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arXiv:1912.08822 · Physical Review X

Deconfined Critical Point in a Doped Random Quantum Heisenberg Magnet

Darshan G. Joshi, Chenyuan Li, Grigory Tarnopolsky, Antoine Georges, Subir Sachdev A

Published May 12, 2020• 35 citations
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Abstract

We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interaction 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 nonzero 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 þ 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 SUðMÞ.We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.

DOI
10.1103/physrevx.10.021033

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We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interaction 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 nonzero 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 þ 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 SUðMÞ.We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.
We examine the metal-insulator transition in a half-filled Hubbard model of electrons with random and all-to-all hopping and exchange, and an on-site nonrandom repulsion, the Hubbard UUU. We argue that recent numerical results of Cha et al. [arXiv:2002.07181] can be understood in terms of a deconfined critical point between a disordered Fermi liquid and an insulating spin glass. We find a deconfined critical point in a previously proposed large MMM theory, which generalizes the SU(2) spin symmetry to SU(M)\mathrm{SU}(M)SU(M) and obtains exponents for the electron and spin correlators which agree with those of Cha et al. This critical point is expected to have the maximal quantum Lyapunov exponent. We also present a renormalization group analysis, and argue for the presence of an additional metallic spin glass phase at half-filling and small UUU.
We numerically study a model of interacting spin-1/21/21/2 electrons with random exchange coupling on a fully connected lattice. This model hosts a quantum critical point separating two distinct metallic phases as a function of doping: a Fermi-liquid phase with a large Fermi-surface volume and a low-doping phase with local moments ordering into a spin glass. We show that this quantum critical point has non-Fermi-liquid properties characterized by TTT-linear Planckian behavior, $\ensuremath{\omega}/T$ scaling, and slow spin dynamics of the Sachdev-Ye-Kitaev type. The $\ensuremath{\omega}/T$ scaling function associated with the electronic self-energy is found to have an intrinsic particle-hole asymmetry, a hallmark of a ``skewed'' non-Fermi liquid.
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 approximate dynamic mean-field equations of realistic, nonrandom, 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-reparameterization symmetry, akin to Sachdev–Ye–Kitaev (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.
We present exact diagonalization results on finite clusters of a t-J model of spin-1/2 electrons with random all-to-all hopping and exchange interactions. We argue that such random models capture qualitatively the strong local correlations needed to describe the cuprates and related compounds, while avoiding lattice space group symmetry breaking orders. The previously known spin glass ordered phase in the insulator at doping p=0 extends to a metallic spin glass phase up to a transition p=p_{c}≈1/3. The dynamic spin susceptibility shows signatures of the spectrum of the Sachdev-Ye-Kitaev models near p_{c}. We also find signs of the phase transition in the entropy, entanglement entropy, and compressibility, all of which exhibit a maximum near p_{c}. The electron energy distribution function in the metallic phase is consistent with a disordered extension of the Luttinger-volume Fermi surface for p>p_{c}, while this breaks down for p<p_{c}.
A previous work [Joshi et al., Phys. Rev. X 10, 021033 (2020)] found a deconfined critical point at nonzero doping in a $t\text{\ensuremath{-}}J$ model with all-to-all and random hopping and spin exchange and argued for its relevance to the phenomenology of the cuprates. We extend this model to include all-to-all and random density-density interactions of mean-square strength KKK. In a fixed realization of the disorder, and for specific values of the hopping, exchange, and density interactions, the model is supersymmetric, but we find no supersymmetry after independent averages over the interactions. Using the previously developed renormalization group analysis, we find a new fixed point at nonzero KKK. However, this fixed point is unstable toward the previously found fixed point at K=0K=0K=0 in our perturbative analysis. We compute the exponent characterizing local density fluctuations at both fixed points: This exponent determines the spectrum of electron energy-loss spectroscopy.
Anomalous metals are observed in numerous experiments on disordered two-dimensional systems proximate to superconductivity. A characteristic feature of an anomalous metal is that its low-temperature conductivity has a weakly temperature dependent value, significantly higher than that of a disordered Fermi liquid. We propose a dynamical mean-field model of an anomalous metal: interacting electrons similar in structure to that of the well-studied universal Hamiltonian of mesoscopic metallic grains, but with independent random interactions between pairs of sites, involving Cooper pair hopping and spin exchange. We find evidence for critical anomalous phases or points between a superconducting phase and a disordered Fermi liquid phase in this model. Our results are obtained by a renormalization group analysis in a weak coupling limit, and a complementary solution at large MMM when the spin symmetry is generalized to USp(M)\mathrm{USp}(M)USp(M). The large MMM limit describes the anomalous metal by fractionalization of the electron into spinons, holons, and doublons, with these partons forming critical non-Fermi liquids in the Sachdev-Ye-Kitaev class. We compute the low-temperature conductivity in the large MMM limit and find temperature-independent values moderately enhanced from that in the disordered metal.