arXiv subjects

Chun-Yen Lin

Publications and source records attributed to Chun-Yen Lin.

16 recordsLinked to original sources

arXiv2026

First-principle evolution Hamiltonian operator: derivation from ADM quantum constraints and quantum reference-frame conditions

For any Dirac theory of quantum gravity governed by a set of well-defined quantum constraints, we discover a universal formula for the exact form of the evolution Hamiltonian operator in a variable quantum reference frame of our construction, expressed in terms of the quantum-constraint operators and frame-condition operators as the only inputs. Due to the first-principle nature of the formula, the evolution Hamiltonian operator contains the full interactions encoded in the quantum constraints, and it generates the Schr\"odinger evolution described by the genuine quantum relational observables associated to the frame and acting in the physical Hilbert space solving the quantum constraints.

gr-qc↗

arXiv2026

Anisotropic magnetoresistance and magnetic field-tunable Weyl nodes in Weyl metal SrRuO$_{3}$ thin films

Weyl semimetals are a unique class of topological materials, possessing Fermi-arc surface states and exhibiting the chiral anomaly effect. The chiral anomaly refers to non-equilibrium charge transfer within a Weyl-node pair of opposite chirality under the condition of aligned electric and magnetic fields ($\bf{E} \parallel \bf{B}$), leading to non-conserved chiral charges and thus enhanced electrical conductivity. In experiments, such an enhanced conductivity due to the chiral anomaly manifests as a negative longitudinal magnetoresistance (MR) when the external field $\bf{H}$ is applied along the bias current direction $\bf{I}$. In this work, we present rigorous $\phi$- and $\alpha$-dependent magnetotransport measurements to investigate such a negative longitudinal MR due to the chiral anomaly in a sunbeam-shaped device fabricated from an untwinned Weyl metal SrRuO$_{3}$ (SRO) thin film. Here, $\phi$($\alpha$) represents the angle between $\bf{I}$ and the in-plane $\bf{H}$(SRO monoclinic [001]$_{\rm o}$). Unusual $\phi$ dependences of in-plane MR and Hall effects were uncovered at low temperatures, accompanied by the emergence of the fourfold-symmetric component in the in-plane MR. These results indicate that the chiral anomaly and resistivity anisotropy in SRO play important roles. In particular, the dramatic variation of Weyl nodes near the Fermi level through magnetic field manipulation of the magnetization orientation, as revealed by band structure calculations, is consistent with the observed in-plane MR and Hall effect.

cond-mat.other↗

arXiv2024

Nonlinear and nonreciprocal transport effects in untwinned thin films of ferromagnetic Weyl metal SrRuO$_3$

The identification of distinct charge transport features, deriving from nontrivial bulk band and surface states, has been a challenging subject in the field of topological systems. In topological Dirac and Weyl semimetals, nontrivial conical bands with Fermi-arc surface states give rise to negative longitudinal magnetoresistance due to chiral anomaly effect and unusual thickness dependent quantum oscillation from Weyl-orbit effect, which were demonstrated recently in experiments. In this work, we report the experimental observations of large nonlinear and nonreciprocal transport effects for both longitudinal and transverse channels in an untwinned Weyl metal of SrRuO$_3$ thin film grown on a SrTiO$_{3}$ substrate. From rigorous measurements with bias current applied along various directions with respect to the crystalline principal axes, the magnitude of nonlinear Hall signals from the transverse channel exhibits a simple sin$α$ dependence at low temperatures, where $α$ is the angle between bias current direction and orthorhombic [001]$_{\rm o}$, reaching a maximum when current is along orthorhombic [1-10]$_{\rm o}$. On the contrary, the magnitude of nonlinear and nonreciprocal signals in the longitudinal channel attains a maximum for bias current along [001]$_{\rm o}$, and it vanishes for bias current along [1-10]$_{\rm o}$. The observed $α$-dependent nonlinear and nonreciprocal signals in longitudinal and transverse channels reveal a magnetic Weyl phase with an effective Berry curvature dipole along [1-10]$_{\rm o}$ from surface states, accompanied by 1D chiral edge modes along [001]$_{\rm o}$.

cond-mat.mes-hall↗

arXiv2023

Conformally Invariant Brans-Dicke Loop Quantum Cosmology: A Quantum Geometric Model of Linking Theory

The loop quantization of the conformal Brans-Dicke cosmology is explored in the spatially flat and Bianchi-I setting. The scalar and conformal constraints governing the canonical model are quantized using the loop techniques. The physical Hilbert space of quantum spacetimes satisfying both quantum constraints is then obtained by incorporating the quantum geometric features. The Schrödinger cosmic evolutions are derived with the relational Heisenberg observables describing the dynamical degrees of freedom with respect to the chosen reference degrees of freedom, with the latter providing the physical coordinates for the spatial hypersurfaces and the conformal scales. We show that the emerging Schrödinger theories contain not only the loop quantum cosmology of GR, but also that of the so-called shape dynamics. The exact dictionary between the two theories is achieved via the underlying physical Hilbert space possessing the additional (loop-corrected) conformal symmetry.

gr-qc↗

arXiv2022

The weak coupling theory of all dimensional loop quantum gravity

The weak coupling loop quantum theory with Abelian gauge group provides us a new perspective to study the weak coupling properties of LQG. In this paper, the weak coupling theory of all dimensional loop quantum gravity is established based on a symplectic-morphism between the $SO(D+1)$ holonomy-flux phase space and the $U(1)^{\frac{D(D+1)}{2}}$ holonomy-flux phase space. More explicitly, the Gaussian, simplicity, diffeomorphism and scalar constraint operators in $SO(D+1)$ loop quantum gravity will be generalized to the $U(1)^{\frac{D(D+1)}{2}}$ loop quantum theory based on the symplectic-morphism, and the $U(1)^{\frac{D(D+1)}{2}}$ loop quantum theory equipped with these constraint operators gives the weak coupling $U(1)^{\frac{D(D+1)}{2}}$ loop quantum gravity, with the corresponding Hilbert space is composed by the $U(1)^{\frac{D(D+1)}{2}}$ heat-kernel coherent states which are peaked at the weak coupling region of the $U(1)^{\frac{D(D+1)}{2}}$ holonomy-flux phase space.

gr-qc↗

arXiv2022

The thickness dependence of quantum oscillations in ferromagnetic Weyl metal SrRuO$_{3}$

Quantum oscillations in resistivity and magnetization at high magnetic fields are a macroscopic fingerprint of the energy quantization due to the cyclotron motion of quasiparticles. In a thin Weyl semimetal, a unique thickness dependent Weyl-orbit quantum oscillation was proposed to exist, originating from a nonlocal cyclotron orbit via the electron tunneling between the top and bottom Fermi-arc surface states. Here, untwinned and high crystalline Weyl metal SrRuO$_3$ thin films with different thicknesses were grown on miscut SrTiO$_3$ (001) substrates. Magneto-transport measurements were carried out in magnetic fields up to 35 T, and quantum oscillations with different frequencies were observed and compared to the calculated band structure. In particular, we discovered a frequency $F \approx$ 30 T at low temperatures and above 3 T that corresponds to a small Fermi pocket with a light effective mass. Its oscillation amplitude appears to be at maximum for film thicknesses in a range of 10 to 20 nm, and the phase of the oscillation exhibits a systematic change with the film thickness. After isolating the well separated frequencies, the constructed Landau fan diagram shows an unusual concave downward curvature in the 1/$μ_0H_n$-$n$ curve, where $n$ is the Landau level index. Based on the rigorous analysis of the thickness and field-orientation dependence of the quantum oscillations, the oscillation with $F \approx$ 30 T is attributed to be of surface origin, which is related to the Fermi-arc surface state originating from non-overlapping Weyl nodes projected on the film's surface plane. Those findings can be understood within the framework of the Weyl-orbit quantum oscillation effect with non-adiabatic corrections.

cond-mat.mes-hall↗

arXiv2021

High-sensitivity of initial SrO growth on the residual resistivity in epitaxial thin films of SrRuO$_3$ on SrTiO$_3$ (001)

The growth of SrRuO$_3$ (SRO) thin film with high-crystallinity and low residual resistivity (RR) is essential to explore its intrinsic properties. Here, utilizing the adsorption-controlled growth technique, the growth condition of initial SrO layer on TiO$_2$-terminated SrTiO$_3$ (STO) (001) substrate was found to be crucial for achieving a low RR in the resulting SRO film grown afterward. The optimized initial SrO layer shows a $c$(2 x 2) superstructure that was characterized by electron diffraction, and a series of SRO films with different thicknesses ($t$s) were then grown. The resulting SRO films exhibit excellent crystallinity with orthorhombic-phase down to $t \approx$ 4.3 nm, which was confirmed by high resolution X-ray measurements. From azimuthal X-ray scan for SRO orthorhombic (021) reflection, we uncover four structural domains with a dominant domain of orthorhombic SRO [001] along cubic STO [010] direction. The dominant domain population depends on $t$, STO miscut angle ($α$), and miscut direction ($β$), giving a volume fraction of about 92 $\%$ for $t \approx$ 26.6 nm and ($α$, $β$) ~ (0.14$^{\rm o}$, 5$^{\rm o}$). On the other hand, metallic and ferromagnetic properties were well preserved down to $t \approx$ 1.2 nm. Residual resistivity ratio (RRR = $ρ$(300 K)/$ρ$(5 K)) reduces from 77.1 for $t \approx$ 28.5 nm to 2.5 for $t \approx$ 1.2 nm, while $ρ$(5 K) increases from 2.5 $μΩ$cm for $t \approx$ 28.5 nm to 131.0 $μΩ$cm for $t \approx$ 1.2 nm. The ferromagnetic onset temperature ($T_c\prime$) of around 151 K remains nearly unchanged down to $t \approx$ 9.0 nm and decreases to 90 K for $t \approx$ 1.2 nm. Our finding thus provides a practical guideline to achieve high crystallinity and low RR in ultra-thin SRO films by simply adjusting the growth of initial SrO layer.

cond-mat.mtrl-sci↗

arXiv2020

Geometric parametrization of $SO(D+1)$ phase space of all dimensional loop quantum gravity

To clarify the geometric information encoded in the $SO(D+1)$ spin-network states for the higher dimensional loop quantum gravity, we generalize the twisted-geometry parametrization of the $SU(2)$ phase space for $(1+3)$ dimensional loop quantum gravity to that of the $SO(D+1)$ phase space for the all-dimensional case. The Poisson structure in terms of the twisted geometric variables suggests a new gauge reduction procedure, with respect to the discretized Gaussian and simplicity constraints governing the kinematics of the theory. Endowed with the geometric meaning via the parametrization, our reduction procedure serves to identify proper gauge freedom associated with the anomalous discretized simplicity constraints and subsequently leads to the desired classical state space of the (twisted) discrete ADM data.

gr-qc↗

arXiv2019

Coherent intertwiner solution of simplicity constraint in all dimensional loop quantum gravity

We propose a new treatment of the quantum simplicity constraints appearing in the general ${SO(D+1)}$ formulation of loop quantum gravity for the ${(1+D)}$-dimensional space-time. Instead of strongly imposing the constraints, we construct a specific form of weak solutions by employing the spin net-work states with specific ${SO(D+1)}$ coherent intertwiners. These states weakly satisfy the quantum simplicity constraint via the vanishing expectation values, and the quantum Gaussian constraints can be imposed strongly. Remarkably, those specific ${SO(D+1)}$ coherent intertwiners used to construct our solutions have natural interpretations of the $D$-dimensional polytopes, commonly viewed as basic units of the discrete spatial geometry. Therefore, while the strong imposition of the quantum simplicity constraints leads to an over-constrained solution space, our weak solution space for the constraints may contain the correct semiclassical degrees of freedom for intrinsic geometry of the spatial hypersurfaces. Moreover, some concrete relations are established between our construction and other existing approaches in solving the simplicity constraints in all dimensional loop quantum gravity, providing valuable insights into this unresolved important issue.

gr-qc↗

arXiv2018

Quantum Reference Frames via Transition Amplitudes in Timeless Quantum Gravity

We propose an algorithm of extracting Schrödinger theories under all viable physical time from the Einstein-Hilbert path integral, formulated as the timeless transition amplitudes $\hat{\mathbb{P}}:\mathbb{K} \to \mathbb{K}^*$ between the boundary states in a kinematic Hilbert space $\mathbb{K}$. Each of these Schrödinger theories refers to a certain set of quantum degrees of freedom in $\mathbb{K}$ as a background, with their given values specifying moments of the physical time. Restricted to these specified background values, the relevant elements of $\hat{\mathbb{P}}$ are transformed by the algorithm into the unitary propagator of a corresponding reduced phase space Schrödinger theory. The algorithm embodies the fundamental principle of quantum Cauchy surfaces, such that all the derived Schrödinger theories emerge from one timeless canonical theory defined by $\hat{\mathbb{P}}$ as a rigging map, via the relational Dirac observables referring to the corresponding backgrounds. We demonstrate its application to a FRW loop quantum cosmological model with a massless Klein-Gordon scalar field. Recovering the famous singularity-free quantum gravitational dynamics with the background of the scalar field, we also obtain in another reference frame a modified Klein-Gordon field quantum dynamics with the background of the spatial (quantum) geometry.

gr-qc↗

arXiv2017

Exploring the Tomlin-Varadarajan quantum constraints in $U(1)^3$ loop quantum gravity: solutions and the Minkowski theorem

We explicitly solved the anomaly-free quantum constraints proposed by Tomlin and Varadarajan for the weak Euclidean model of canonical loop quantum gravity, in a large subspace of the model's kinematic Hilbert space which is the space of the charge network states. In doing so, we first identified the subspace on which each of the constraints acts convergingly, and then by explicitly evaluating such actions we found the complete set of the solutions in the identified subspace. We showed that the space of solutions consists of two classes of states, with the first class having a property that involves the condition known from the Minkowski theorem on polyhedra, and the second class satisfying a weaker form of the spatial diffeomorphism invariance.

gr-qc↗

arXiv2015

Quantum Cauchy Surfaces in Canonical Quantum Gravity

For a Dirac theory of quantum gravity obtained from the refined algebraic quantization procedure, we propose a quantum notion of Cauchy surfaces. In such a theory, there is a kernel projector for the quantized scalar and momentum constraints, which maps the kinematic Hilbert space $\mathbb K$ into the physical Hilbert space $\mathbb H$. Under this projection, a quantum Cauchy surface isomorphically represents $\mathbb H$ with a kinematic subspace $\mathbb V \subset\mathbb K$. The isomorphism induces the complete sets of Dirac observables in $\mathbb D$, which faithfully represent the corresponding complete sets of self-adjoint operators in $\mathbb V$. Due to the constraints, a specific subset of the observables would be "frozen" as number operators, providing a background physical time for the rest of the observables. Therefore, a proper foliation with the quantum Cauchy surfaces may provide an observer frame describing the physical states of spacetimes in a Schrödinger picture, with the evolutions under a specific physical background. A simple model will be supplied as an initiative trial.

gr-qc↗

arXiv2014

Larmor precession of the octet baryons in view of the general QCD parametrization

We apply general QCD parametrization to describe an octet baryon at rest in a static and uniform magnetic field, in order to demonstrate a dynamical implementation of the hadron model. The derived evolution has the asymptote of Larmor precession, governed by an effective magnetic dipole moment coupling. The parameters appear in the effective magnetic dipole moment has been studied in the original works in kinematic settings. Here we show that the parameters have actual dynamical meaning, and are indeed measured by the process.

nucl-th↗

arXiv2011

Emergence of General Relativity from Loop Quantum Gravity: A Summary

A model is proposed to demonstrate that classical general relativity can emerge from loop quantum gravity, in a relational description of gravitational field in terms of the coordinates given by matter. Local Dirac observables and coherent states are defined to explore physical content of the model. Expectation values of commutators between the observables for the coherent states recover the four-dimensional diffeomorphism algebra and the large-scale dynamics of the gravitational field relative to the matter coordinates. Both results conform with general relativity up to calculable corrections near singularities.

gr-qc↗

arXiv2011

Emergence of Loop Quantum Cosmology from Loop Quantum Gravity: Lowest Order in h

To derive loop quantum cosmology from loop quantum gravity, I apply the model given in \cite{lin1} to a system with coupled gravitational and matter fields. The matter sector consists of a scalar field $phi$ serving as a cosmological clock, and other fields ${psi}$ providing physical spatial coordinates and frames. The physical Hilbert space of the model is constructed from the kinematical Hilbert space of loop quantum gravity, and the local observables in the physical Hilbert space are constructed using the matter coordinates and frames. A specific coherent physical state is then chosen, whose expectation values of the local observables give rise to homogeneous, isotropic and spatially flat gravitational and $phi$ fields at a late clock time. The equations governing these fields may be derived using the symmetry of the physical Hilbert space. When the matter back reactions from ${psi}$ are negligible, the result gives a specific loop quantum cosmological model in the $O(hbar^0)$ approximation, with calculable higher order corrections.

gr-qc↗

arXiv2011

Emergence of General Relativity from Loop Quantum Gravity

A model is proposed to demonstrate that classical general relativity can emerge from loop quantum gravity, in a relational description of gravitational field in terms of coordinates given by matter. Local Dirac observables and coherent states are defined to explore physical content of the model. Expectation values of commutators between the observables for the coherent states recover the four-dimensional diffeomorphism algebra and the large-scale dynamics of the gravitational field relative to the matter coordinates. Both results conform with general relativity up to calculable corrections near singularities.

gr-qc↗