Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0106473 · Physical Review Letters

Phase Diagram and Dynamics of the Projected SO(5) Symmetric Model of High- Tc Superconductivity

Ansgar Dorneich, Werner R. Hanke, Enrico Arrigoni, Matthias Troyer, Shoucheng Zhang

Published Jan 22, 2002• 24 citations
arXivHTMLPDF

Abstract

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 their physical properties. Moreover, we address the question of asymptotic restoring of the SO(5) symmetry at the critical point.

DOI
10.1103/physrevlett.88.057003

Related papers

Projected SO(5) models

Shoucheng Zhang, Jiangping Hu, Enrico Arrigoni +2 more

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-${T}_{c}$ superconductors and account for many of their physical properties.

arXiv:cond-mat/9904142•Physical review. B, Condensed matter•Nov 1, 1999•52 citations

Phase Diagram of a Superconducting and Antiferromagnetic System with SO(5) Symmetry

Xiao Hu, Tomio Koyama, Masashi Tachiki

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 near the cross point of the AF transition line and the first-order melting line of flux lattice; there is a tricritical point on the AF transition line from which the AF ordering becomes second order.

arXiv:cond-mat/9812031•Physical Review Letters•Mar 22, 1999•20 citations

Global Phase Diagram of the High-Tc Cuprates

Han-Dong Chen

We propose a bosonic effective quantum Hamiltonian based on the projected SO(5) model with extended interactions, which can be derived from the microscopic models of the cuprates. The global phase diagram of this model is obtained using mean‐field theory and the quantum Monte Carlo simulation. We show that this single quantum model can account for most salient features observed in the high‐Tc cuprates, with different families of the cuprates attributed to different traces in the global phase diagram. A particular prediction of this theory is the checkerboard state of the d‐wave hole pairs formed at certain magic filling fractions. We shall describe various properties of this state and present evidence that this novel state has been detected in recent STM and transport experiments.

AIP conference proceedings•Jan 1, 2006•4 citations

Global phase diagram of the high- Tc cuprates

Han-Dong Chen, Sylvain Capponi, Fabien Alet +1 more

The high-${T}_{c}$ cuprates have a complex phase diagram with many competing phases. We propose a bosonic effective quantum Hamiltonian based on the projected $\text{SO}(5)$ model with extended interactions, which can be derived from the microscopic models of the cuprates. The global phase diagram of this model is obtained using mean-field theory and the quantum Monte Carlo simulation, which is possible because of the absence of the minus sign problem. We show that this single quantum model can account for most salient features observed in the high-${T}_{c}$ cuprates, with different families of the cuprates attributed to different traces in the global phase diagram. Experimental consequences are discussed and theoretical predictions are presented.

arXiv:cond-mat/0312660•Physical Review B•Jul 26, 2004•24 citations

SU(4) Model of High-Temperature Superconductivity: Manifestation of Dynamical Symmetry in Cuprates

Yang Sun

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 order; an SU(2) limit that may be interpreted as a d‐wave pairing condensate; and an SO(5) limit that may be interpreted as a doorway state between the antiferromagnetic order and the superconducting order. It is demonstrated that with a slightly broken SO(5) but under constraint of the parent SU(4) symmetry, the model is capable of describing the rich physics that is crucial in explaining why cuprate systems that are antiferromagnetic Mott insulators at half filling become superconductors through hole doping.

arXiv:cond-mat/0502074•AIP conference proceedings•Jan 1, 2005•1 citation

Simulation of fermionic and bosonic critical points with emergent SO(5) symmetry

Toshihiro Sato, Zhenjiu Wang, Yuhai Liu +4 more

We introduce a model of Dirac fermions in $2+1$ dimensions with a semimetallic, a quantum spin-Hall insulating (QSHI), and an $s$-wave superconducting (SSC) phase. The phase diagram features a multicritical point at which all three phases meet as well as a QSHI-SSC deconfined critical point. The QSHI and SSC orders correspond to mutually anticommuting mass terms of the Dirac Hamiltonian. Based on this algebraic property, SO(5) symmetric field theories have been put forward to describe both types of critical points. Using quantum Monte Carlo simulations, we directly study the operator that rotates between QSHI and SSC states. The results suggest that it commutes with the low-energy effective Hamiltonian at criticality but has a gap in the ordered phases. This implies an emergent SO(5) symmetry at both the multicritical and the deconfined critical points.

arXiv:2212.11395•Physical review. B./Physical review. B•Sep 21, 2023•3 citations
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 their physical properties. Moreover, we address the question of asymptotic restoring of the SO(5) symmetry at the critical point.
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-Tc{T}_{c}Tc​ superconductors and account for many of their physical properties.
Temperature vs chemical-potential phase diagrams of an SO(5) model for high- Tc{T}_{c}Tc​ 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 near the cross point of the AF transition line and the first-order melting line of flux lattice; there is a tricritical point on the AF transition line from which the AF ordering becomes second order.
We propose a bosonic effective quantum Hamiltonian based on the projected SO(5) model with extended interactions, which can be derived from the microscopic models of the cuprates. The global phase diagram of this model is obtained using mean‐field theory and the quantum Monte Carlo simulation. We show that this single quantum model can account for most salient features observed in the high‐Tc cuprates, with different families of the cuprates attributed to different traces in the global phase diagram. A particular prediction of this theory is the checkerboard state of the d‐wave hole pairs formed at certain magic filling fractions. We shall describe various properties of this state and present evidence that this novel state has been detected in recent STM and transport experiments.
The high-Tc{T}_{c}Tc​ cuprates have a complex phase diagram with many competing phases. We propose a bosonic effective quantum Hamiltonian based on the projected SO(5)\text{SO}(5)SO(5) model with extended interactions, which can be derived from the microscopic models of the cuprates. The global phase diagram of this model is obtained using mean-field theory and the quantum Monte Carlo simulation, which is possible because of the absence of the minus sign problem. We show that this single quantum model can account for most salient features observed in the high-Tc{T}_{c}Tc​ cuprates, with different families of the cuprates attributed to different traces in the global phase diagram. Experimental consequences are discussed and theoretical predictions are presented.
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 order; an SU(2) limit that may be interpreted as a d‐wave pairing condensate; and an SO(5) limit that may be interpreted as a doorway state between the antiferromagnetic order and the superconducting order. It is demonstrated that with a slightly broken SO(5) but under constraint of the parent SU(4) symmetry, the model is capable of describing the rich physics that is crucial in explaining why cuprate systems that are antiferromagnetic Mott insulators at half filling become superconductors through hole doping.
We introduce a model of Dirac fermions in 2+12+12+1 dimensions with a semimetallic, a quantum spin-Hall insulating (QSHI), and an sss-wave superconducting (SSC) phase. The phase diagram features a multicritical point at which all three phases meet as well as a QSHI-SSC deconfined critical point. The QSHI and SSC orders correspond to mutually anticommuting mass terms of the Dirac Hamiltonian. Based on this algebraic property, SO(5) symmetric field theories have been put forward to describe both types of critical points. Using quantum Monte Carlo simulations, we directly study the operator that rotates between QSHI and SSC states. The results suggest that it commutes with the low-energy effective Hamiltonian at criticality but has a gap in the ordered phases. This implies an emergent SO(5) symmetry at both the multicritical and the deconfined critical points.