arXiv subjects

Ming-Chien Hsu

Publications and source records attributed to Ming-Chien Hsu.

13 recordsLinked to original sources

arXiv2023

A Gell-Mann & Low Theorem Perspective on Quantum Computing: New Paradigm for Designing Quantum Algorithm

The Gell-Mann & Low theorem is a cornerstone of Quantum Field Theory (QFT) and condensed matter physics, and many-body perturbation theory is a foundational tool for treating interactions. However, their integration into quantum algorithms remains a largely unexplored area of research, with current quantum simulation algorithms predominantly operating in the Schrödinger picture, leaving the potential of the interaction picture largely untapped. Our Variational Interaction-Picture S-matrix Ansatz (VIPSA) now fills this gap, specifically in the context of the Fermi-Hubbard model -- a canonical paradigm in condensed matter physics which is intricately connected to phenomena such as high-temperature superconductivity and Mott insulator transitions. This work offers a new conceptual perspective for variational quantum computing based upon the Gell-Mann & Low theorem. We achieve this by employing an innovative mathematical technique to explicitly unfold the normalized S-matrix, thereby enabling the systematic reconstruction of the Dyson series on a quantum computer, order by order. This method stands in contrast to the conventional reliance on Trotter expansion for adiabatic time evolution, marking a conceptual shift towards more sophisticated quantum algorithmic design. We leverage the strengths of the recently developed ADAPT-VQE algorithm, tailoring it to reconstruct perturbative terms effectively. Our simulations indicate that this method not only successfully recovers the Dyson series but also exhibits robust and stable convergence. We believe that our approach shows great promise in generalizing to more complex scenarios without increasing algorithmic complexity.

quant-ph↗

arXiv2022

Quantum state tomography via non-convex Riemannian gradient descent

The recovery of an unknown density matrix of large size requires huge computational resources. The recent Factored Gradient Descent (FGD) algorithm and its variants achieved state-of-the-art performance since they could mitigate the dimensionality barrier by utilizing some of the underlying structures of the density matrix. Despite their theoretical guarantee of a linear convergence rate, the convergence in practical scenarios is still slow because the contracting factor of the FGD algorithms depends on the condition number $κ$ of the ground truth state. Consequently, the total number of iterations can be as large as $O(\sqrtκ\ln(\frac{1}{\varepsilon}))$ to achieve the estimation error $\varepsilon$. In this work, we derive a quantum state tomography scheme that improves the dependence on $κ$ to the logarithmic scale; namely, our algorithm could achieve the approximation error $\varepsilon$ in $O(\ln(\frac{1}{κ\varepsilon}))$ steps. The improvement comes from the application of the non-convex Riemannian gradient descent (RGD). The contracting factor in our approach is thus a universal constant that is independent of the given state. Our theoretical results of extremely fast convergence and nearly optimal error bounds are corroborated by numerical results.

quant-ph↗

arXiv2021

Natural Negative-Refractive-Index Materials

Our calculation shows that negative refractive index (NRI), which was known to exist only in metamaterials in the past, can be found in Dirac semimetals (DSM). Electrons in DSM have zero effective mass and hence the system carries no nominal energy scale. Therefore, unlike those of ordinary materials, the electromagnetic responses of the electrons in DSM will not be overwhelmed by the physical effects related to electron mass. NRI is induced by the combination of the quantum effect of vacuum polarization and its finite temperature correction which is proportional to $T^4$ at low temperature. It is a phenomenon of resonance between the incident light and the unique structure of Dirac cones, which allows numerous states to participate in electron-hole pair production excited by the incident light with similar dispersion relation to that of Dirac cones. NRI phenomenon of DSM manifests in an extensive range of photon frequency and wave number and can be observed around giga Hertz range at temperature slightly higher than room temperature.

cond-mat.other↗

arXiv2021

Aspects of symmetry and topology in the charge density wave phase of 1T-TiSe2

The charge density wave (CDW) in 1T-TiSe2 accompanied by the periodic lattice distortion has a nontrivial symmetry configuration. The symmetry is important as an indication of the mechanism and a cue for experimental probes. We examine the symmetry of the system and clear up the connection of electronic structures between the normal and the CDW states. Especially, we unravel the consequential irreducible representations (IRs) of electronic states and, more ahead, those of gap functions among bands when the CDW occurs. Normally symmetry-related topology will be achieved directly, so we assert that the theory is valuable and practical for the search of topological CDW insulators.

cond-mat.mtrl-sci↗

arXiv2021

Topological theory of inversion-breaking charge-density-wave monolayer 1\textit{T}-TiSe$_2$

A charge density wave (CDW) of a nonzero ordering vector $\mathbf{q}$ couple electronic states at $\mathbf{k}$ and $\mathbf{k}+\mathbf{q}$ statically, giving rise to a reduced Brillouin zone (RBZ) due to the band folding effect. Its structure, in terms of an irreducible representation of the little group of $\mathbf{q}$, would change the symmetry of the system and electronic structure accompanying possible change of band inversion, offering a chance of the topological phase transition. Monolayer 1\textit{T}-TiSe$_2$ is investigated for it shows an unconventional CDW phase having a triple-$q$ $M_1^-$ structure. Moreover, the coupling between the triple-$q$ component of the $M_1^-$ CDW will inevitably produce a small $M_1^+$ CDW. The CDW yields a band inversion in 1\textit{T}-TiSe$_2$ but different types of CDW can affect the electronic structure and system topology differently. The impact of CDW of different types was studied by utilizing a symmetrization-antisymmetrization technique to extract the $M_1^-$ and $M_1^+$ CDW contributions in the DFT-based tight-binding model and study their effects. The results are consistent with the parity consideration, improving understanding of topology for a CDW system with and without parity.

cond-mat.mtrl-sci↗

arXiv2020

Machine learning on the electron-boson mechanism in superconductors

To unravel pairing mechanism of a superconductor from limited, indirect experimental data is always a difficult task. It is common but sometimes dubious to explain by a theoretical model with some tuning parameters. In this work, we propose that the machine learning might infer pairing mechanism from observables like superconducting gap functions. For superconductivity within the Migdal-Eliashberg theory, we perform supervised learning between superconducting gap functions and electron-boson spectral functions. For simple spectral functions, the neural network can easily capture the correspondence and predict perfectly. For complex spectral functions, an autoencoder is utilized to reduce the complexity of the spectral functions to be compatible to that of the gap functions. After this complexity-reduction process, relevant information of the spectral function is extracted and good performance restores. Our proposed method can extract relevant information from data and can be applied to general function-to-function mappings with asymmetric complexities either in physics or other fields.

physics.comp-ph↗

arXiv2019

Topological photocurrent responses from chiral surface Fermi arcs

The nonlinear optical responses from topological semimetals are crucial in both understanding the fundamental properties of quantum materials and designing next-generation light-sensors or solar-cells. However, previous work was focusing on the optical effects from bulk states only, disregarding topological surface responses. Here we propose a new (hitherto unknown) surface-only topological photocurrent response from chiral Fermi arcs. Using the ideal topological chiral semimetal RhSi as a representative, we quantitatively compute the topologically robust photocurrents from Fermi arcs on different surfaces. By rigorous crystal symmetry analysis, we demonstrate that Fermi arc photocurrents can be perpendicular to the bulk injection currents regardless of the choice of materials' surface. We then generalize this finding to all cubic chiral space groups and predict material candidates. Our theory reveals a powerful notion where common crystalline-symmetry can be used to induce universal topological responses as well as making it possible to completely disentangle bulk and surface topological responses in many conducting material families.

cond-mat.mes-hall↗

arXiv2019

Topologically distinct Weyl-fermion pairs: on the effect of magnetic tunnelling

A Weyl semimetal has Weyl nodes that always come in pairs with opposite chiralities. Notably, different ways of connection between nodes are possible and would lead to distinct topologies. Here we identify their differences in many respects from two proposed models with different vorticities. One prominent feature is the behaviour of zeroth Landau levels (LLs) under magnetic field. We demonstrate that the magnetic tunnelling does not always expel LLs from zero energy because the number of zero-energy modes is linked to the vorticity of the Weyl nodes, instead of the chirality. Other respects in disorder effects for weak (anti-)localization, surface Fermi arcs, and Weyl-node annihilation, are interesting consequences that await future exploration.

cond-mat.mes-hall↗

arXiv2019

Photoionization of Xe and Rn from the relativistic random-phase theory

Photoionization cross section $σ_{nκ}$, asymmetry parameter $β_{nκ}$, and polarization parameters $ξ_{nκ}$, $η_{nκ}$, $ζ_{nκ}$ of Xe and Rn are calculated in the fully relativistic formalism. To deal with the relativistic and correlation effects, we adopt the relativistic random-phase theory with channel couplings among different subshells. Energy ranges for giant \emph{d}-resonance regions are especially considered.

physics.atom-ph↗

arXiv2018

Systematic analysis for triple points in all magnetic symmorphic systems and symmetry-allowed coexistence of Dirac points and triple points

Similar to Weyl fermions, a recently discovered topological fermion "triple point" can be generated from the splitting of Dirac fermion while the system has inversion symmetry (IS) breaking or time reversal symmetry (TRS) breaking. Inducing triple points in IS breaking symmorphic systems have been well studied, whereas in TRS breaking symmorphic systems have not yet. In this work, we extend the theory of searching triple points to all symmorphic magnetic systems. We list all $k$ paths of all symmorphic systems which allow the existence of triple points. With this systematic study, we also find out that the coexistence of Dirac points and triple points is symmetrically allowed in some particular symmetric systems. Our works will not only be helpful for searching triple points but also extend the knowledge of such a new topological fermion.

cond-mat.mes-hall↗

arXiv2017

Inducing 3-component fermions in centrosymmetric system by breaking TRS

Recent researches show that by breaking inversion symmetry Dirac fermions can split into new fermions with 3-component. In this article, we demonstrate that Dirac fermions can also split into 3-component fermions with time reversal symmetry (TRS) breaking while inversion symmetry is preserved. Firstly, we conduct a symmetry analysis with the commutation relations among all symmetry operators of a Dirac semimetal and find out the symmetry conditions of Dirac fermions splitting into 3-component fermions. With the symmetry conditions, we derive the $k\cdot P$ effective Hamiltonian of TRS breaking and compare it with the Hamiltonian of inversion symmetry breaking. We find that they are different in $Γ$ point eigenenergies. This can be considered as consequence of Kramers degeneracy breaking which is a clear signature of TRS breaking. Moreover, with the $k\cdot P$ effective Hamiltonian of the system we show that TRS-breaking-induced 3-component fermions can split into Weyl fermions while a small magnetic field is applied. At the end, we show our first principles calculation results are consistent with the symmetry analysis and the $k\cdot P$ predictions. Our work clarifies the similarities and the differences between TRS-breaking-induced 3-component fermions and inversion-symmetry-breaking-induced 3-component fermions and extends the scope of 3-component fermion behaviors.

cond-mat.mtrl-sci↗

arXiv2011

An Envelope Disrupted by a Quadrupolar Outflow in the Pre-Planetary Nebula IRAS19475+3119

IRAS 19475+3119 is a quadrupolar pre-planetary nebula (PPN), with two bipolar lobes, one in the east-west (E-W) direction and one in the southeast-northwest (SE-NW) direction. We have observed it in CO J=2-1 with the Submillimeter Array at ~ 1" resolution. The E-W bipolar lobe is known to trace a bipolar outflow and it is detected at high velocity. The SE-NW bipolar lobe appears at low velocity, and could trace a bipolar outflow moving in the plane of the sky. Two compact clumps are seen at low velocity around the common waist of the two bipolar lobes, spatially coincident with the two emission peaks in the NIR, tracing dense envelope material. They are found to trace the two limb-brightened edges of a slowly expanding torus-like circumstellar envelope produced in the late AGB phase. This torus-like envelope originally could be either a torus or a spherical shell, and it appears as it is now because of the two pairs of cavities along the two bipolar lobes. Thus, the envelope appears to be disrupted by the two bipolar outflows in the PPN phase.

astro-ph.SR↗

arXiv2009

Collimated Fast Wind in the Pre-Planetary Nebula CRL 618

Collimated fast winds (CFWs) have been proposed to operate during the post-AGB evolutionary phase (and even earlier during the late AGB phase), responsible for the shaping of pre-planetary nebulae (PPNs) and young planetary nebulae (PNs). This paper is a follow-up to our previous study of CFW models for the well-studied PPN CRL 618. Previously, we compared our CFW models with optical observations of CRL 618 in atomic and ionic lines and found that a CFW with a small opening angle can readily reproduce the highly collimated shape of the northwestern (W1) lobe of CRL 618 and the bow-like structure seen at its tip. In this paper, we compare our CFW models with recent observations of CRL 618 in CO J=2-1, J=6-5, and H2 1-0 S(1). In our models, limb-brightened shell structures are seen in CO and H2 at low velocity arising from the shocked AGB wind in the shell, and can be identified as the low-velocity (LV) components in the observations. However, the shell structure in CO J=2-1 is significantly less extended than that seen in the observations. None of our models can properly reproduce the observed high-velocity (HV) molecular emission near the source along the body of the lobe. In order to reproduce the HV molecular emission in CRL 618, the CFW is required to have a different structure. One possible CFW structure is the cylindrical jet, with the fast wind material confined to a small cross section and collimated to the same direction along the outflow axis.

astro-ph.GA↗