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Mo-Lin Ge

Publications and source records attributed to Mo-Lin Ge.

At least 37 records · Page 2Linked to original sources
arXiv2010

Yangian symmetry in molecule {V6} and four-spin Heisenberg model

The symmetry operator $Q=Y^2$ is introduced to re-describe the Heisenberg spin triangles in the \{V6\} molecule, where $\mathbf{Y}$ stands for the Yangian operator which can be viewed as special form of Dzyaloshiky-Moriya (DM) interaction for spin 1/2 systems. Suppose a parallelogram Heisenberg model that is comprised of four 1/2-spins commutes with $Q$, which means that it possesses Yangian symmetry, we show that the ground state of the Hamiltonian $H_4$ for the model allows to take the total spin S=1 by choosing some suitable exchange constants in $H_4$. In analogy to the molecular \{V6\} where the two triangles interact through Yangian operator we then give the magnetization for the theoretical molecule "\{V8\}" model which is comprised of two parallelograms. Following the example of molecule \{V15\}, we give another theoretical molecule model regarding the four 1/2-spins system with total spin S=1 and predict the local moments to be 1/10u_B, 9/10u_B, 1/10u_B,9/10u_B respectively.

quant-ph↗
arXiv2010

Extraspecial Two-Groups, Generalized Yang-Baxter Equations and Braiding Quantum Gates

In this paper we describe connections among extraspecial 2-groups, unitary representations of the braid group and multi-qubit braiding quantum gates. We first construct new representations of extraspecial 2-groups. Extending the latter by the symmetric group, we construct new unitary braid representations, which are solutions to generalized Yang-Baxter equations and use them to realize new braiding quantum gates. These gates generate the GHZ (Greenberger-Horne-Zeilinger) states, for an arbitrary (particularly an \emph{odd}) number of qubits, from the product basis. We also discuss the Yang-Baxterization of the new braid group representations, which describes unitary evolution of the GHZ states. Our study suggests that through their connection with braiding gates, extraspecial 2-groups and the GHZ states may play an important role in quantum error correction and topological quantum computing.

quant-ph↗
arXiv2010

The $\ell_{1}$-norm in quantum information via the approach of Yang-Baxter Equation

The role of $\ell_{1}$-norm in Quantum Mechanics (QM) has been studied through Wigner's D-functions where $\ell_{1}$-norm means $\sum_{i}\left|C_{i}\right|$ for $\left|Ψ\right\rangle =\sum_{i}C_{i}\left|ψ_{i}\right\rangle $ if $\left|ψ_{i}\right\rangle $ are uni-orthogonal and normalized basis. It was shown that the present two types of transformation matrix acting on the natural basis in physics consist in an unified braiding matrix, which can be viewed as a particular solution of the Yang-Baxter equation (YBE). The maximum of the $\ell_{1}$-norm is connected with the maximally entangled states and topological quantum field theory (TQFT) with two-component anyons while the minimum leads to the permutation for fermions or bosons.

quant-ph↗
arXiv2009

The geodesic form of light-ray trace in the inhomogeneous media

The canonical equations of the optical cloaking proposed by Shurig, Pendry and Smith has been proved to be equivalent to the geodesic in a 3-dimensional curved space. Carrying out the argument we extend to the 4-dimensional Riemannian space where the extra time item appears as the potential term in the canonical equations. The physical meaning of the results is interpreted.

physics.optics↗
arXiv2008

Principal Realization of the Yangian Y(gl(n))

Motivated to simplify the structure of tensor representations we give a new set of generators for the Yangian $Y(sl(n))$ using the principal realization in simple Lie algebras. The isomorphism between our new basis and the standard Cartan-Weyl basis is also given. We show by example that the principal basis simplifies the Yangian action significantly in the tensor product of the fundamental representation and its dual.

math.QA↗
arXiv2008

Exact Solution of a Yang-Baxter Spin-1/2 Chain Model and Quantum Entanglement

Entanglement is believed to be crucial in macroscopic physical systems for understanding the collective quantum phenomena such as quantum phase transitions. We start from and solve exactly a novel Yang-Baxter spin-1/2 chain model with inhomogeneous and anisotropic short-range interactions. For the ground state, we show the behavior of neighboring entanglement in the parameter space and find that the inhomogeneous coupling strengths affect entanglement in a distinctive way from the homogeneous case, but this would not affect the coincidence between entanglement and quantum criticality.

quant-ph↗
arXiv2008

Optical Simulation of Yang-Baxter Equation

In this paper, several proposals of optically simulating Yang-Baxter equations have been presented. Motivated by the recent development of anyon theory, we apply Temperley-Lieb algebra as a bridge to recast four-dimentional Yang-Baxter equation into its two-dimensional counterpart. In accordance with both representations, we find the corresponding linear-optical simulations, based on the highly efficient optical elements. Both the freedom degrees of photon polarization and location are utilized as the qubit basis, in which the unitary Yang-Baxter matrices are decomposed into combination of actions of basic optical elements.

quant-ph↗
arXiv2008

Bogoliubov Hamiltonian as Derivative of Dirac Hamiltonian via Braid Relation

In this paper we discuss a new type of 4-dimensional representation of the braid group. The matrices of braid operations are constructed by q-deformation of Hamiltonians. One is the Dirac Hamiltonian for free electron with mass m, the other, which we find, is related to the Bogoliubov Hamiltonian for quasiparticles in $^3$He-B with the same free energy and mass being m/2. In the process, we choose the free q-deformation parameter as a special value in order to be consistent with the anyon description for fractional quantum Hall effect with $ν= 1/2$.

quant-ph↗
arXiv2007

Braiding transformation, entanglement swapping and Berry phase in entanglement space

We show that braiding transformation is a natural approach to describe quantum entanglement, by using the unitary braiding operators to realize entanglement swapping and generate the GHZ states as well as the linear cluster states. A Hamiltonian is constructed from the unitary $\check{R}_{i,i+1}(θ,ϕ)$-matrix, where $ϕ=ωt$ is time-dependent while $θ$ is time-independent. This in turn allows us to investigate the Berry phase in the entanglement space.

quant-ph↗
arXiv2007

Generation of Two-Flavor Vortex Atom Laser from a Five-State Medium

Two-flavor atom laser in a vortex state is obtained and analyzed via electromagnetically induced transparency (EIT) technique in a five-level $M$ type system by using two probe lights with $\pm z$-directional orbital angular momentum $\pm l\hbar$, respectively. Together with the original transfer technique of quantum states from light to matter waves, the present result can be extended to generate continuous two-flavor vortex atom laser with non-classical atoms.

quant-ph↗
arXiv2007

GHZ States, Almost-Complex Structure and Yang--Baxter Equation (I)

Recent study suggests that there are natural connections between quantum information theory and the Yang--Baxter equation. In this paper, in terms of the generalized almost-complex structure and with the help of its algebra, we define the generalized Bell matrix to yield all the GHZ states from the product base, prove it to form a unitary braid representation and present a new type of solution of the quantum Yang--Baxter equation. We also study Yang-Baxterization, Hamiltonian, projectors, diagonalization, noncommutative geometry, quantum algebra and FRT dual algebra associated with this generalized Bell matrix.

quant-ph↗
arXiv2006

Quantum Algebras Associated With Bell States

The antisymmetric solution of the braided Yang--Baxter equation called the Bell matrix becomes interesting in quantum information theory because it can generate all Bell states from product states. In this paper, we study the quantum algebra through the FRT construction of the Bell matrix. In its four dimensional representations via the coproduct of its two dimensional representations, we find algebraic structures including a composition series and a direct sum of its two dimensional representations to characterize this quantum algebra. We also present the quantum algebra using the FRT construction of Yang--Baxterization of the Bell matrix.

math-ph↗
arXiv2006

Virtual Extension of Temperley--Lieb Algebra

The virtual knot theory is a new interesting subject in the recent study of low dimensional topology. In this paper, we explore the algebraic structure underlying the virtual braid group and call it the virtual Temperley--Lieb algebra which is an extension of the Temperley--Lieb algebra by adding the group algebra of the symmetrical group. We make a connection clear between the Brauer algebra and virtual Temperley--Lieb algebra, and show the algebra generated by permutation and its partial transpose to be an example for the virtual Temperley--Lieb algebra and its important quotients.

math-ph↗
arXiv2006

Quantum Spin Current Induced Through Optical Fields

We propose a scheme to generate quantum spin current via optical dipole transition process. By coupling a three-level system based on the spin states of charged particles (electrons or holes in semiconductor) to the angular momentum states of the radiation, we show that a pure quantum spin current can be generated. No spin-orbit interaction is needed in this scheme. We also calculate the effect of nonmagnetic impurities on the created spin currents and show that the vertex correction of the spin hall conductivity in the ladder approximation is exactly zero.

cond-mat.mes-hall↗
arXiv2006

Su(3) Algebraic Structure of the Cuprate Superconductors Model based on the Analogy with Atomic Nuclei

A cuprate superconductor model based on the analogy with atomic nuclei was shown by Iachello to have an $su(3)$ structure. The mean-field approximation Hamiltonian can be written as a linear function of the generators of $su(3)$ algebra. Using algebraic method, we derive the eigenvalues of the reduced Hamiltonian beyond the subalgebras $u(1)\bigotimes u(2)$ and $so(3)$ of $su(3)$ algebra. In particular, by considering the coherence between s- and d-wave pairs as perturbation, the effects of coherent term upon the energy spectrum are investigated.

cond-mat.other↗
arXiv2006

Yangian and Applications

In this paper, the Yangian relations are tremendously simplified for Yangians associated to SU(2), SU(3), SO(5) and SO(6) based on RTT relations that much benefit the realization of Yangian in physics. The physical meaning and some applications of Yangian have been shown.

quant-ph↗