wilczek-Zee Realization of Uhlmann Parallel Transport

The Uhlmann phase extends geometric phases to mixed quantum states via a parallel-transport condition on purification amplitudes, yet its direct implementation under standard Hamiltonian dynamics is obstructed by the non-Hermitian nature of the purification. We establish that for any smooth one-dimensional closed loop of full-rank qubit density matrices, there exists a four-level Hermitian parent Hamiltonian whose doubly degenerate ground-state subspace carries a Wilczek--Zee connection exactly equal to the Uhlmann connection. Consequently, the Uhlmann holonomy is faithfully reproduced by adiabatic evolution in the enlarged system. We further prove that this auxiliary-field construction is obstructed in generic two-dimensional parameter spaces by a Frobenius integrability condition, which we derive explicitly. The one-dimensional Uhlmann phase is thus placed on the same footing as the non-Abelian Berry phase, offering a purely Hermitian, Hamiltonian-based route to simulating mixed-state geometric phases. Numerical integration of the adiabatic dynamics confirms the exact correspondence and validates the convergence to the Uhlmann holonomy in the large-gap limit.

quant-ph↗

arXiv2026

Electrical-Circuit Simulation of the Uhlmann Phase

The Uhlmann phase extends the concept of geometric phases to mixed quantum states through a parallel-transport condition on purification amplitudes, but its experimental realization has so far required sophisticated quantum platforms with carefully engineered auxiliary degrees of freedom. In this work, we reformulate the Uhlmann parallel-transport condition as a linear matrix differential equation and vectorize it to obtain an effective dynamical generator. This generator can be directly mapped onto the admittance matrix of a classical RC circuit, thereby translating the Uhlmann dynamics into the evolution of circuit node voltages. We illustrate the mapping using the equatorial-loop model and, via a rotating-frame transformation followed by a real decomposition, derive a time-independent, real-valued dynamical system suitable for analog implementation. LTspice simulations of the resulting active RC network faithfully reproduce the Uhlmann geometric phase and its topological transition at the critical purity, demonstrating that classical electrical circuits offer a simple and accessible platform for probing mixed-state geometric phases.

quant-ph↗

arXiv2026

Defect Holonomy Near Rank-Deficient Mixed States

We investigate the geometry of mixed quantum states near rank-changing points, showing that these singularities function as effective geometric defects. The Uhlmann connection is well-defined on the full-rank sector of the density-matrix manifold, while rank-deficient states form singular boundary strata where the bundle structure degenerates. By restricting to a punctured state manifold that excludes the singular set, we obtain a well-defined gauge structure and identify an asymptotically robust invariant: the Uhlmann holonomy around noncontractible loops encircling the defect on a restricted two-dimensional punctured submanifold. In an exactly solvable qutrit model, a restricted submanifold emerges on which the connection is locally flat yet carries nontrivial monodromy, analogous to flat connections with Aharonov--Bohm-type transport. The holonomy depends only on the ratios of the vanishing eigenvalues under frozen radial dependence of the eigenbasis geometry and a fixed angular loop. In contrast, the Uhlmann curvature may diverge path-dependently when eigenvalues shrink with distinct powers, with a leading spectral-prefactor scaling law, establishing that the holonomy survives as a universal asymptotic invariant while the curvature remains non-universal. Within the effective SU(2) defect sector, the conjugacy class of the holonomy, equivalently the Wilson loop variable, provides a continuous, non-quantized classification of the asymptotic monodromy surrounding the rank-deficient defect. This non-quantization does not imply a lack of robustness: the asymptotic holonomy is an invariant of the restricted punctured submanifold and is insensitive to smooth deformations of the loop or the radial profile within the fixed spectral-ratio sector.

quant-ph↗

arXiv2026

Geometry near rank-changing points on the mixed-state manifold: Bures metric, conical singularities, and Lindblad dynamics

We elucidate the Bures metric in quantum state space near a rank-changing point of the density matrix and show contrasting behavior for two-level ($N=2$) systems versus higher-level systems. Due to the smooth pure-state boundary for $N=2$, we prove the apparent metric divergences to be merely coordinate artifacts and present three Lindblad processes exhibiting qualitatively different evolution near rank-changing points, showing geodesic approach, power-law scaling, and pure-state escape law. For higher-dimensional ($N\ge 3$) systems, the geometry near a rank-changing point differs fundamentally. Under suitable restrictions of the density matrix and its approach towards a pure state, the Bures metric reduces to a conical metric with the pure state at the cone tip. Such a conic geometry leads to genuine curvature singularities: A two-dimensional cone exhibits a Dirac delta-function curvature near the tip while a higher-dimensional cone shows a power-law divergence of the curvature towards the cone tip. A construction of Lindblad evolution for $N=3$ systems with conic singularities is presented, along with possible implications for future experimental and theoretical research.

quant-ph↗

arXiv2026

Geometric and Topological Obstructions to Hermitianization in Quasi-Hermitian Quantum Systems

Quasi-Hermitian quantum systems, including $\mathcal{PT}$-symmetric ones, can be mapped to equivalent Hermitian systems via a similarity transformation that redefines the inner product with a positive-definite metric operator. Although an instantaneous algebraic Hermitianization can be obtained locally from a positive metric operator, a stronger requirement is needed for dynamical equivalence: the similarity transformation must be proper, globally single-valued, and compatible with the modified quasi-Hermitian Schrodinger equation. We identify two distinct obstructions: geometric obstructions arising from the curvature of a metric-induced connection, and topological obstructions originating from non-trivial holonomies around non-contractible loops in parameter space. We derive explicit criteria for these obstructions and illustrate them with concrete examples. Our results establish a geometric and topological foundation for the Hermitianization of quasi-Hermitian systems, clarifying when they can be globally reduced to Hermitian ones and when intrinsic non-Hermitian features persist.

quant-ph↗

arXiv2026

Evolution of quantum geometric tensor of 1D periodic systems after a quench

We investigate the post-quench dynamics of the quantum geometric tensor (QGT) of 1D periodic systems with a suddenly changed Hamiltonian. The diagonal component with respect to the crystal momentum gives a metric corresponding to the variance of the time-evolved position, and its coefficient of the quadratic term in time is the group-velocity variance, signaling ballistic wavepacket dispersion. The other diagonal QGT component with respect to time reveals the energy variance. The off-diagonal QGT component features a real part as a covariance and an imaginary part representing a quench-induced curvature. Using the Su-Schrieffer-Heeger (SSH) model as an example, our numerical results of different quenches confirm that the post-quench QGT is governed by physical quantities and local geometric objects from the initial state and post-quench bands, such as the Berry connection, group velocities, and energy variance. Furthermore, the connections between the QGT and physical observables suggest the QGT as a comprehensive probe for nonequilibrium phenomena.

quant-ph↗

arXiv2026

Curvature-driven shifts of the Potts transition on spherical Fibonacci graphs: a graph-convolutional transfer-learning study

We investigate the ferromagnetic $q$-state Potts model on spherical Fibonacci graphs. These graphs are constructed by embedding quasi-uniform sites on a sphere and defining interactions via a chord-distance cutoff chosen to yield a network approximating four-neighbor connectivity. By combining Swendsen-Wang cluster Monte Carlo simulations with graph convolutional networks (GCNs), which operate directly on the adjacency structure and node spins, we develop a unified phase-classification framework applicable to both regular planar lattices and curved, irregular spherical graphs. Benchmarks on planar lattices demonstrate an efficient transfer strategy: after a fixed binarization of Potts spins into an effective Ising variable, a single GCN pretrained on the Ising model can localize the transition region for different $q$ values without retraining. Applying this strategy to spherical graphs, we find that curvature- and defect-induced connectivity irregularities produce only modest shifts in the inferred transition temperatures relative to planar baselines. Further analysis shows that the curvature-induced shift of the critical temperature is most pronounced at small $q$ and diminishes rapidly as $q$ increases; this trend is consistent with the physical picture that, in two dimensions, the Potts model undergoes a transition from a continuous phase transition to a weakly first-order one for $q>4$, accompanied by a pronounced reduction of the correlation length.

cond-mat.stat-mech↗

arXiv2025

Machine learning of the Ising model on a spherical Fibonacci lattice

We investigate the Ising model on a spherical surface, utilizing a Fibonacci lattice to approximate uniform coverage. This setup poses challenges in achieving consistent lattice distribution across the sphere for comparison with planar models. We employ Monte Carlo simulations, principal component analysis (PCA), graph convolutional networks (GCNs) to study spin configurations across a range of temperatures and to determine phase transition temperatures. The Fibonacci lattice, despite its uniformity, contains irregular sites that influence spin behavior. In the ferromagnetic case, sites with fewer neighbors exhibit a higher tendency for spin flips at low temperatures, though this effect weakens as temperature increases, leading to a higher phase transition temperature than in the planar Ising model. In the antiferromagnetic case, lattice irregularities induce geometric frustration, resulting in highly degenerate ground states and the phase transition temperature lower than the planar square lattice. Phase transition temperatures are derived through specific heat, magnetic susceptibility analysis and GCNs predictions, yielding $T_c$ values for both ferromagnetic and antiferromagnetic scenarios. This work emphasizes the impact of the Fibonacci lattice's geometric properties-namely curvature and connectivity-on spin interactions in non-planar systems, with relevance to microgravity environments.

physics.comp-ph↗

arXiv2025

Bound-like State in a 1D Self-Similar Delta-Barrier Array

We investigate a one-dimensional quantum system with a self-similar arrangement of delta-function potential barriers, exhibiting discrete scale invariance. The singular potential induces kinematically enforced symmetry breaking at $x=0$, decoupling the positive and negative spatial regions and leading to non-symmetric zero-energy states. We demonstrate that the system supports a unique zero-energy wavefunction, which, though not square-integrable, decays to zero at infinity and acts as a bound-like state with self-similar properties under discrete scaling transformations, akin to Efimov physics but limited to a single state. In momentum space, this wavefunction exhibits a threshold singularity at low momenta, with behavior depending on the scaling exponent $α$:power-law divergence and log-periodic modulations for $0 < α< 1$, logarithmic divergence for $α= 1$, and a finite limit for $α> 1$, which may be observable through time-of-flight or spectroscopic measurements in cold atom experiments. The system's continuous spectrum, starting at zero energy, lacks discrete bound states. These findings highlight the role of singular potentials in generating scale-invariant quantum phenomena and provide a minimal framework for studying discrete scale symmetry and its potential experimental signatures.

quant-ph↗

arXiv2025

Mixed-state geometric phases of coherent and squeezed spin states

Two mixed-state geometric phases, known as the Uhlmann phase and interferometric geometric phase (IGP), of spin coherent states (CSSs) and spin squeezed states (SSSs) are analyzed. Exact solutions and numerical results of selected examples are presented. For the $j = 3/2$ CSS, the Uhlmann phase exhibits finite-temperature topological phase transitions characterized by abrupt jumps. The IGP for the same state similarly shows discontinuous jumps as the temperature varies. In the case of the $j = 1$ one-axis SSS, both Uhlmann phase and IGP display discrete finite-temperature jumps. By contrast, the $j = 1$ two-axis SSS shows no such transitions because the Uhlmann phase and IGP both vary smoothly with temperature. We also briefly discuss potential realizations and simulations related to these phenomena in spin systems.

quant-ph↗

arXiv2025

Thermal Uhlmann-Chern Number: Bridging Pure and Mixed States

Topological properties of quantum systems at finite temperatures, described by mixed states, pose significant challenges due to the triviality of the Uhlmann bundle. We introduce the thermal Uhlmann-Chern number, a generalization of the Chern number, to characterize the topological properties of mixed states. By inserting the density matrix into the Chern character, we introduce the thermal Uhlmann-Chern number, a generalization of the Chern number that reduces to the pure-state value in the zero-temperature limit and vanishes at infinite temperature, providing a framework to study the temperature-dependent evolution of topological features in mixed states. We provide, for the first time, a rigorous mathematical proof that the first- and higher-order Uhlmann-Chern numbers converge to the corresponding Chern numbers in the zero-temperature limit, differing only by a factor of $1/D$ for $D$-fold degenerate ground states. We demonstrate the utility of this framework through applications to a two-level system, the coherent state model, the 2D Haldane model, and a four-band model, highlighting the temperature-dependent behavior of topological invariants. Our results establish a robust bridge between the topological properties of pure and mixed states, offering new insights into finite-temperature topological phases.

quant-ph↗

arXiv2025

Geometry effect of the dynamical quantum phase transitions at finite temperatures

Dynamical quantum phase transitions (DQPTs) probe the nonequilibrium evolution of quantum systems, unveiling their geometric and topological characteristics. In this study, we introduce the concepts of parallel quench and dynamic geometrical order parameter (DGOP) for non-band models, where these quantities capture the geometric shifts associated with DQPTs. At zero temperature, the DGOP corresponds to the Pancharatnam geometric phase, while at finite temperatures, it extends to the interferometric geometric phase. We further generalize the dynamic topological order parameter (DTOP) to finite-temperature band models, examining its behavior in the Su-Schrieffer-Heeger (SSH) model. Our analysis shows that thermal fluctuations and boundary effects at finite temperatures disrupt the quantization of the DTOP, yet it retains signatures of topological transitions. These findings deepen the understanding of geometric and topological properties in quantum dynamics, illuminating DQPTs across both non-band and band frameworks.

quant-ph↗

arXiv2024

Mathematical Foundation of the U$^N(1)$ Quantum Geometric Tensor

In this paper, we systematically establish the mathematical foundation for the $\text{U}^N(1)$ quantum geometric tensor (QGT) of mixed states Explicitly, we present a description based on the $\text{U}^N(1)$ principal bundle and derive a Pythagorean-like distance decomposition equation. Additionally, we offer a comprehensive comparison of its properties with those of the U(1) principal bundle description of the pure-state QGT. Finally, we prove a fundamental inequality for the $\text{U}^N(1)$ QGT and discuss its physical implication.

math-ph↗

arXiv2024

Uhlmann quench and geometric dynamic quantum phase transition of mixed states

Dynamic quantum phase transitions (DQPT) following quantum quenches exhibit singular behavior of the overlap between the initial and evolved states. Here we present a formalism to incorporate a geometric phase into quench dynamics of mixed quantum states, a process named the Uhlmann quench, based on the Uhlmann parallel transport. To overcome the incompatibility between the Uhlmann parallel-transport condition and Hamiltonian dynamics, we formulate the evolution of purification of the density matrix in a form which not only respects the dynamics according to the density matrix but also follows the Uhlmann parallel-transport condition to generate a geometric phase after a quantum quench. For cyclic processes exemplified by a spin-1/2 system, geometric DQPTs (GDQPTs) can emerge with both singular behavior in the dynamic analogue of the free energy and jumps of the geometric phase. Moreover, the Uhlmann phase reflecting the holonomy is generated at the end of each cycle. The Uhlmann quench thus paves the way for investigating the interplay between quantum dynamics and geometric processes in mixed states.

quant-ph↗

arXiv2024

Local geometry and quantum geometric tensor of mixed states

The quantum geometric tensor (QGT) is a fundamental concept for characterizing the local geometry of quantum states. After casting the geometry of pure quantum states and extracting the QGT, we generalize the geometry to mixed quantum states via the density matrix and its purification. The gauge-invariant QGT of mixed states is derived, whose real and imaginary parts are the Bures metric and the Uhlmann form, respectively. In contrast to the imaginary part of the pure-state QGT that is proportional to the Berry curvature, the Uhlmann form vanishes identically for ordinary physical processes. Moreover, there exists a Pythagorean-like equation that links different local distances and reflect the underlying fibration. The Bures metric of mixed states is shown to reduce to the corresponding Fubini-Study metric of the ground state as temperature approaches zero, establishing a correspondence despite the different underlying fibrations. We also present two examples with contrasting local geometries and discuss experimental implications.

quant-ph↗