Phase Diagram and Dynamics of the Projected SO(5) Symmetric Model of High-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>Superconductivity

Dorneich, A.; Hanke, W.; Arrigoni, Enrico; Troyer, Matthias; Zhang, SC

doi:10.1103/physrevlett.88.057003

Cited by 28 publications

(42 citation statements)

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“…We apply the Contractor Renormalization (CORE) method of Morningstar and Weinstein 5 to the plaquettized lattice (see Fig.1) in a one step transformation. We find that the bosonic part of the effective Hamiltonian is closely related to the projected SO(5) (pSO(5)) theory 6,7 ; a theory of four bosons: a hole pair and a (antiferro)magnon triplet. The pSO(5) model describes the competition between antiferromagnetism and superconductivity in a quantum mechanical framework.…”

Section: Introductionmentioning

confidence: 99%

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Plaquette boson-fermion model of cuprates

2002

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The strongly interacting Hubbard model on the square lattice is reduced to the low energy Plaquette Boson Fermion Model (PBFM). The four bosons (an antiferromagnon triplet and a d-wave hole pair), and the fermions are defined by the lowest plaquette eigenstates. We apply the Contractor Renormalization method of Morningstar and Weinstein to compute the boson effective interactions. The range-3 truncation error is found to be very small, signaling short hole-pair and magnon coherence lengths. The pair-hopping and magnon interactions are comparable, which explains the rapid destruction of antiferromagnetic order with emergence of superconductivity, and validates a key assumption of the projected SO(5) theory. A vacuum crossing at larger doping marks a transition into the overdoped regime. With hole fermions occupying small Fermi pockets and Andreev coupled to hole pair bosons, the PBFM yields several testable predictions for photoemmission, tunneling asymmetry and entropy measurements.

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Section: Introductionmentioning

confidence: 99%

“…(7,17) for the magnon and hole pair expectation values. These coefficients, which determine the transition temperatures, as well as the doping concentration x are plotted as a function of chemical potential in Fig.8.…”

Section: Four Boson Mean Field Theorymentioning

confidence: 99%

Plaquette boson-fermion model of cuprates

2002

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“…-0.6 10 -1 -1 0. 4 -3 For J c ∼ 2, H 0 is approximately SO(5) symmetric at the mean field level 27,30,33 .…”

Section: Hamiltonian Of the Modelmentioning

confidence: 99%

“…Therefore, simulations can be carried out for systems with sizes much larger than the ones available with fermionic QMC simulation in the physically interesting region. The pioneering numerical works 30,31,32,33,74,75 show that the projected SO(5) model can give a realistic description of the phase diagram of the HTSC cuprates and account for many of their physical properties. In this section, we shall present the simulation of the SO(5) model with extended interactions using the Stochastic Series Expansion (SSE) method 76,77,78 with operator-loop update 78 .…”

Section: Phase Diagram Obtained From Quantum Monte-carlo Simulatiomentioning

confidence: 99%

“…Restricted within the subspace of these five local states, the Hamiltonian describing their propagation and interaction is completely expressed in terms of bosonic operators and can be studied reliably by the quantum Monte Carlo (QMC) calculations. The simplest form of the projected SO(5) model has been studied extensively by the QMC method both in two dimensions 30,31,32 and in three dimensions 33 . The overall topology of the phase diagram, the scaling properties near the multi-critical point and the nature of the collective excitations can be reliably obtained from the QMC method, within the parameter regime of experimental interests.…”

Section: Introductionmentioning

confidence: 99%

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Global Phase Diagram of the High-Tc Cuprates

Chen¹,

Zhang²

2006

AIP Conference Proceedings

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The high Tc cuprates have a complex phase diagram with many competing phases. 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, 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 cuprates, with different families of the cuprates attributed to different traces in the global phase diagram. Experimental consequences are discussed and new theoretical predictions are presented.

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Antiferromagnetic and superconducting gaps and their interrelation in high-Tc cuprates

Arrigoni¹,

Zacher²,

Eckl³

et al. 2003

Ann. Phys.

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This work is dedicated to Professor E. Müller-Hartmann on the occasion of his 60 th birthday.We propose a phenomenological model, comprising a microscopic SO(5) model plus the on-site Hubbard interaction U (projected SO(5) model) to understand the interrelation between the d-wave-gap modulation observed by recent angle-resolved photoemission experiments in the insulating antiferromagnet Ca2CuO2Cl2 and the d-wave gap of high-Tc superconducting materials. The on-site interaction U is important in order to produce a Mott gap of the correct order of magnitude, which would be absent in an exact SO(5) theory. The projected SO(5)-model explains the gap characteristics, namely both the symmetry and the different order of magnitude of the gap modulations between the antiferromagnetic and the superconducting phases. Furthermore, it is shown that the projected SO(5) theory can provide an explanation for a recent observation [E. Pavarini et al., Phys. Rev. Lett. 87, 47003 (2001)], i. e. that the maximum Tc observed in a large variety of high-Tc cuprates scales with the next-nearest-neighbor hopping matrix element Ann. Phys. (Leipzig) 12, No. 5 (2003) 321 the Hilbert space. The central hypothesis of the projected-SO(5) (p-SO(5) ) theory is that the model is accurate in describing both the static and dynamic properties in the high-T c superconductors (HTSC).On the basis of a numerically exact Quantum-Monte-Carlo (QMC) calculation of the p-SO(5) bosonic model, it has recently indeed been shown that this model gives a realistic description of the phase diagram of the HTSC materials and properly accounts for many of their physical properties [10]. Among those are the neutron-scattering resonance, which appears as a Goldstone mode in the p-SO(5) description, as well as an unusual chemical potential dependence on doping found in the prototype material La 2−x Sr x CuO 4 [11], which signals a possible (microscopic) phase separation [12]. One crucial point of this bosonic p-SO(5) model is that, on the basis of a newly implemented Stochastic Series Expansion QMC technique, it can be simulated up to unprecedented system sizes of about 10 4 sites, which is more than one order of magnitude larger than corresponding fermionic QMC simulations. This fact allowed, for the first time, for an approximate finite-size-study of the p-SO(5) bosonic model in the three-dimensional case, and for extracting the scaling properties close to the bicritical (AF-SC) point. The numerical results point to a partial asymptotic restoring of the SO(5) symmetry at this critical point, i. e. at long distances. This is very interesting, since the projection destroys the symmetry at the Hamiltonian level (The Hamiltonian no longer commutes with the SO(5) generators). While the mean-field classical p-SO(5) Hamiltonian of [8] conserves its SO(5) invariant form, quantum fluctuations break the symmetry. However, as shown in [13], at finite temperature quantum fluctuations become less and less important, and one can hope that symmetry-breaking effects due to the proje...

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

Cited by 28 publications

References 25 publications

Plaquette boson-fermion model of cuprates

Plaquette boson-fermion model of cuprates

Global Phase Diagram of the High-Tc Cuprates

Antiferromagnetic and superconducting gaps and their interrelation in high-Tc cuprates

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