Subarea law of entanglement in nodal fermionic systems

The scaling of entanglement entropy in a honeycomb lattice on a torus

The entanglement entropy of a noninteracting fermionic system confined to a two-dimensional honeycomb lattice on a torus is calculated. We find that the entanglement entropy can characterize Lifshitz phase transitions without a local order parameter. In the noncritical phase and critical phase with a nodal Fermi surface, the entanglement entropy satisfies an area law. The leading subarea term is a constant in the gapped phase rather than a logarithmic additive term in the gapless regime. The tuning of chemical potential allows for a nonzero Fermi surface, whose variation along a particular dir…

Fermion nodes and nodal cells of noninteracting and interacting fermions

A fermion node is subset of fermionic configurations for which a real wave function vanishes due to the antisymmetry and the node divides the configurations space into compact nodal cells (domains). We analyze the properties of fermion nodes of fermionic ground state wave functions for a number of systems. For several models we demonstrate that noninteracting spin-polarized fermions in dimension two and higher have closed-shell ground state wave functions with the minimal two nodal cells for any system size and we formulate a theorem which sumarizes this result. The models include periodic fer…

Diamagnetism of nodal fermions

Free nodal fermionic excitations are simple but interesting examples of fermionic quantum criticality in which the dynamic critical exponent $z=1$, and the quasiparticles are well defined. They arise in a number of physical contexts. We derive the scaling form of the diamagnetic susceptibility, $χ$, at finite temperatures and for finite chemical potential. From measurements in graphene, or in $\mathrm{Bi_{1-x}Sb_{x}}$ ($x=0.04$), one may be able to infer the striking Landau diamagnetic susceptibility of the system at the quantum critical point. Although the quasiparticles in the mean field des…

节线超导体中费米子相互作用与无序效应之间相互影响的研究

Effects of the interplay between fermionic interactions and disorders in the nodal-line superconductors

本文利用重整化群方法研究非中心对称节线超导体中费米子相互作用与四类无序散射的耦合效应，揭示了不同无序的低能相关/无关行为、无序间的竞争与诱导机制，以及费米子速度和耦合参数在无序共存下的演化规律。

Spin frustration and fermionic entanglement in an exactly solved hybrid diamond chain with the localized Ising spins and mobile electrons

The strongly correlated spin-electron system on a diamond chain containing localized Ising spins on its nodal lattice sites and mobile electrons on its interstitial sites is exactly solved in a magnetic field using the transfer-matrix method. We have investigated in detail all available ground states, the magnetization processes, the spin-spin correlation functions around an elementary plaquette, fermionic quantum concurrence and spin frustration. It is shown that the fermionic entanglement between mobile electrons hopping on interstitial sites and the kinetically-induced spin frustration are …

Suppressing ionic terms with number counting Jastrow factors in real space

We demonstrate that 4-body real space Jastrow factors are, with the right type of Jastrow basis function, capable of performing successful wave function stenciling to remove unwanted ionic terms from an overabundant fermionic reference without unduly modifying the remaining components. In addition to greatly improving size consistency (restoring it exactly in the case of a geminal power), real-space wave function stenciling is, unlike its Hilbert space predecessors, immediately compatible with diffusion Monte Carlo, allowing it to be used in the pursuit of compact, strongly correlated trial fu…

量子液体普适纠缠特征作为费米子临界性的指南

Universal entanglement signatures of quantum liquids as a guide to fermionic criticality

本研究通过重整化群方法揭示费米液体及非费米液体在动量空间中的普适对数面积律违反，提出基于纠缠的量子液体分类框架，并验证于二维Hubbard模型临界点。

Entanglement entropies and fermion signs of critical metals

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 correlati…