Critical metallic phase in the overdoped random $t$-$J$ model

Abstract

We investigate a model of electrons with random and all-to-all hopping and spin exchange interactions, with a constraint of no double occupancy. The model is studied in a Sachdev-Ye-Kitaev-like large-$M$ limit with SU($M$) spin symmetry. The saddle point equations of this model are similar to appoximate dynamic mean field equations of realistic, non-random, $t$-$J$ models. We use numerical studies on both real and imaginary frequency axes, along with asymptotic analyses, to establish the existence of a critical non-Fermi-liquid metallic ground state at large doping, with the spin correlation exponent varying with doping. This critical solution possesses a time-reparametrization symmetry, akin to SYK models, which contributes a linear-in-temperature resistivity over the full range of doping where the solution is present. It is therefore an attractive mean-field description of the overdoped region of cuprates, where experiments have observed a linear-$T$ resistivity in a broad region. The critical metal also displays a strong particle-hole asymmetry, which is relevant to Seebeck coefficient measurements. We show that the critical metal has an instability to a low-doping spin-glass phase, and compute a critical doping value. We also describe the properties of this metallic spin-glass phase.

arXiv commentMain: 8 pages, 8 figures; SI: 17 pages, 13 figures. v2: several corrections and modifications. PNAS format

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Cited by in corpus (11)

• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• Flat bands, strange metals, and the Kondo effect
• Phases of $\mathcal{N}=2$ Sachdev-Ye-Kitaev models
• Antiferromagnetic bosonic $t$-$J$ models and their quantum simulation in tweezer arrays
• T-linear resistivity, optical conductivity and Planckian transport for a holographic local quantum critical metal in a periodic potential
• Strange metals and planckian transport in a gapless phase from spatially random interactions
• Equilibrium dynamics of infinite-range quantum spin glasses in a field
• Exact Solution for the Transverse Field Sherrington-Kirkpatrick Spin Glass Model with Continuous-Time Quantum Monte Carlo Method
• The Strange Metal State of the high-Tc Cuprates
• Bipartite Sachdev-Ye Models with Read-Saleur Symmetries
• $\mathcal{N}=2$ SYK models with dynamical bosons and fermions