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arXiv:cond-mat/0312660 · Physical Review B

Global phase diagram of the high- Tc cuprates

Han-Dong Chen, Sylvain Capponi, Fabien Alet, Shoucheng Zhang

Published Jul 26, 2004• 24 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.70.024516

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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.
Abstract We benchmark five microscopic cuprate superconductivity theories against ten experimental constraints using continuous figures of merit fi∈[0,1]f_i\in[0,1]fi​∈[0,1] with explicit acceptance windows. At mean-field level, Model~B (SVILC) scores highest (F=0.96±0.02F=0.96\pm0.02F=0.96±0.02), followed by Model~E (spin fluctuation, 0.91±0.030.91\pm0.030.91±0.03). Failure analysis identifies four ingredients that appear necessary at mean-field level: Mott physics, spin-fluctuation pairing, loop-current order, and three-band CuO2_22​ structure. A unified Hamiltonian incorporating all four yields Δ0=28\Delta_0=28Δ0​=28~meV and μorb=0.06  μB\mu_{\mathrm{orb}}=0.06\;\mu_{ B }μorb​=0.06μB​/Cu on a 24×2424\times2424×24 cluster. The multi-observable scoring framework provides concrete targets for quantum simulation of cuprate Hamiltonians and enables systematic validation of quantum-computed phase diagrams. Four falsifiable predictions are derived.
High-temperature superconductivity in copper oxides (cuprates, e.g. La2−xSrxCuO4, YBa2Cu3O6+δ or Bi2Sr2CaCu2O8+δ) remains among the most spectacular phenomena in condensed matter physics. Since its discovery in 1986, an enormous number (∼ 105) of papers on the subject have appeared. So far, there is no single, commonly accepted theory of high-temperature superconductivity. However, it is widely believed that a basic description of this phenomenon can be provided by a single-band Hubbard model or its derivative, the t-J model. The latter model is regarded as a minimal microscopic model, capable of describing the essential aspects of the complex physics of the cuprates. Unfortunately, in general case, neither of those two models can be solved exactly and therefore various approximate methods are used. Among them, the so-called mean-field methods provide a simple, yet fairly reasonable description of the cuprates. In particular, some of the main qualitative features of the phase diagram and the essential features of electronic spectrum are roughly reproduced. A standard mean-field approach to the t-J model, known under the name of renormalized mean-field theory (RMFT) goes beyond the Hartree-Fock approximation. Consequently, its fully consistent treatment requires a novel theoretical approach. This has been our original motivation to develop a general approach to the mean-field models, which is based on the maximum entropy (MaxEnt) principle. The method is presented in detail in Part II of this Thesis, and in Part III it is applied to study RMFT of the t-J model. First, we compare the results obtained within our formalism with those of the frequently used non-variational approach based entirely on the self-consistent equations. Also, various versions of RMFT are compared, and the most satisfactory of them is selected. This optimal version is subsequently used to study different versions of the original t-J Hamiltonian. As a result, upper critical concentration and doping dependence of the selected physical quantities (e.g. the superconducting gap and the Fermi velocity) is determined at low temperatures and in the absence of external magnetic field. We compare our findings both with theoretical results obtained from the Variational Monte Carlo (VMC) methods, as well as with the experimental data for selected cuprates. We show that the version of RMFT approach formulated in this Thesis provides a reasonable qualitative and in some cases semiquantitative rationalization of the principal characteristics of the hole-doped high-temperature superconductors at the optimal doping and in the overdoped regime. Possible extensions of the proposed analysis are mentioned at the end.
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.
Based on an improved SU(2) slave-boson approach showing coupling between the charge and spin degrees of freedom, we derive a phase diagram of high-Tc{T}_{c}Tc​ cuprates which displays both the superconducting and pseudogap phases in the plane of temperature vs hole doping rate. It is shown that phase fluctuations in the order parameters result in a closer agreement with the observed phase diagram of an arch shape, by manifesting the presence of an optimal doping rate closer to observation, compared to the U(1) slave-boson theory.