Doped Mott Matter and the Pseudogap Evidence Problem

A pseudogap is an operational suppression of low-energy spectral weight without a complete charge gap. In doped Mott matter it is established most securely by consistent momentum-resolved spectra, local density of states, spin response, and thermodynamics. Those observables do not by themselves select a unique mechanism: short-range antiferromagnetism, precursor pairing, intertwined order, correlation-driven zeros, and fractionalized descriptions can overlap over finite temperature windows.

Required background. Use spectral-weight transfer and cluster-DMFT validity. Helpful background. Competing orders and ARPES inference supply key alternatives and probe effects.

Operational pseudogap definitions

For a specified momentum sector, define a spectral pseudogap by a suppression of $A(\mathbf k,\omega)$ around $\omega=0$ relative to both neighboring frequencies and a controlled high-temperature or doping baseline. A local pseudogap uses $A_{\mathrm{loc}}(0)$; a spin pseudogap uses suppression of the uniform spin susceptibility or low-frequency spin spectral weight. These crossover temperatures need not coincide.

Cluster methods commonly find momentum differentiation: antinodal low-energy weight is suppressed before nodal weight. A multi-observable statement should report

$$A(\mathbf k,\omega),\qquad \chi_s(T),\qquad \kappa(T),\qquad S(\mathbf q,\omega),\qquad S_{\mathrm{therm}}(T),$$

with normalizations, temperature, doping, and uncertainty. No single entry is a mechanism label.

Method and probe dependence

Cluster size and geometry determine the available momenta; periodizing $\Sigma$, the cumulant, or $G$ can move apparent gap edges. Analytic continuation broadens and correlates spectral features. In photoemission, matrix elements, backgrounds, surface conditions, and resolution modify intensity. Broken symmetry, disorder, or selection of one data subset can also suppress low-energy weight.

Within the two-dimensional Hubbard model, cluster calculations establish pseudogap regimes in specified parameter windows and show nontrivial competition with superconductivity Gull, Parcollet, and Millis 2013, article 216405. That model result does not uniquely identify the origin of every cuprate pseudogap. The broader material evidence and competing frameworks are reviewed in Keimer et al. 2015, pp. 179–186.

Evidence boundary through 10 August 2026

Sources checked through 10 August 2026 continue to support a pseudogap in doped Hubbard-model regimes while differing in approximation and mechanism emphasis. For example, a real-frequency TPSC+DMFT calculation links the suppression to nonlocal spin fluctuations in its moderate-coupling domain Geng, Yan, and Werner 2025, §§ III–IV, whereas cluster-DMFT results retain strong-coupling and momentum-selective interpretations. This agreement on an operational phenomenon does not close the causal question. Changing model, material, and method assessments belong in the dated Quantum Matter and Emergence Research record.

A defensible conclusion therefore states the observed suppression, its momentum and probe dependence, the controlled method domain, and the alternatives still compatible with the data. It does not turn “pseudogap” into a unique phase or pairing mechanism.

Exercises

A continued cluster spectrum shows suppressed antinodal $A(\mathbf k,0)$, but imaginary-time $G(\mathbf k,\beta/2)$ changes only within error when the cluster is enlarged. What is the strongest conclusion?

Solution

The finite-cluster continuation suggests an antinodal suppression, but its thermodynamic robustness is not established. One should report the continuation- and cluster-dependent tendency, examine covariance and alternative periodizations, and avoid a phase or mechanism claim until an imaginary-axis or size-stable observable corroborates it.

References

• Lei Geng, Jiawei Yan, and Philipp Werner, “Two-Particle Self-Consistent Approach Combined with Dynamical Mean Field Theory: A Real-Frequency Study of the Square-Lattice Hubbard Model,” Physical Review B 111 (2025) 115143, doi:10.1103/PhysRevB.111.115143.
• Emanuel Gull, Olivier Parcollet, and Andrew J. Millis, “Superconductivity and the Pseudogap in the Two-Dimensional Hubbard Model,” Physical Review Letters 110 (2013) 216405, doi:10.1103/PhysRevLett.110.216405, Open PDF.
• Bernhard Keimer, Steven A. Kivelson, Michael R. Norman, Shin-ichi Uchida, and Jan Zaanen, “From Quantum Matter to High-Temperature Superconductivity in Copper Oxides,” Nature 518 (2015) 179–186, doi:10.1038/nature14165.