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AIP conference proceedings

Global Phase Diagram of the High-Tc Cuprates

Han-Dong Chen

Published Jan 1, 2006• 4 citations
Publisher

Abstract

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.

DOI
10.1063/1.2178037

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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.
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 develop a classical Monte Carlo algorithm based on a quasi-classical approximation for a pseudospin S = 1 Hamiltonian in real space to construct a phase diagram of a model cuprate with a high T c . A model description takes into account both local and nonlocal correlations, Heisenberg spin-exchange interaction, correlated single-particle, and two-particle transport. We formulate a state selection algorithm for a given parameterization of the wave function in order to ensure a uniform distribution of states in the phase space. The simulation results show a qualitative agreement with the experimental phase diagrams.
A possibility of holon (boson) pair condensation is explored for hole-doped high-Tc{T}_{c}Tc​ cuprates, by using the U(1)U(1)U(1) slave-boson representation of the $t\ensuremath{-}J$ Hamiltonian with the inclusion of hole-hole repulsion. A phase diagram of the hole doped high-Tc{T}_{c}Tc​ cuprates is deduced by allowing both the holon pairing and spinon pairing channels. It is shown that the spin gap size remains nearly unchanged below the holon pair condensation temperature. We find that the s-wave holon pairing under the condition of d-wave spin singlet pairing is preferred, thus allowing d-wave hole pairing.
The extended Hubbard model describes fermions on a lattice coupled through on-site, UUU, and first-neighbor, VVV, interactions. In the context of high-Tc{T}_{c}Tc​ cuprates, antiferromagnetic fluctuations may lead to an attractive channel, hence to superconductivity. Despite interest in the two-dimensional version of the model, the current knowledge about the phase diagram is still far from complete. Here, we report on the results of extensive determinant quantum Monte Carlo simulations for this model at half filling, in which we have used the average sign of the product of fermionic determinants as an additional observable to locate critical points. We arrive at a ground state phase diagram in the $U\text{\ensuremath{-}}V$ plane in which the boundaries involving antiferromagnetic, charge-ordered, sss- and ddd-wave superconductivity, and phase-separated phases are quantitatively set with good accuracy. We have also proposed a partial phase diagram, Tc(U,V){T}_{c}(U,V)Tc​(U,V), featuring critical temperatures for the charge-density wave and sss-wave superconducting phases.
We show in a mean-field calculation that phase diagrams remarkably similar to those recently proposed for the cuprates arise in simple microscopic models of interacting electrons near half-filling. The models are extended Hubbard models with nearest-neighbor interaction and correlated hopping. The underdoped region of the phase diagram features ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ density-wave (DDW) order. In a certain regime of temperature and doping, DDW order coexists with antiferromagnetic order. For larger doping, it coexists with ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity. While phase diagrams of this form are robust, they are not inevitable. For other reasonable values of the coupling constants, drastically different phase diagrams are obtained. We comment on implications for the cuprates.