arXiv subjects
Publications and source records attributed to Shou-Cheng Zhang.
In this talk I give a brief update on the recent progress in the SO(5) theory of high T_c superconductivity (Science, 275: 1089,1997). Reviewed topics include SO(5) ladders, the unification of BCS and SDW quasi-particles in the SO(5) theory and the microscopic origin of the condensation energy.
In this work we investigate properties of fermions in the SO(5) theory of high Tc superconductivity. We show that the adiabatic time evolution of a SO(5) superspin vector leads to a non-Abelian SU(2) holonomy of the SO(5) spinor states. Physically, this non-trivial holonomy arises from the non-zero overlap between the SDW and BCS quasi-particle states. While the usual Berry's phase of a SO(3) spinor is described by a Dirac magnetic monopole at the degeneracy point, the non-Abelian holonomy of a SO(5) spinor is described by a Yang monopole at the degeneracy point, and is deeply related to the existence of the second Hopf map from $S^7$ to $S^4$. We conclude this work by extending the bosonic SO(5) nonlinear sigma model to include the fermionic states around the gap nodes as 4 component Dirac fermions coupled to SU(2) gauge fields in 2+1 dimensions.
We discuss properties of an exactly SO(5) symmetric ladder model. In the strong coupling limit we demonstrate how the SO(3)-symmetric description of spin ladders in terms of bond Bosons can be upgraded to an SO(5)-symmetric bond-Boson model, which provides a particularly simple example for the concept of SO(5) symmetry. Based on this representation we show that antiferro- magnetism on one hand and superconductivity on the other hand can be understood as condensation of either magnetic or charged Bosons into an RVB vacuum. We identify exact eigenstates of a finite cluster with general multiplets of the SO(5) group, and present numerical results for the single particle spectra and spin/charge correlation functions of the SO(5)-symmetric model and identify `fingerprints' of SO(5) symmetry in these. In particluar we show that SO(5) symmetry implies a `generalized rigid band behavior' of the photoemission spectrum, i.e. spectra for the doped case are rigorously identical to spectra for spin-polarized states at half-filling. We discuss the problem of adiabatic continuity between the SO(5) symmetric ladder and the actual t-J ladder and demonstrate the feasibility of a `Landau mapping' between the two models.
We construct an SO(5) symmetric electron model on a two-chain ladder with purely local interactions on a rung. The ground state phase diagram of this model is determined in the strong-coupling limit. The relationship between the spin-gap magnon mode of the spin-gap insulator and the $π$ resonance mode of the d-wave pairing phase is discussed. We also present the exact ground state for an SO(5) superspin model.
In this paper, we present analytical and numerical calculations of the pi resonance in the t-J model. We show in detail how the pi resonance in the particle-particle channel couples to and appears in the dynamical spin correlation function in a superconducting state. The contribution of the pi resonance to the spin excitation spectrum can be estimated from general model-independent sum rules, and it agrees with our detailed calculations. The results are in overall agreement with the exact diagonalization studies of the t-J model. Earlier calculations predicted the correct doping dependence of the neutron resonance peak in the YBCO superconductor, and in this paper detailed energy and momentum dependence of the spin correlation function is presented. The microscopic equations of motion obtained within current formalism agree with that of the SO(5) nonlinear sigma model, where the pi resonance is interpreted as a pseudo Goldstone mode of the spontaneous SO(5) symmetry breaking.
In this talk I outline the general strategy behind the SO(5) theory of high $T_c$ superconductivity. Progress in the direction of exact SO(5) models, numerical exact diagonalization and possible experimental tests are reviewed. I also address the criticisms raised recently against the SO(5) theory and point out directions for future exploration.
We construct a class of microscopic electron models with exact SO(5) symmetry between antiferromagnetic and d-wave superconducting ground states. There is an exact one-to-one correspondence between both single-particle and collective excitations in both phases. SO(5) symmetry breaking terms can be introduced and classified according to irreducible representations of the exact SO(5) algebra. The resulting phase diagram and collective modes are identical to that of the SO(5) nonlinear sigma model.
We show that a superconducting vortex in underdoped high T_c superconductors could have an antiferromagnetic core. This type of vortex configuration arises as a topological solution in the recently constructed SO(5) nonlinear sigma model and in Ginzburg-Landau theory with competing antiferromagnetic and superconducting order parameters. Experimental detection of this type of vortex by μSR and neutron scattering is proposed.
We derive a continuum equation for the magnetization of a conducting ferromagnet in the presence of a spin-polarized current. Current effects enter in the form of a topological term in the Landau-Lifshitz equation . In the stationary situation the problem maps onto the motion of a classical charged particle in the field of a magnetic monopole. The spatial dependence of the magnetization is calculated for a one-dimensional geometry and suggestions for experimental observation are made. We also consider time-dependent solutions and predict a spin-wave instability for large currents.
Greiter claimed erroneously that the pi-excitation of the Hubbard model has an energy of the order of U. This mistake originates from a inconsistent treatment of the two particle Hartree energy and the Hartee correction to the chemical potential. In any self-consistent calculations, these two contributions cancel exactly, as shown by Kohn, Luttinger and Ward. We also show that his interpretation of the finite-size studies is inconsistent.
This paper gives a simple introduction to the SO(5) theory of high T_c superconductivity. Current status and relation to experiments are summarized.
We present numerical evidence for the approximate SO(5) symmetry of the Hubbard model on a 10 site cluster. Various dynamic correlation functions involving the $π$ operators, the generators of the SO(5) algebra, are studied using exact diagonalisation, and are found to possess sharp collective peaks. Our numerical results also lend support on the interpretation of the recent resonant neutron scattering peaks in the YBCO superconductors in terms of the Goldstone modes of the spontaneously broken SO(5) symmetry.
We show that the complex phase diagram of high $T_c$ superconductors can be deduced from a simple symmetry principle, a $SO(5)$ symmetry which unifies antiferromagnetism with $d$ wave superconductivity. We derive the approximate $SO(5)$ symmetry from the microscopic Hamiltonian and show furthermore that this symmetry becomes exact under the renormalization group flow towards a bicritical point. With the help of this symmetry, we construct a $SO(5)$ quantum nonlinear $σ$ model to describe the effective low energy degrees of freedom of the high $T_c$ superconductors, and use it to deduce the phase diagram and the nature of the low lying collective excitations of the system. We argue that this model naturally explains the basic phenomenology of the high $T_c$ superconductors from the insulating to the underdoped and the optimally doped region.
By mapping the relativistic version of the Chern-Simons-Landau-Ginzburg theory in 2+1 dimensions to the 3D lattice Villain x-y model coupled with the Chern-Simons gauge field, we investigate phase transitions of Chern-Simons bosons in the limit of strong coupling. We construct algebraically exact duality and flux attachment transformations of the lattice theories, corresponding to analogous transformations in the continuum limit. These transformations are used to convert the model with arbitrary fractional Chern-Simons coefficient $α$ to a model with $α$ either zero or one. Depending on this final value of $α$, the phase transition in the original model is either in the universality class of the 3D x-y model or a ``fermionic'' universality class, unless the irrelevant corrections of cubic and higher power in momenta render the transition of the first order.
In this series of papers we present a detailed study of the particle--particle collective excitations of the Hubbard model, and their contribution to the density and spin excitation spectrum. In the first paper, we shall investigate the singlet particle--particle pair with momentum $(π,π)$, the $η$ particle, of the negative--$U$ Hubbard model. We review three previously obtained theorems about the $η$ particle and develop a self-consistent linear response theory which takes into account its contribution to the density excitation spectrum in the superconducting state. We show that this self--consistent theory agrees with the exact theorems as well as the results of numerical Monte Carlo simulations.
Recent polarized neutron scattering experiments on $YBa_2 Cu_3 O_7$ have revealed a sharp spectral peak at the $(π,π)$ in reciprocal lattice centered around the energy transfer of $41\ meV$. We offer a theoretical explanation of this remarkable experiment in terms of a new collective mode in the particle particle channel of the Hubbard model. This collective mode yields valuable information about the symmetry of the superconducting gap.
At strong magnetic fields double-layer two-dimensional-electron-gas systems can form an unusual broken symmetry state with spontaneous inter-layer phase coherence. In this paper we explore the rich variety of quantum and finite-temperature phase transitions associated with this broken symmetry. We describe the system using a pseudospin language in which the layer degree-of-freedom is mapped to a fictional spin 1/2 degree-of-freedom. With this mapping the spontaneous symmetry breaking is equivalent to that of a spin 1/2 easy-plane ferromagnet. In this language spin-textures can carry a charge. In particular, vortices carry e/2 electrical charge and vortex-antivortex pairs can be neutral or carry charge e. We derive an effective low-energy action and use it to discuss the charged and collective neutral excitations of the system. We have obtained the parameters of the Landau-Ginzburg functional from first-principles estimates and from finite-size exact diagonalization studies. We use these results to estimate the dependence of the critical temperature for the Kosterlitz-Thouless phase transition on layer separation.
We study the phase transition between the quantum Hall liquid state and the insulating state within the framework of the Chern-Simons-Landau-Ginzburg theory of the quantum Hall effect. For the transition induced by a background periodic potential in the absence of disorder, the model is described by a relativistic scalar field coupled to the Chern-Simons gauge field. For this system, we show that the transition is of the first order, induced by the fluctuations of the gauge field, rather than second order, with statistical angle-dependent scaling exponent.