Studies on the Chiral Order Parameter in the Schwinger Model

Based on an analytical technique using a unitary transformation and the variational method, we study the chiral order parameter in the Schwinger model in the lattice formalism with Kogut-Susskind fermions. The fermion condensate (ψψ)fo r any coupling constant and fermion mass are calculated. Chiral symmetry is shown to be broken in the massless limit and good scaling behavior is obtained.     

Topological Fermi liquids from Coulomb interactions in the doped honeycomb lattice

We propose a simple method for obtaining time reversal symmetry (T) broken phases in simple lattice models based on enlarging the unit cell. As an example we study the honeycomb lattice with nearest neighbor hopping and a local nearest neighbor Coulomb interaction V. We show that when the unit cell is enlarged to host six atoms that permits Kekulé distortions, self-consistent currents spontaneously form creating nontrivial magnetic configurations with total zero flux at high electron densities. A very rich phase diagram is obtained within a variational mean field approach that includes metallic phases with broken time reversal symmetry (T). The predominant (T) breaking configuration is an anomalous Hall phase, a realization of a topological Fermi liquid.     

EVALUATION OF EFFECTIVE POTENTIAL FOR GROSS-NEVEU MCDEL WITH TADPOLE DIAGRAM METHOD

The effective potential of Gross-Neveu model with o(1/N) corrections is calculated by using tadpole diagrams and dimensional regularization technique. After the high order of the effective potential is taken into account the continuous symmetry will not be violated while the discrete chiral symmetry still remains broken. This provides an interesting example of Coleman's theorem in two-dimensional field theory. The calculation results are in agreement with those of R.G. Root who had summed up a sort of infinite diagrams. Our conclusion is also consistent with that of the variational method based on BCS wave functions.     

Theory of oxide high temperature superconductivity

We propose a model Hamiltonian for the high temperature superconductivity from the analogy of the BCS model hamiltonian. We seek a possibility of real space electron pairing. It follows then the magnetic exchange interaction is not a source of pairing and we propose a form of pairing interaction from the argument of the broken symmetry of electron number conservation. Based on a variational wave function, the ground state energy of our model is studied.     

Generalized Hartree-Fock theory and the Hubbard model

The familiar unrestricted Hartree-Fock variational principles is generalized to include quasi-free states. As we show, these are in one-to-one correspondence with the one-particle density matrices and these, in turn, provide a convenient formulation of a generalized Hartree-Fock variational principle, which includes the BCS theory as a special case. While this generalization is not new, it is not well known and we begin by elucidating it. The Hubbard model, with its particle-hole symmetry, is well suited to exploring this theory because BCS states for the attractive model turn into usual HF states for the repulsive model. We rigorously determine the true, unrestricted minimizers for zero and for nonzero temperature in several cases, notably the half-filled band. For the cases treated here, we can exactly determine all broken and unbroken spatial and gauge symmetries of the Hamiltonian.Dedicated to Philippe Choquard on his 65th birthday.     

Time-Dependent Variational Approach to Ground-State Phase Transition and Phonon Dispersion Relation of the Quantum Double-Well Model

The ground-state phase transition and the phonon dispersion relation of the quantum double-well model are studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction. The single-particle state is taken to be a frozen Jackiw-Kerman wavefunction. Under the condition of minimum uncertainty relation, we obtain an effective classical Hamiltonian for the system and equations of motion for the particle＇s expectation values. It is shown that the effective substrate potential transits from a symmetric double-well potential to a symmetric single-well potential, and the ground state exhibits a transition from a broken symmetry phase to a restored symmetry phase as increasing the strength of quantum fluctuations. We also obtain the phonon dispersion relations and the phonon gaps at the two phases.     

线性塞曼劈裂对自旋-轨道耦合玻色-爱因斯坦凝聚体中亮孤子动力学的影响

利用变分近似及基于Gross-Pitaevskii方程的直接数值模拟方法,研究了自旋-轨道耦合玻色-爱因斯坦凝聚体中线性塞曼劈裂对亮孤子动力学的影响,发现线性塞曼劈裂将导致体系具有两个携带有限动量的静态孤子,以及它们在微扰下存在一个零能的Goldstone激发模和一个频率与线性塞曼劈裂有关的谐振激发模.同时给出了描述孤子运动的质心坐标表达式,发现线性塞曼劈裂明显影响孤子的运动速度和振荡周期.     

对称性、对称性破缺和相变

本文将扼要介绍物理学中对称性的分类及其特征,说明对称性破缺与一物理系统从无序到有序的相变过程间的关系,并讨论了对称性破缺出现的前提     

Parity Symmetry and Parity Breaking in the Quantum Rabi Model with Addition of Ising Interaction

We explore the possibility to generate new parity symmetry in the quantum Rabi model after a bias is introduced. In contrast to a mathematical treatment in a previous publication [J. Phys. A 46(2013) 265302], we consider a physically realistic method by involving an additional spin into the quantum Rabi model to couple with the original spin by an Ising interaction, and then the parity symmetry is broken as well as the scaling behavior of the ground state by introducing a bias. The rule can be found that the parity symmetry is broken by introducing a bias and then restored by adding new degrees of freedom. Experimental feasibility of realizing the models under discussion is investigated.     

Left-right symmetric theories and vacuum domain walls and strings

Theories in which a discrete left-right symmetry is spontaneously broken are expected to lead to the formation of vacuum domain walls. Although the existence of such walls at the present epoch is observationally excluded, we show that such theories are allowed if the discrete symmetry is embedded in a larger continuous symmetry, e.g., SO(10), spontaneously broken at higher temperatures. In this case vacuum strings are formed when the larger symmetry is broken, and these become connected by domain walls when the discrete symmetry is broken. The bounded domain walls tend to shrink, and the system of strings and domain walls decays before its energy density becomes comparable to that of matter. In particular, our arguments allow the symmetry breaking pattern SO(10) → … S[O(6)×O(4)] → SU(3)×SU(2)×U(1) which has been proposed by others.     

Replica Method and Finite Volume Corrections

In this note we introduce a method to calculate the finite volume corrections to the mean field results for the free energy when replica symmetry is broken at one-step. We find that the naive results are modified by the presence of additional corrections: these corrections can be interpreted as arising from fluctuations in the size of the blocks in the replica approach. The computation suggests a new approach for deriving the replica broken results in a rigorous way.     

Interface dynamics in liquid crystals

We have experimentally observed the pattern instabilities of an Ising wall formed in a nematic or cholesteric liquid crystal layer. We have deduced an envelope equation, relevant close to the Fréedericksz transition, from which we derived an equation for the dynamics of the interface in the vicinity of its bifurcation. In the case of the zig-zag instability, this model is characterized by a conservative and variational order parameter whose gradient satisfies a Cahn-Hilliard equation. We have also investigated the influence of slightly broken symmetries on the dynamical behaviour of the system. The disappearance of the interface translational invariance or of the reflection symmetry along the wall axis may induce new interfacial patterns which have been both experimentally and theoretically pointed out. Received 5 August 1999 and Received in final form 13 September 1999     

Observation of the exceptional point in superconducting qubit with dissipation controlled by parametric modulation

Open physical systems described by the non-Hermitian Hamiltonian with parity-time-reversal(PT) symmetry show peculiar phenomena, such as the presence of an exceptional point(EP) at which the PT symmetry is broken and two resonant modes of the Hamiltonian become degenerate. Near the EP, the system could be more sensitive to external perturbations and this may lead to enhanced sensing. In this paper, we present experimental results on the observation of PT symmetry broken transition and the EP using a tunable superconducting qubit. The quantum system of investigation is formed by the two levels of the qubit and the energy loss of the system to the environment is controlled by a method of parametric modulation of the qubit frequency. This method is simple with no requirements for additional elements or qubit device modifications. We believe it can be easily implemented on multi-qubit devices that would be suitable for further exploration of non-Hermitian physics in more complex and diverse systems.     

Complex mean fields and unnatural parity pairing in the Hartree-Fock-Bogoliubov problem with symmetry-projection before the variation

The Hartree-Fock-Bogoliuboy problem with restoration of the broken symmetries before the variation as it has been formulated recently within the VAMPIR and EXCITED VAMPIR approaches is studied in more detail. Special emphasis is put on the implications of various symmetry restrictions imposed on the quasiparticle transformations. It is shown that the use of essentially complex transformations provides a possibility to account for time-odd unnatural parity pairing correlations in the wavefunctions without being forced to give up axial and time-reversal symmetry. It is illustrated that together with parity and neutron-proton mixing the use of such complex mean fields extends the applicability of the VAMPIR and EXCITED VAMPIR approaches to states with arbitrary spin and parity in both doubly even and doubly odd nuclear systems. The corresponding variational equations are explicitly evaluated and the numerical feasibility of their solution is investigated.     

Dynamical mass function of quark and effective potential in QCD

Direct variational method is applied to the problem of the dynamical breaking of chiral symmetry in QCD. The minimum of the effective potential corresponding to the phase with spontaneous chiral symmetry breaking is found.     

Estimating ground-state energies in supersymmetric quantum mechanics: (1) Broken case

For a class of the dynamically broken supersymmetric quantum-mechanical models proposed by Witten, we examine various methods of estimating the ground-state energy, including the instanton method developed by Salomonson and van Holten. We show that no existing method is entirely satisfactory, and develop a method using all stationary points of the Schrödinger potential (including those in the complex plane) in conjunction with the Rayleigh-Ritz variational method, thus combining perturbative and nonperturbative effects. Generalisations to more than one degree of freedom and to field theory are discussed.     

Non-linear realization of superconformal symmetry

Within a framework of the non-linear realization, we investigate the transformation law and the effective lagrangian when superconformal symmetry is spontaneously broken down to super-Poincaré symmetry. We show that the determinant of the “supervierbein” provides an effective lagrangian which describes the interaction among the dilaton, the “axion” and the dilatino. We also briefly discuss the case in which the superconformal group is broken down to the Poincaré group.     

Variational Bounds for the Generalized Random Energy Model

We compute the pressure of the random energy model (REM) and generalized random energy model (GREM) by establishing variational upper and lower bounds. For the upper bound, we generalize Guerra’s “broken replica symmetry bounds,” and identify the random probability cascade as the appropriate random overlap structure for the model. For the REM the lower bound is obtained, in the high temperature regime using Talagrand’s concentration of measure inequality, and in the low temperature regime using convexity and the high temperature formula. The lower bound for the GREM follows from the lower bound for the REM by induction. While the argument for the lower bound is fairly standard, our proof of the upper bound is new.     

Electromagnetic scattering by a time reversal symmetry broken topological insulator sphere

An exact solution of electromagnetic wave scattering by a time reversal symmetry broken topological insulator sphere is researched. According to the constitute relations of topological insulator, we modified magnetic vector potential and electric vector potential of standard Mie theory and derived scattered electromagnetic fields and scattered coefficients. Numerical results show that, when the time reversal symmetry is broken, the extinction efficiencies and the scattering efficiencies are influenced by topological magneto-electric polarizability.