Mottness collapse and statistical quantum criticality

Abstract

We forward here the case that the anomalous electron states found in cuprate superconductors and related systems are rooted in a deeply non-classical fermion sign structure. The collapse of Mottness as advocated by Phillips and supported by recent DCA results on the Hubbard model is setting the necessary microscopic conditions. The crucial insight is due to Weng who demonstrated that in the presence of Mottness the fundamental workings of quantum statistics changes and we will elaborate on the effects of this Weng statistics with an emphasis on characterizing these further using numerical methods. The pseudogap physics of the underdoped regime appears as a consequence of the altered statistics and the profound question is how to connect this by a continuous quantum phase transition to the overdoped regime ruled by normal Fermi-Dirac statistics. Proof of principle follows from Ceperley's constrained path integral formalism where states can be explicitly constructed showing a merger of Fermi-Dirac sign structure and scale invariance of the quantum dynamics.

27 pages, 4 figures, submitted to theme issue of Phil. Trans. R. Soc. A

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• Critical role of the sign structure in the doped Mott insulator: Superconductivity vs. Fermi liquid
• Mott-driven BEC-BCS crossover in a doped spin liquid candidate, kappa-(BEDT-TTF)4Hg2.89Br8
• Two-Hole Ground State: Dichotomy in Pairing Symmetry
• Low-temperature spin dynamics of a valence bond glass in Ba2YMoO6
• Charge modulation as fingerprints of phase-string triggered interference
• Universal features of Thermopower in High Tc systems and Quantum Criticality
• Low-Temperature Pseudogap Phenomenon: Precursor of High-$T_c$ Superconductivity
• Electron fractionalization and unconventional order parameters of the t-J model
• Hidden spin current in doped Mott antiferromagnets
• Two-hole ground state wavefunction: Non-BCS pairing in a $t$-$J$ two-leg ladder system
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• Intrinsic translational symmetry breaking in a doped Mott insulator
• Mott physics, sign structure, ground state wavefunction, and high-Tc superconductivity
• Exact sign structure of the $t$-$J$ chain and the single hole ground state
• Modern Physics of the Condensed State: Strong Correlations and Quantum Topology
• Charge-spin mutual entanglement: A case study by exact diagonalization of the one hole doped $t$-$J$ loop
• Phenomenological Single-Particle Green's Function for the Pseudogap and Superconducting Phases of High-T${}_c$ Cuprates
• Crossover from Fermi Arc to Full Fermi Surface
• Topological states in strongly correlated systems
• Monopoles, confinement and charge localization in the t-J model with dilute holes
• Mottness, Phase String, and High-$T_c$ Superconductivity
• Revealing quantum phase string effect in doped Mott-insulator: a tensor network state approach
• Pseudogap and strange metal states in the square-lattice Hubbard model: A comprehensive study
• An Emergent World of Gauge Force and Partons
• Quantum entanglement in the t-J chain: From charge-spin separation to recombination
• Strange Metals from Quantum Geometric Fluctuations of Interfaces