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Hsien-chung Kao

Publications and source records attributed to Hsien-chung Kao.

At least 19 recordsLinked to original sources
arXiv2023

{SSH coupled-spring systems

It is known that there is also a topological phase in the SSH coupled-spring system with the fixed-end boundary conditions. When this is the case, there would exist edge modes on its boundaries. In contrast, if the system satisfies the free-end boundary conditions, there is no edge mode, even if it is the topological phase. We show that by varying the force constant of the spring by the boundary in such a system, edge modes would generally appear independent of whether the bulk of the system is in the topological or trivial phases. Moreover, edge modes could exist even if the system satisfies the free-end boundary conditions.

cond-mat.other↗
arXiv2023

Quasi-Hermitian extended SSH models

We consider the quasi Hermitian limit of a non-Hermitian extended Su Schrieffer Heeger model, in which the hopping amplitudes obey a specific relation so that the system may be mapped to a corresponding Hermitian one and its energy spectrum is completely real. Analogous to the Hermitian case, one may use the modified winding number to determine the total number of edge states on the boundaries to achieve a modified bulk-boundary correspondence. Due to the skin effect in nonHermitian systems, the spectral winding numbers must be used to classify such systems further. It dictates how the edge states would be distributed over the left and right boundaries. We then naively extend the criteria to the cases that the quasi Hermitian condition is violated. For all the cases that we consider, no inconsistency has been found.

quant-ph↗
arXiv2022

Unified intermediate coupling description of the pseudogap and the strange metal phases of cuprates

A one band Hubbard model with intermediate coupling is shown to describe the two most important unusual features of a normal state: linear resistivity strange metal and the pseudogap. Both the spectroscopic and transport properties of the cuprates are considered on the same footing by employing a relatively simple postgaussian approximation valid for the intermediate couplings $U/t=1.5-4$ in relevant temperatures $T>100{\rm K}.$ In the doping range $\ p=0.1-0.3$, the value of $U$ is smaller than that in the parent material. For a smaller doping, especially in the Mott insulator phase, the coupling is large compared to the effective tight binding scale and a different method is required. This scenario provides an alternative to the paradigm that the coupling should be strong, say $U/t>6$, in order to describe the strange metal. We argue that to obtain phenomenologically acceptable underdoped normal state characteristics like $T^{\ast }$, pseudogap values, and spectral weight distribution, a large value of $U$ is detrimental. Surprisingly the resistivity in the above temperature range is linear $ρ=ρ_{0}+α\frac{m^{\ast }}{e^{2}n\hbar }T$ with the "Planckian" coefficient $α$ of order one.

cond-mat.str-el↗
arXiv2022

Winding number and Zak phase in multi-band SSH models

We use multi-band SSH models to demonstrate a prescription for calculating the correct Zak phase and winding number of multi-band systems. We verify our prescription by comparing the resultant winding number of a four-band SSH model with the edge states of a semi-infinite chain which we find by solving the equation of motion. We then also carry out an extensive comparison with the numerical results obtained by solving the matrix eigenvalue problem of finite chains with various number of sites. As a double check of our prescription, we also confirm the bulk edge correspondence in a six-band SSH model. Similar to the usual SSH model, the winding numbers associated to the left and right boundaries in a finite chain may be different if space inversion symmetry is violated in the system. We believe the prescription we propose here may also be applied to other 1D multi-band systems.

cond-mat.mes-hall↗
arXiv2020

Connection between the winding number and the Chern number

Bulk-edge correspondence is one of the most distinct properties of topological insulators. In particular, the 1D winding number $\n$ has a one-to-one correspondence to the number of edge states in a chain of topological insulators with boundaries. By properly choosing the unit cells, we carry out numerical calculation to show explicitly in the extended SSH model that the winding numbers corresponding to the left and right unit cells may be used to predict the numbers of edge states on the two boundaries in a finite chain. Moreover, by drawing analogy between the SSH model and QWZ model, we show that the extended SSH model may be generalized to the extended QWZ model. By integrating the ``magnetic field'' over the momentum strip $0\le p_2 \le π, 0\le p_1 2π$ in the Brillouin zone, we show a identity relating the 2D Chern number and the difference between the 1D winding numbers at $p_2=0 $ and $p_2 =π$.

cond-mat.mes-hall↗
arXiv2014

Chiral zero modes in superconducting nanowires with Dresselhaus spin-orbit coupling

Using chiral decomposition, we are able to find analytically the zero modes and the conditions for such modes to exist in the Kitaev ladder model and superconducting nanowires with Dresselhaus spin-orbit coupling. As a result, we are able to calculate the number of zero modes in these systems for arbitrary given parameters in the semi-infinite limit. Moreover, we find that when suitable resonance condition is satisfied exact zero modes exist even in finite systems contrary to the common belief.

cond-mat.mes-hall↗
arXiv2013

Partition Function of Chiral Boson on 2-Torus from Floreanini-Jackiw Lagrangian

We revisit the problem of quantizing a chiral boson on a torus. The conventional approach is to extract the partition function of a chiral boson from the path integral of a non-chiral boson. Instead we compute it directly from the chiral boson Lagrangian of Floreanini and Jackiw modified by topological terms involving auxiliary fields. A careful analysis of the gauge-fixing condition for the extra gauge symmetry reproduces the correct results for the free chiral boson, and has the advantage of being applicable to a wider class of interacting chiral boson theories.

hep-th↗
arXiv2008

Quasinormal Modes of Kerr Black Holes in Four and Higher Dimensions

We analytically calculate to leading order the asymptotic form of quasinormal frequencies of Kerr black holes in four, five and seven dimensions. All the relevant quantities can be explicitly expressed in terms of elliptical integrals. In four dimensions, we confirm the results obtained by Keshest and Hod by comparing the analytic results to the numerical ones.

gr-qc↗
arXiv2005

Large N Cosmology

We motivate inflationary scenarios with many scalar fields, and give a complete formulation of adiabatic and entropy perturbations. We find that if the potential is very flat, or if the theory has a SO(N) symmetry, the calculation of the fluctuation spectrum can be carried out in terms of merely two variables without any further assumption. We do not have to assume slow roll or SO(N) invariance for the background fields. We give some examples to show that, even if the slow roll assumption holds, the spectrum of fluctuations can be quite different from the case when there is a single inflaton.

hep-th↗
arXiv2000

Mass Spectra of N=2 Supersymmetric SU(n) Chern-Simons-Higgs Theories

An algebraic method is used to work out the mass spectra and symmetry breaking patterns of general vacuum states in N=2 supersymmetric SU(n) Chern-Simons-Higgs systems with the matter fields being in the adjoint representation. The approach provides with us a natural basis for fields, which will be useful for further studies in the self-dual solutions and quantum corrections. As the vacuum states satisfy the SU(2) algebra, it is not surprising to find that their spectra are closely related to that of angular momentum addition in quantum mechanics. The analysis can be easily generalized to other classical Lie groups.

hep-th↗
arXiv1999

The Chern-Simons Coefficient in Supersymmetric Non-abelian Chern-Simons Higgs Theories

By taking into account the effect of the would be Chern-Simons term, we calculate the quantum correction to the Chern-Simons coefficient in supersymmetric Chern-Simons Higgs theories with matter fields in the fundamental representation of SU(n). Because of supersymmetry, the corrections in the symmetric and Higgs phases are identical. In particular, the correction is vanishing for N=3 supersymmetric Chern-Simons Higgs theories. The result should be quite general, and have important implication for the more interesting case when the Higgs is in the adjoint representation.

hep-th↗
arXiv1999

Binding Transition in Quantum Hall Edge States

We study a class of Abelian quantum Hall (QH) states which are topologically unstable (T-unstable). We find that the T-unstable QH states can have a phase transition on the edge which causes a binding between electrons and reduces the number of gapless edge branches. After the binding transition, the single-electron tunneling into the edge gains a finite energy gap, and only certain multi-electron co-tunneling (such as three-electron co-tunneling for $ν=9/5$ edges) can be gapless. Similar phenomenon also appear for edge state on the boundary between certain QH states. For example edge on the boundary between $ν=2$ and $ν=1/5$ states only allow three-electron co-tunneling at low energies after the binding transition.

cond-mat.mes-hall↗
arXiv1997

The Non-abelian Chern-Simons Coefficient in the Higgs Phase

We calculate the one loop corrections to the Chern-Simons coefficient $κ$ in the Higgs phase of Yang-Mills Chern-Simons Higgs theories. When the gauge group is SU(N), we show, by taking into account the effect of the would be Chern-Simons term, that the corrections are always integer multiples of ${1\over 4π}$, as they should for the theories to be quantum-mechanically consistent. In particular, the correction is vanishing for SU(2). The same method can also be applied to the case that the gauge group is SO(N). The result for SO(2) agrees with that found in the abelian Chern-Simons theories. Therefore, the calculation provides with us a unified understanding of the quantum correction to the Chern-Simons coefficient.

hep-th↗
arXiv1996

The BPS Domain Wall Solutions in Self-Dual Chern-Simons-Higgs Systems

We study domain wall solitons in the relativistic self-dual Chern-Simons Higgs systems by the dimensional reduction method to two dimensional spacetime. The Bogomolny bound on the energy is given by two conserved quantities in a similar way that the energy bound for BPS dyons is set in some Yang-Mills-Higgs systems in four dimensions. We find the explicit soliton configurations which saturate the energy bound and their nonrelativistic counter parts. We also discuss the underlying N=2 supersymmetry.

hep-th↗
arXiv1996

Exact Solution of Frenkel-Kontorova Models with a Complete Devil's Staircase in Higher Dimensions

We solve exactly a class of Frenkel-Kontorova models with piecewise parabolic potential, which has $d$ sub-wells in a period. With careful analysis, we show that the phase diagram of the minimum enthalpy configurations exhibits the structure of a complete $d$-dimensional devil's staircase. The winding number of a minimum enthalpy configuration is locked to rational values, while the fraction of atoms in each sub-well is locked to values which are sub-commensurable with the winding number.

solv-int↗
arXiv1996

$Zb\bar{b}$ Loop Correction with Charge 2/3 Singlet Quarks

We calculate the non-universal correction to the $Zb\bar{b}$ vertex in a simple extension of the Standard Model, where a charge $+2/3$ isosinglet quark is added to the standard spectrum. Comparison is made with other solutions to $R_b$ (and $R_c$) that demand particles lighter than $M_W$.

hep-ph↗
arXiv1996

Farey Tree and the Frenkel-Kontorova Model

We solved the Frenkel-Kontorova model with the potential $V(u)= -\frac{1}{2} |λ|(u-{\rm Int}[u]-\frac{1}{2})^2$ exactly. For given $|λ|$, there exists a positive integer $q_c$ such that for almost all values of the tensile force $σ$, the winding number $ω$ of the ground state configuration is a rational number in the $q_c$-th level Farey tree. For fixed $ω=p/q$, there is a critical $λ_c$ when a first order phase transition occurs. This phase transition can be understood as the dissociation of a large molecule into two smaller ones in a manner dictated by the Farey tree. A kind of ``commensurate-incommensurate'' transition occurs at critical values of $σ$ when two sizes of molecules co-exist. ``Soliton'' in the usual sense does not exist but induces a transformation of one size of molecules into the other.

solv-int↗