Entanglement Entropy of theν=1/2Composite Fermion Non-Fermi Liquid State

Abstract

The so-called "non-Fermi liquid" behavior is very common in strongly correlated systems. However, its operational definition in terms of "what it is not" is a major obstacle against theoretical understanding of this fascinating correlated state. Recently there has been much interest in entanglement entropy as a theoretical tool to study non-Fermi liquids. So far explicit calculations have been limited to models without direct experimental realizations. Here we focus on a two dimensional electron fluid under magnetic field and filling fraction ν = 1/2, which is believed to be a non-Fermi liquid state. Using the composite fermion (CF) wave-function which captures the ν = 1/2 state very accurately, we compute the second Rényi entropy using variational Monte-Carlo technique and an efficient parallel algorithm. We find the entanglement entropy scales as L log L with the length of the boundary L as it does for free fermions, albeit with a pre-factor twice that of the free fermion. We contrast the results against theoretical conjectures and discuss the implications of the results.Despite its ubiquity in strongly correlated materials, the metallic 'non-Fermi liquid' behavior has been challenging to characterize theoretically. At the phenomenological level, non-Fermi liquid behavior is defined by a metallic system exhibiting physical properties that are qualitatively inconsistent with Landau's Fermi-liquid theory. Examples of non-Fermi liquid metals include the strange-metal phase of the high T c cuprates[1], systems near a metallic quantum critical point[2-4] and twodimensional electron system subject to a magnetic field at filling ν = 1/2 (often referred to as Fermi-liquid-like state) [5][6][7]. However, there are many ways in which a system can deviate from a normal Fermi-liquid, such as diverging effective mass, vanishing quasiparticle weight, and anomalous transport [3,[8][9][10][11][12] and little is known about how different forms of deviation can be related. Hence the theoretical challenge of addressing a problem without a weakly interacting quasiparticle description has been compounded by the lack of a measure that can be used to define and classify non-Fermi liquids.Here we turn to a quantum information measure that is sensitive to entangled nature of many-body wavefunctions: the bi-partite entanglement entropy. For gapped systems, the entanglement entropy of the reduced density matrix ρ A ≡ Tr B |Ψ Ψ| of a subsystem A with respect to its complement B for a given ground state wave-function |Ψ is widely believed to follow the area law, i.e., asymptotically proportional to the contact area of two subsystems, with rigorous arguments for lattice systems [13,14]. On the other hand, an explicit formula for a multiplicative logarithmic correction to the area law was suggested by Gioev and Klich [15] based on the Widom conjecture [16] and numerically confirmed in Ref. [17] for free fermions at dimensions d > 1. This dramatic violation of the area law for free fermions is in stark contrast to the area law found for crit...

Luttinger Theorem for the Strongly Correlated Fermi Liquid of Composite Fermions

“…For technical reasons, we are not able to go to systems with N > 81 (which requires filling the tenth Landau-like level of composite fermions, where the numerics become unstable). We have therefore also studied the CFFS in the torus geometry [37,72,73], where we can go up to N ¼ 153, and find that the results are consistent with our spherical results. Results in the torus geometry are presented in [35].…”

Composite Fermions as Deformed Oscillators: Wavefunctions and Entanglement

“…Accordingly, the considered entanglement and its entropy concern two constituents of the bipartite CF. These features make our approach and analysis essentially different from some recent works on the entanglement entropy of a system of free or composite fermions, see, e.g., [20,21], where the spatial size of a subsystem plays the basic role, and entanglement entropy was viewed in a way different from our one.…”

“…The entanglement entropy S (α) ent (θ 1 , θ 2 , θ 3 , φ 2 ) of a CF in the αth mode stems from (21) with "symmetrized" squared absolute values of Schmidt coefficients:…”

Rényi entropies of interacting fermions from determinantal quantum Monte Carlo simulations

“…For the replica switching method, we obtained a considerably smaller number of measurements for the switching probabilities in (20) in the same allocated computing time. For the largest cut, i.e.…”

“…While a generalization of the numerical schemes to calculate entanglement entropies also for these many-fermion systems is highly desirable, progress so far has been limited to variational Monte Carlo techniques [17][18][19][20] . The first step to develop an approach based on determinantal Monte Carloan unbiased, auxiliary field technique that has become the method of choice for large-scale simulations of interacting fermion systems -has recently been reported by Grover 21 , whose approach is based on a decomposition of the entanglement entropy in terms of free-fermion Green's functions.…”