May 3, 2004
Antiferromagnetism and superconductivity are both fundamental and common states of matter. In many strongly correlated systems, including the high Tc cuprates, the heavy fermion compounds and the organic superconductors, they occur next to each other in the phase diagram and influence each other's physical properties. The SO(5) theory unifies these two basic states of matter by a symmetry principle and describes their rich phenomenology through a single low energy effective model. In this paper, we review the framework of the SO(5) theory, and its detailed comparison with numerical and experimental results.
Similar papers 1
April 16, 1997
This paper gives a simple introduction to the SO(5) theory of high T_c superconductivity. Current status and relation to experiments are summarized.
May 31, 1999
We use generalized coherent states to analyze the SO(5) theory of high-temperature superconductivity and antiferromagnetism. We demonstrate that the SO(5) symmetry can be embedded in a larger algebra that allows it to be interpreted as a critical dynamical symmetry interpolating between antiferromagnetic and superconducting phases. This dynamical interpretation suggests that SO(5) defines a phase with the character of a spin-glass for a significant range of doping.
September 26, 1997
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.
June 22, 2001
We present numerical studies of a quantum ``projected'' SO(5) model which aims at a unifying description of antiferromagnetism and superconductivity in the high-T$_c$ cuprates, while properly taking into account the Mott insulating gap. Our numerical results, obtained by the Quantum Monte Carlo technique of Stochastic Series Expansion, show that this model can give a realistic description of the global phase diagram of the high-$T_c$ superconductors and accounts for many of t...
May 19, 1999
A model unifying superconductivity and antiferromagnetism using an underlying approximate SO(5) symmetry has injected energy into the field of high-temperature superconductivity. This model might lead to a variety of interesting solitons. In this paper, the idea that superconducting vortices may have antiferromagnetic cores is presented, along with the results of some preliminary numerical work. An outlook for future work, including speculations about other possible exotic so...
March 9, 1999
We present an SU(4) model of high-$T_c$ superconductivity. One dynamical symmetry of this model corresponds to the previously proposed SO(5) model for unification of superconductivity and antiferromagnetism, but there are two additional dynamical symmetries: SO(4), associated with antiferromagnetic order and SU(2), associated with a D-wave pairing condensate. These provide a 3-phase microscopic model of high-$T_c$ superconductivity and permit a clear understanding of the role...
July 22, 1997
In this work, we present numerical results which support SO(5) symmetry as a concept unifying superconductivity and antiferromagnetism in the high-temperature superconductors. Using exact cluster diagonalization, we verify the recently proposed SO(5) multiplet structures for a widely used microscopic model, the t-J model. Our results show that the d-wave superconducting ground states away from half-filling are obtained from the higher spin states at half-filling through SO(5)...
October 17, 1996
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 $\sigma$ ...
December 2, 1998
Temperature vs. chemical-potential phase diagrams of an SO(5) model for high-(T_c) cuprates are calculated by Monte Carlo simulation. There is a bicritical point where the second-order antiferromagnetism (AF) and superconductivity transition lines merge tangentially into a first-order line, and the SO(5) symmetry is achieved. In an external magnetic field, the AF ordering is first order in the region where the first-order melting line of flux lattice joins in. There is a tric...
November 10, 1996
We construct the low-energy effective theory for the SO(5) model of high-T_c superconductivity, recently proposed by S.C. Zhang (cond-mat/9610140). This permits us to develop a systematic expansion for low-energy observables in powers of the small symmetry-breaking interactions. The approximate SO(5) symmetry predicts relations amongst these observables, which are model-independent consequences of Zhang's proposed symmetry-breaking pattern.