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Register a new userMonte Carlo Studies of Quantum Critical Metals
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Metallic quantum critical phenomena are believed to play a key role in many strongly correlated materials, including high temperature superconductors. Theoretically, the problem of quantum criticality in the presence of a Fermi surface has proven to be highly challenging. However, it has recently been realized that many models used to describe such systems are amenable to numerically exact solution by quantum Monte Carlo (QMC) techniques, without suffering from the fermion sign problem. In this article, we review the status of the understanding of metallic quantum criticality, and the recent progress made by QMC simulations. We focus on the cases of spin density wave and Ising nematic criticality. We describe the results obtained so far, and their implications for superconductivity, non-Fermi liquid behavior, and transport in the vicinity of metallic quantum critical points. Some of the outstanding puzzles and future directions are highlighted.
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We present numerically exact results from sign-problem free quantum Monte Carlo simulations for a spin-fermion model near an $O(3)$ symmetric antiferromagnetic (AFM) quantum critical point. We find a hierarchy of energy scales that emerges near the quantum critical point. At high energy scales, there is a broad regime characterized by Landau-damped order parameter dynamics with dynamical critical exponent $z=2$, while the fermionic excitations remain coherent. The quantum critical magnetic fluctuations are well described by Hertz-Millis theory, except for a $T^{-2}$ divergence of the static AFM susceptibility. This regime persists down to a lower energy scale, where the fermions become overdamped and concomitantly, a transition into a $d-$wave superconducting state occurs. These findings resemble earlier results for a spin-fermion model with easy-plane AFM fluctuations of an $O(2)$ SDW order parameter, despite noticeable differences in the perturbative structure of the two theories. In the $O(3)$ case, perturbative corrections to the spin-fermion vertex are expected to dominate at an additional energy scale, below which the $z=2$ behavior breaks down, leading to a novel $z=1$ fixed point with emergent local nesting at the hot spots [Schlief et al., PRX 7, 021010 (2017)]. Motivated by this prediction, we also consider a variant of the model where the hot spots are nearly locally nested. Within the available temperature range in our study ($Tge E_F/200$), we find substantial deviations from the $z=2$ Hertz-Millis behavior, but no evidence for the predicted $z=1$ criticality.
We explore the Matsubara quasiparticle fraction and the pseudogap of the two-dimensional Hubbard model with the dynamical cluster quantum Monte Carlo method. The character of the quasiparticle fraction changes from non-Fermi liquid, to marginal Fermi liquid to Fermi liquid as a function of doping, indicating the presence of a quantum critical point separating non-Fermi liquid from Fermi liquid character. Marginal Fermi liquid character is found at low temperatures at a very narrow range of doping where the single-particle density of states is also symmetric. At higher doping the character of the quasiparticle fraction is seen to cross over from Fermi Liquid to Marginal Fermi liquid as the temperature increases.
As the building blocks of topological quantum computation, Majorana zero modes (MZMs) have attracted tremendous attention in recent years. Scalable mesoscopic island designs with MZMs show great potential in quantum information processing. However, these systems are susceptible to quasi-particle poisoning which would induce various parity-breaking errors. To solve this problem, we modify the mesoscopic islands with gate-tunable valves and non-topological backbones. We study the lifetime of the Majorana qubits on these modified islands which are coupled to local bosonic and fermionic thermal baths. We consider both the parity-breaking and parity-preserving errors, and propose a parity correction scheme. By using Jordan-Wigner transformation, we analyze the probability of logical X and Y errors. The open quantum system is described by the Pauli master equation, and standard Monte Carlo simulations are applied to observe the behavior of the system when the parity correction proposal is implemented. The results demonstrate that (1) our parity correction proposal is effective to most of the parity-breaking errors; (2) the lifetime of the qubit benefits from larger island size before it meets the threshold; (3) small chemical potential $ mu $ on the non-topological backbones and fine tuned paring potential $ Delta $ of the topological bulk segment are required for high probability of correctness. Our results provide an effective error correction scheme for the parity-breaking errors.
We study the effects of finite temperature on normal state properties of a metal near a quantum critical point to an antiferromagnetic or Ising-nematic state. At $T = 0$ bosonic and fermionic self-energies are traditionally computed within Eliashberg theory and obey scaling relations with characteristic power-laws. Quantum Monte Carlo (QMC) simulations have shown strong systematic deviations from these predictions, casting doubt on the validity of the theoretical analysis. We extend Eliashberg theory to finite $T$ and argue that for the $T$ range accessible in the QMC simulations, the scaling forms for both fermionic and bosonic self energies are quite different from those at $T = 0$. We compare finite $T$ results with QMC data and find good agreement for both systems. This, we argue, resolves the key apparent contradiction between the theory and the QMC simulations.
The author reports on new high-fidelity simulations of charge carriers in the high-T$_c$ cuprate materials using quantum Monte Carlo techniques applied to the first principles Hamiltonian. With this high accuracy technique, the doped ground state is found to be a spin polaron, in which charge is localized through a strong interaction with the spin. This spin polaron has calculated properties largely similar to the phenomenology of the cuprates, and may be the object which forms the Fermi surface and charge inhomogeneity in these materials. The spin polaron has some unique features that should be visible in X-ray, EELS, and neutron experiments. The results contained in this paper comprise an accurate first principles derived paradigm from which to study superconductivity in the cuprates.
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