Excitation spectra of quantum matter without quasiparticles. II. Random t − J models

We present numerical solutions of the spectral functions of large dimension t−J models with random nearest-neighbor exchange and global 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 saddl...

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Bibliographic Details
Published in:Physical review. B 2021-02, Vol.103 (7), p.1, Article 075142
Main Authors: Tikhanovskaya, Maria, Guo, Haoyu, Sachdev, Subir, Tarnopolsky, Grigory
Format: Article
Language:English
Subjects:
CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Cuprates
Electrical resistivity
Electron spin
Elementary excitations
Exchanging
Excitation spectra
Gravitons
Green's functions
Low frequencies
M theory
MATERIALS SCIENCE
Mathematical models
Operators (mathematics)
Physics
Quantum gravity
Saddle points
Temperature dependence
Two dimensional models
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Summary:We present numerical solutions of the spectral functions of large dimension t−J models with random nearest-neighbor exchange and global 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−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.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.103.075142