Entanglement entropies and fermion signs of critical metals

Abstract

The fermion sign problem is often viewed as a sheer inconvenience that plagues numerical studies of strongly interacting electron systems. Only recently, it has been suggested that fermion signs are fundamental for the universal behavior of critical metallic systems and crucially enhance their degree of quantum entanglement. In this work we explore potential connections between emergent scale invariance of fermion sign structures and scaling properties of bipartite entanglement entropies. Our analysis is based on a wavefunction ansatz that incorporates collective, long-range backflow correlations into fermionic Slater determinants. Such wavefunctions mimic the collapse of a Fermi liquid at a quantum critical point. Their nodal surfaces -- a representation of the fermion sign structure in many-particle configurations space -- show fractal behavior up to a length scale $\xi$ that diverges at a critical backflow strength. We show that the Hausdorff dimension of the fractal nodal surface depends on $\xi$, the number of fermions and the exponent of the backflow. For the same wavefunctions we numerically calculate the second Rényi entanglement entropy $S_2$. Our results show a cross-over from volume scaling, $S_2\sim {\ell }^{\theta }$ ($\theta =2$ in $d=2$ dimensions), to the characteristic Fermi-liquid behavior $S_2\sim \ell \ln \ell$ on scales larger than $\xi$. We find that volume scaling of the entanglement entropy is a robust feature of critical backflow fermions, independent of the backflow exponent and hence the fractal dimension of the scale invariant sign structure.

arXiv comment9.5 pages, 10 figures

References in corpus (38)

• Entropy and Area
• Average Entropy of a Subsystem
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• On Geometric Entropy
• Quantum entanglement in condensed matter systems
• The break up of heavy electrons at a quantum critical point
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Violation of the entropic area law for Fermions
• Hall-effect evolution across a heavy-fermion quantum critical point
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Hidden Fermi surfaces in compressible states of gauge-gravity duality
• Powerlaw optical conductivity with a constant phase angle in high Tc superconductors
• Molecular Dissociation in Hot, Dense Hydrogen
• Effects of Backflow Correlation in the Three-Dimensional Electron Gas: Quantum Monte Carlo Study
• Average Entropy of a Subsystem
• Entanglement Entropy and the Fermi Surface
• Ring exchange, the Bose metal, and bosonization in two dimensions
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Entanglement Entropy in the O(N) model
• Topological Entanglement Entropy in the Quantum Dimer Model on the Triangular Lattice
• Entanglement entropy of critical spin liquids
• Anomalies in the Entanglement Properties of the Square Lattice Heisenberg Model
• Scaling Behavior of Entanglement in Two- and Three-Dimensional Free Fermions
• Quantum Disentangled Liquids
• Backflow Correlations for the Electron Gas and Metallic Hydrogen
• How universal is the entanglement spectrum?
• Role of backflow correlations for the non-magnetic phase of the t-t' Hubbard model
• Unconventional Bose-Einstein Condensations Beyond the "No-node" Theorem
• Entanglement entropies in free fermion gases for arbitrary dimension
• Entanglement entropy scaling in the bilayer Heisenberg spin system
• Entanglement entropy across the superfluid-insulator transition : a signature of bosonic criticality
• Renyi Entropy of the Interacting Fermi Liquid
• Conformal Field Theory on the Fermi Surface
• Violation of Entanglement-Area Law in Bosonic Systems with Bose Surfaces: Possible Application to Bose Metals
• Entanglement and the Sign Structure of Quantum States
• Fermionic quantum criticality and the fractal nodal surface
• Probing Critical Surfaces in Momentum Space Using Real-Space Entanglement Entropy: Bose versus Fermi
• The entanglement spectrum and Rényi entropies of non-relativistic conformal fermions

Cited by in corpus (4)

• Holographic unitary renormalization group for correlated electrons -- II: insights on fermionic criticality
• Many-body quantum sign structures as non-glassy Ising models
• Entanglement scaling and charge fluctuations in a Fermi liquid of composite fermions
• Universal entanglement signatures of quantum liquids as a guide to fermionic criticality