November 5, 2002
Previously one of us presented a conjecture [APF-4 Proceedings] to model antiferromagnetism and high temperature superconductivity and their 'unification' by quantum group symmetry rather than the corresponding classical symmetry in view of the critique by Baskaran and Anderson of Zhang's classical SO(5) model. This conjecture was further sharpened, experimental evidence and the important role of 1-d systems [stripes] was emphasized and moreover the relationship between quant...
July 10, 1998
We study excitations of the predicted antiferromagnetically ordered vortex cores in the superconducting phase of the newly proposed SO(5) model of strongly correlated electrons. Using experimental data from the literature we show that the susceptibilities in the spin sector and the charge sector are nearly equal, and likewise for the stiffnesses. In the case of strict equality SO(5) symmetry is possible, and we find that if present the vortices give rise to an enhanced neutro...
March 16, 2004
Motivated by recent experiments with Bechgaard salts, we investigate the competition between antiferromagnetism and triplet superconductivity in quasi one-dimensional electron systems. We unify the two orders in an SO(4) symmetric framework, and demonstrate the existence of such symmetry in one-dimensional Luttinger liquids. SO(4) symmetry, which strongly constrains the phase diagram, can explain coexistence regions between antiferromagnetic, superconducting, and normal phase...
January 28, 1998
It has been proposed that the effective Hamiltonian describing high T_c superconductivity in cuprate materials has an approximate SO(5) symmetry relating the superconducting (SC) and antiferromagnetic (AF) phases of these systems. We show that robust consequences of this proposal are potentially large optical conductivities and Raman scattering rates in the AF phase, due to the electromagnetic response of the doubly-charged pseudo Goldstone bosons which must exist there. This...
February 2, 2005
The mechanism that leads to high-temperature superconductivity in cuprates remains an open question despite intense study for nearly two decades. Here, we introduce an SU(4) model for cuprate systems having many similarities to dynamical symmetries known to play an important role in nuclear structure physics and in elementary particle physics. Analytical solutions in three dynamical symmetry limits of this model are found: an SO(4) limit associated with antiferromagnetic orde...
April 10, 1999
We construct a class of projected SO(5) models where the Gutzwiller constraint of no-double-occupancy is implemented exactly. We introduce the concept of projected SO(5) symmetry where all static correlation functions are exactly SO(5) symmetric and discuss the signature of the projected SO(5) symmetry in dynamical correlation functions. We show that this class of projected SO(5) models can give a realistic description of the global phase diagram of the high T_c superconducto...
August 16, 2002
An SU(4) model of high-temperature superconductivity and antiferromagnetism has recently been proposed. The SO(5) group employed by Zhang is embedded in this SU(4) as a subgroup, suggesting a connection between our SU(4) model and the Zhang SO(5) model. In order to understand the relationship between the the two models, we have used generalized coherent states to analyze the nature of the SO(5) subgroup. By constructing coherent-state energy surfaces, we demonstrate explicitl...
May 21, 1997
We set up the effective field theories which describe the SO(5)-invariant picture of the high-Tc cuprates in various regimes. We use these to get quantitative conclusions concerning the size of SO(5)-breaking effects. We consider two applications in detail: (i) the thermodynamic free energy, which describe the phase diagram and critical behaviour, and (ii) the Lagrangian governing the interactions of the pseudo-Goldstone bosons with each other and with the electron quasiparti...
November 11, 2000
By large scale Monte Carlo simulations it is shown that the stable fixed point of the SO(5) theory is either bicritical or tetracritical depending on the effective interaction between the antiferromagnetism and superconductivity orders. There are no fluctuation-induced first-order transitions suggested by epsilon expansions. Bicritical and tetracritical scaling functions are derived for the first time and critical exponents are evaluated with high accuracy. Suggestions on exp...
July 28, 1997
Zhang recently conjectured an approximate SO(5) symmetry relating antiferromagnetic and superconducting states in high-T_c cuprates. Here, an exact SO(5) symmetry is implemented in a generalized Hubbard model (with long-range interactions) on a lattice. The possible relation to a more realistic extended Hubbard Hamiltonian is discussed.