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arXiv:2006.13947 · Physical review. B./Physical review. B

Anomalous density fluctuations in a random t−J model

Darshan G. Joshi, Subir Sachdev A

Published Oct 23, 2020• 9 citations
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Abstract

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 $K$. 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 $K$. However, this fixed point is unstable toward the previously found fixed point at $K=0$ 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.

DOI
10.1103/physrevb.102.165146

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A previous work [Joshi et al., Phys. Rev. X 10, 021033 (2020)] found a deconfined critical point at nonzero doping in a t\ensuremath-Jt\text{\ensuremath{-}}Jt\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.
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 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 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}.
We consider the one-dimensional lattice model of interacting fermions with disorder studied previously by Oganesyan and Huse [Phys. Rev. B 75, 155111 (2007)]. To characterize a possible many-body localization transition as a function of the disorder strength WWW, we use an exact renormalization procedure in configuration space that generalizes the Aoki real-space renormalization procedure for Anderson localization one-particle models [H. Aoki, J. Phys. C 13, 3369 (1980)]. We focus on the statistical properties of the renormalized hopping VL{V}_{L}VL​ between two configurations separated by a distance LLL in configuration space (distance being defined as the minimal number of elementary moves to go from one configuration to the other). Our numerical results point toward the existence of a many-body localization transition at a finite disorder strength Wc{W}_{c}Wc​. In the localized phase W>WcW>{W}_{c}W>Wc​, the typical renormalized hopping ${V}_{L}^{typ}\ensuremath{\equiv}{e}^{\overline{\text{ln}\text{ }{V}_{L}}}$ decays exponentially in LLL as $(\text{ln}\text{ }{V}_{L}^{typ})\ensuremath{\simeq}\ensuremath{-}\frac{L}{{\ensuremath{\xi}}_{loc}}$ and the localization length diverges as ${\ensuremath{\xi}}_{loc}(W)\ensuremath{\sim}{(W\ensuremath{-}{W}_{c})}^{\ensuremath{-}{\ensuremath{\nu}}_{loc}}$ with a critical exponent of order ${\ensuremath{\nu}}_{loc}\ensuremath{\simeq}0.45$. In the delocalized phase W<WcW<{W}_{c}W<Wc​, the renormalized hopping remains a finite random variable as $L\ensuremath{\rightarrow}\ensuremath{\infty}$ and the typical asymptotic value ${V}_{\ensuremath{\infty}}^{typ}\ensuremath{\equiv}{e}^{\overline{\text{ln}\text{ }{V}_{\ensuremath{\infty}}}}$ presents an essential singularity $(\text{ln}\text{ }{V}_{\ensuremath{\infty}}^{typ})\ensuremath{\sim}\ensuremath{-}{({W}_{c}\ensuremath{-}W)}^{\ensuremath{-}\ensuremath{\kappa}}$ with an exponent of order $\ensuremath{\kappa}\ensuremath{\sim}1.4$. Finally, we show that this analysis in configuration space is compatible with the localization properties of the simplest two-point correlation function in real space.
We study by the strong disorder renormalization group (RG) method the low-energy properties of the one-dimensional Hubbard model with random-hopping matrix-elements tmin<t<tmax{t}_{min}<t<{t}_{max}tmin​<t<tmax​, and with random onsite Coulomb repulsion terms $0\ensuremath{\leqslant}{U}_{min}<U<{U}_{max}$. There are two critical phases, corresponding to an infinite randomness spin random singlet for strong interactions (Umin>tmax)({U}_{min}>{t}_{max})(Umin​>tmax​) and to an orbital infinite randomness fixed point for vanishing interactions $({U}_{max}∕{t}_{max}\ensuremath{\rightarrow}0)$. To each critical infinite randomness fixed point is connected a Griffiths phase, the correlation length, and dynamical exponent of which have well defined asymptotic dependences on the corresponding quantum control parameter. The theoretical predictions for the scaling in the vicinity of the critical points compare well to numerical RG simulations.
We study the nature of the two-dimensional quantum critical point separating two phases with and without long-range spin-density-wave order, which has been recently observed in cuprate superconductors. We consider the Landau-Ginzburg-Wilson Hamiltonian associated with the spin-density critical modes, perform a mean-field analysis of the phase diagram, and study the corresponding renormalization-group flow in two different perturbative schemes at five and six loops, respectively. The analysis supports the existence of a stable fixed point in the full theory whose basin of attraction includes systems with collinear spin-density-wave order, as observed in experiments. The stable fixed point is characterized by an enlarged $\mathrm{O}(4)\ensuremath{\bigotimes}\mathrm{O}(3)$ symmetry. The continuous transition observed in experiments is expected to belong to this universality class. The corresponding critical exponents are $\ensuremath{\nu}=0.9(2)$ and $\ensuremath{\eta}=0.15(10)$.