Excitation spectra of quantum matter without quasiparticles. II. Random <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>t</mml:mi><mml:mo>−</mml:mo><mml:mi>J</mml:mi></mml:math> models
Maria Tikhanovskaya, Haoyu Guo, Subir Sachdev, Grigory Tarnopolsky
Abstract
We present numerical solutions of the spectral functions of large dimension $t\text{\ensuremath{-}}J$ models with random nearest-neighbor exchange and global $\mathrm{SU}(M)$ spin rotation symmetry. The solutions are obtained from the saddle-point equations of the large dimension limit, followed by the large $M$ limit. The same saddle point equations also apply to the model with all-to-all and random hopping and exchange. Such a $t\text{\ensuremath{-}}J$ model realizes a deconfined critical state proposed as a model for the optimally doped cuprates. The large $M$ theory involves 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 experimentally observable 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.