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

TL;DR

This paper numerically analyzes the spectral functions of random $t$-$J$ models with SU(M) symmetry, revealing insights into their low-frequency behavior, gauge invariance, and temperature-dependent resistivity, drawing parallels with SYK models.

Contribution

It introduces a numerical solution framework for spectral functions in random $t$-$J$ models, connecting saddle-point equations with SYK-like relations and analyzing gauge-invariant observables.

Findings

Good agreement between numerical spectral functions and analytic operator scaling dimensions.

Identification of the time reparameterization mode's contribution to observables.

Linear temperature dependence of the d.c. resistivity due to soft mode effects.

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.