Monte Carlo Studies of Quantum Critical Metals

Abstract

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.

arXiv comment23 pages, 7 figures. Review article; Published in Annual Review of Condensed Matter Physics

References in corpus (87)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Quantum Criticality in Heavy Fermion Metals
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• The break up of heavy electrons at a quantum critical point
• Progress and perspectives on the electron-doped cuprates
• Divergent nematic susceptibility in an iron arsenide superconductor
• Hidden Magnetism and Quantum Criticality in the Heavy Fermion Superconductor CeRhIn5
• Magnetic-Field Induced Quantum Critical Point in YbRh${}_2$Si${}_2$
• Singular quasiparticle scattering in the proximity of charge instabilities
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order
• Quantum critical point lying beneath the superconducting dome in iron-pnictides
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• On the low energy properies of fermions with singular interactions
• Field-Induced Quantum Critical Point in CeCoIn5
• A Sharp Peak of the Zero-Temperature Penetration Depth at Optimal Composition in BaFe2(As1-xPx)2
• Ubiquitous signatures of nematic quantum criticality in optimally doped Fe-based superconductors
• Enhancement of superconductivity near a nematic quantum critical point
• Avoided Antiferromagnetic Order and Quantum Critical Point in CeCoIn${}_5$
• Are non-Fermi-liquids stable to Cooper pairing?
• Pseudogap state from quantum criticality
• Non-Fermi Liquid Fixed Point in 2+1 Dimensions
• Linear-T resistivity and change in Fermi surface at the pseudogap critical point of a high-Tc superconductor
• Monte Carlo evaluation of path integrals for the nuclear shell model
• A sufficient condition for the absence of the sign problem in the fermionic quantum Monte-Carlo algorithm
• Quantum Criticality without Tuning in the Mixed Valence Compound beta-YbAlB4
• Soft Fermi Surfaces and Breakdown of Fermi Liquid Behavior
• Spin correlations in the electron-doped high-transition-temperature superconductor Nd{2-x}Ce{x}CuO{4+/-delta}
• Quasiparticle mass enhancement approaching optimal doping in a high-Tc superconductor
• Deviations from Fermi-liquid behavior above $T_c$ in 2D short coherence length superconductors
• Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point
• A relation between the resonance neutron peak and ARPES data in cuprates
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• Recent Developments in Non-Fermi Liquid Theory
• Solving fermion sign problem in quantum Monte Carlo by Majorana representation
• Observation of incipient charge nematicity in Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$
• Quantum-critical behavior of itinerant ferromagnets
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Spin-fermion model near the quantum critical point: one-loop renormalization group results
• Nematic susceptibility of hole- and electron-doped BaFe2As2 iron-based superconductors from shear modulus measurements
• Renormalization Group Approach to Low Temperature Properties of a Non-Fermi Liquid Metal
• Perturbative non-Fermi liquids from dimensional regularization
• Competing orders and quantum criticality in doped antiferromagnets
• Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates
• Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
• Fermion-induced quantum critical points
• Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations
• Non-perturbative behavior of the quantum phase transition to a nematic Fermi fluid
• Charged fermions coupled to ${\mathbb{Z}}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions
• What makes the Tc of monolayer FeSe on SrTiO3 so high: a sign-problem-free quantum Monte Carlo study
• The fermion bag approach to lattice field theories
• Non-Fermi liquid behavior of large N_B quantum critical metals
• Theory of the Quantum Critical Fluctuations in Cuprates
• Instabilities near the onset of spin density wave order in metals
• Metallic quantum critical points with finite BCS couplings
• Solution to sign problems in half-filled spin-polarized electronic systems
• Critical Quadrupole Fluctuations and Collective Modes in Iron Pnictide Superconductors
• Cascade of phase transitions in the vicinity of a quantum critical point
• Self-Learning Monte Carlo Method in Fermion Systems
• Superconductivity near a quantum-critical point: The special role of the first Matsubara frequency
• Competing Orders in a Nearly Antiferromagnetic Metal
• Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
• Anomalous dynamical scaling from nematic and U(1)-gauge field fluctuations in two dimensional metals
• Fermi liquid near Pomeranchuk quantum criticality
• Self-Learning Determinantal Quantum Monte Carlo Method
• Quasiparticles beyond the Fermi liquid and heavy fermion criticality
• Quantum critical properties of a metallic spin density wave transition
• Strong coupling theory of heavy fermion criticality
• Multiscale quantum criticality: Pomeranchuk instability in isotropic metals
• Non-Fermi liquid behavior from two-dimensional antiferromagnetic fluctuations: a renormalization-group and large-N analysis
• A controlled expansion for certain non-Fermi liquid metals
• Quantum-Critical Fluctuations in 2D Metals: Strange Metals and Superconductivity in Antiferromagnets and in Cuprates
• Thermopower across the pseudogap critical point of La(1.6-x)Nd(0.4)Sr(x)CuO(4): Evidence for a quantum critical point in a hole-doped high-Tc superconductor
• Depleted Kondo Lattices
• Superconductivity mediated by quantum critical antiferromagnetic fluctuations: The rise and fall of hot spots
• Quantum-critical superconductivity in underdoped cuprates
• Itinerant quantum critical point with frustration and non-Fermi-liquid
• Enhancement of superconductivity at the onset of charge-density-wave order in a metal
• The nature of effective interaction in cuprate superconductors: a sign-problem-free quantum Monte-Carlo study
• Emergence of a control parameter for the antiferromagnetic quantum critical metal
• Quantum Criticality in Quasi-Two Dimensional Itinerant Antiferromagnets
• Is charge order induced near an antiferromagnetic quantum critical point?
• Superconductivity and quantum criticality in heavy fermions CeIrSi${}_3$ and CeRhSi${}_3$
• Finite temperature scaling close to Ising-nematic quantum critical points in two-dimensional metals
• Non-perturbative emergence of non-Fermi liquid behaviour in $d=2$ quantum critical metals
• A Framework for Studying a Quantum Critical Metal in the Limit $N_f\to 0$
• Critical behavior of itinerant fermions - role of finite size effects

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