Excitation spectra of quantum matter without quasiparticles II: random $t$-$J$ models

Abstract

We present numerical solutions of the spectral functions of $t$-$J$ models with random and all-to-all exchange and global SU($M$) spin rotation symmetry. The solutions are obtained from the saddle-point equations of the large volume limit, followed by the large $M$ limit. These saddle point equations involve Green's functions for fractionalized spinons and holons carrying emergent U(1) gauge charges, obeying relations similar to those of the Sachdev-Ye-Kitaev (SYK) models. The low frequency spectral functions are compared with an analytic analysis of the operator scaling dimensions, with good agreement. We also compute the low frequency and temperature behavior of gauge-invariant observables: the electron Green's function, the local spin susceptibility and the optical conductivity; along with the temperature dependence of the d.c. resistivity. The time reparameterization soft mode (equivalent to the boundary graviton in holographically dual models of two-dimensional quantum gravity) makes important contributions to all observables, and provides a linear-in-temperature contribution to the d.c. resistivity.

40 pages, 15 figures

References in corpus (4)

• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• A Generalization of Sachdev-Ye-Kitaev
• Dispersive SYK model: band structure and quantum chaos
• Quantum phase transition at non-zero doping in a random $t$-$J$ model

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• Non-local reparametrization action in coupled Sachdev-Ye-Kitaev models
• Quantum phase transition at non-zero doping in a random $t$-$J$ model
• Critical metallic phase in the overdoped random $t$-$J$ model
• Thermalization at Low Temperatures via Weakly-Damped Multi-Site Baths
• A unified theory of strong coupling Bose polarons: From repulsive polarons to non-Gaussian many-body bound states
• $\mathcal{N}=2$ SYK models with dynamical bosons and fermions
• Precise Low-Temperature Expansions for the Sachdev-Ye-Kitaev model
• The quantum $p$-spin glass model: A user manual for holographers
• High-frequency transport and zero-sound in an array of SYK quantum dots
• Critical anomalous metals near superconductivity in models with random interactions
• Near-Equilibrium Approach to Transport in Complex Sachdev-Ye-Kitaev Models