Deconfined critical point in a doped random quantum Heisenberg magnet

Abstract

We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interactions between any pair of sites and a constraint of no double occupancy. A perturbative renormalization group analysis yields a critical point with fractionalized excitations at a non-zero critical value $p_c$ of the hole doping $p$ away from the half-filled insulator. We compute the renormalization group to two loops, but some exponents are obtained to all loop order. We argue that the critical point $p_c$ is flanked by confining phases: a disordered Fermi liquid with carrier density $1+p$ for $p>p_c$, and a metallic spin glass with carrier density $p$ for $p<p_c$. Additional evidence for the critical behavior is obtained from a large $M$ analysis of a model which extends the SU(2) spin symmetry to SU($M$). We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.

arXiv comment22+32 pages, 13 figures

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• Quantum phase transition at non-zero doping in a random $t$-$J$ model
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• Excitation spectra of quantum matter without quasiparticles II: random $t$-$J$ models
• Critical metallic phase in the overdoped random $t$-$J$ model
• Anomalous density fluctuations in a random $t$-$J$ model
• $SL(2,R)$ lattices as information processors
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• Fermi-surface Reconstruction in the Repulsive Fermi-Hubbard Model