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arXiv:2012.14449 · Physical review. B./Physical review. B

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

Maria Tikhanovskaya, Haoyu Guo, Subir Sachdev A, Grigory Tarnopolsky

Published Feb 24, 2021• 18 citations
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Abstract

We present numerical solutions of the spectral functions of large dimension $t\text{\ensuremath{-}}J$ models with random nearest-neighbor exchange and global $\mathrm{SU}(M)$ 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 $t\text{\ensuremath{-}}J$ 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.

DOI
10.1103/physrevb.103.075142

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We present numerical solutions of the spectral functions of large dimension t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J models with random nearest-neighbor exchange and global SU(M)\mathrm{SU}(M)SU(M) spin rotation symmetry. The solutions are obtained from the saddle-point equations of the large dimension limit, followed by the large MMM limit. The same saddle point equations also apply to the model with all-to-all and random hopping and exchange. Such a t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model realizes a deconfined critical state proposed as a model for the optimally doped cuprates. The large MMM 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.
We study the low-frequency spectra of complex Sachdev-Ye-Kitaev models at general densities. The analysis applies also to SU(M)\mathrm{SU}(M)SU(M) magnets with random exchange at large MMM. The spectral densities are computed by numerical analysis of the saddle-point equations on the real frequency $\ensuremath{\omega}$ axis at zero temperature TTT. The asymptotic low-$\ensuremath{\omega}$ behaviors are found to be in excellent agreement with the scaling dimensions of irrelevant operators which perturb the conformally invariant critical states. Of possible experimental interest is our computation of the universal spin spectral weight of the SU(M)\mathrm{SU}(M)SU(M) magnets at low $\ensuremath{\omega}$ and TTT; this includes a contribution from the time reparametrization mode, which is the boundary graviton of the holographic dual. This analysis is extended to a random $t\ensuremath{-}J$ model in the following paper [M. Tikhanovskaya et al., following paper, Phys. Rev. B 103, 075142 (2021)].
The discovery of high-temperature superconductors has raises questions that extend beyond the scope of quasiparticles, a foundational concept in condensed matter theory. This dissertation explores new theoretical approaches to quantum matter without quasiparticle excitations, with a particular focus on quantum criticality and the associated superconductivity in correlated electron compounds. The soluble Sachdev-Ye-Kitaev (SYK) model has recently emerged as a fascinating platform to address the unusual metallic states with T-linear resistivity. We first consider differ- ent variants of random Hubbard models, which share many similarities to key aspects of the original SYK model. Using a large M analysis and a renormalization group method, we propose the existence of quantum critical points with fractionalized excitations separating two distinct phases, which provides insights into the quantum phase transitions and non-Fermi liquid behaviors observed in cuprate superconductors. In the second part of this dissertation, we examine the interplay between non-Fermi liquids and superconductivity with two different pairing mechanisms. Under the framework of random Hubbard model, we demonstrate that superconductivity emerging from non-Fermi liquids strongly deviates from the BCS theory by tuning the relative strength of hopping and exchange interactions. Furthermore, we investigate a two-dimensional Yukawa-SYK model with spatially randomn interactions coupling a Fermi surface to a scalar field associated with a quantum phase transition. Our theory agrees well with transport properties analysed in cuprates, such as a T-linear resistivity and Planckian dissipation.
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 describe the phases of a solvable $t\text{\ensuremath{-}}J$ model of electrons with infinite-range, and random, hopping, and exchange interactions, similar to those in the Sachdev-Ye-Kitaev models. The electron fractionalizes, as in an ``orthogonal metal,'' into a fermion fff, which carries both the electron spin and charge, and a boson $\ensuremath{\phi}$. Both fff and $\ensuremath{\phi}$ carry emergent Z2{\mathbb{Z}}_{2}Z2​ gauge charges. The model has a phase in which the $\ensuremath{\phi}$ bosons are gapped, and the fff fermions are gapless and critical, and so the electron spectral function is gapped. This phase can be considered as a toy model for the underdoped cuprates, without spatial structure. The model also has an extended, critical, ``quasi-Higgs'' phase where both $\ensuremath{\phi}$ and fff are gapless, and the electron operator $\ensuremath{\sim}f\ensuremath{\phi}$ has a Fermi liquid-like $1/\ensuremath{\tau}$ propagator in imaginary time, $\ensuremath{\tau}$. So while the electron spectral function has a Fermi liquid form, other properties are controlled by Z2{\mathbb{Z}}_{2}Z2​ fractionalization and the anomalous exponents of the fff and $\ensuremath{\phi}$ excitations. This quasi-Higgs phase is proposed as a toy model of the overdoped cuprates. We also describe the critical state separating these two phases.
Low energy properties of the metallic state of the two-dimensional t - J model are presented for second neighbor hopping with hole-doping ( ) and electron-doping ( ), with various superexchange energy J . We use a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory . These equations reproduce the known low energies features of the large U Hubbard model in infinite dimensions. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity, Hall number and cotangent Hall angle. The spectral features display high thermal sensitivity at modest T for density , implying a suppression of the effective Fermi-liquid temperature by two orders of magnitude relative to the bare bandwidth. The cotangent Hall angle exhibits a T 2 behavior at low T , followed by an interesting kink at higher T . The Hall number exhibits strong renormalization due to correlations. Flipping the sign of changes the curvature of the resistivity versus T curves between convex and concave. Our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter.
A real spin-charge separation scheme is found based on a saddle-point state of the t-J model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at finite doping so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic residual couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at (\ensuremath{\pi}/a,\ensuremath{\pi}/a) with a doping-dependent width (\ensuremath{\propto} \ensuremath{\surd}\ensuremath{\delta} , \ensuremath{\delta} is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exists a characteristic temperature scale below thich a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a finite energy regime. In the transport, a strong-range phase intereference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-T resistivity and a T2{\mathit{T}}^{2}T2 Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.