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Abstract Interactions between electrons and phonons play a crucial role in quantum materials. Yet, there is no universal method that would simultaneously accurately account for strong electron-phonon interactions and electronic correlations. By combining methods of the variational quantum eigensolver and the variational non-Gaussian solver, we develop a hybrid quantum-classical algorithm suitable for this type of correlated systems. This hybrid method tackles systems with arbitrarily strong electron-phonon coupling without increasing the number of required qubits and quantum gates, as compared to purely electronic models. We benchmark our method by applying it to the paradigmatic Hubbard-Holstein model at half filling, and show that it correctly captures the competition between charge density wave and antiferromagnetic phases, quantitatively consistent with exact diagonalization. 

Electron-hole bound pairs, or excitons, are common excitations in semiconductors. They can spontaneously form and condense into a new insulating ground state—the so-called excitonic insulator—when the energy of electron-hole Coulomb attraction exceeds the band gap. In the presence of electron-phonon coupling, a periodic lattice distortion often concomitantly occurs. However, a similar structural transition can also be induced by electron-phonon coupling itself, therefore hindering the clean identification of bulk excitonic insulators (e.g., which instability is the driving force of the phase transition). Using high-resolution synchrotron x-ray diffraction and angle-resolved photoemission spectroscopy, we identify key electron-phonon coupling effects in a leading excitonic insulator candidate Ta 2 NiSe 5 . These include an extensive unidirectional lattice fluctuation and an electronic pseudogap in the normal state, as well as a negative electronic compressibility in the charge-doped broken-symmetry state. In combination with first principles and model calculations, we use the normal state electronic spectra to quantitatively determine the electron-phonon interaction vertex g and interband Coulomb interaction V in the minimal lattice model, the solution to which captures the experimental observations. Moreover, we show how the Coulomb and electron-phonon coupling effects can be unambiguously separated based on the solution to quantified microscopic models. Finally, we discuss how the strong lattice fluctuations enabled by low dimensionality relate to the unique electron-phonon interaction effects beyond the textbook Born-Oppenheimer approximation. 

Strange metals—ubiquitous in correlated quantum materials—transport electrical charge at low temperatures but not by the individual electronic quasiparticle excitations, which carry charge in ordinary metals. In this work, we consider two-dimensional metals of fermions coupled to quantum critical scalars, the latter representing order parameters or fractionalized particles. We show that at low temperatures (T), such metals generically exhibit strange metal behavior with aT-linear resistivity arising from spatially random fluctuations in the fermion-scalar Yukawa couplings about a nonzero spatial average. We also find aTln(1/T) specific heat and a rationale for the Planckian bound on the transport scattering time. These results are in agreement with observations and are obtained in the largeNexpansion of an ensemble of critical metals withNfermion flavors. 

Perturbative considerations account for the properties of conventional metals, including the range of temperatures where the transport scattering rate is 1/ τ tr  = 2 π λ T , where λ is a dimensionless strength of the electron–phonon coupling. The fact that measured values satisfy λ  ≲ 1 has been noted in the context of a possible “Planckian” bound on transport. However, since the electron–phonon scattering is quasielastic in this regime, no such Planckian considerations can be relevant. We present and analyze Monte Carlo results on the Holstein model which show that a different sort of bound is at play: a “stability” bound on λ consistent with metallic transport. We conjecture that a qualitatively similar bound on the strength of residual interactions, which is often stronger than Planckian, may apply to metals more generally.