Oscillating terms in the Renyi entropy of Fermi gases and liquids

Swingle, Brian; McMinis, Jeremy; Tubman, Norm M.

doi:10.1103/physrevb.87.235112

Cited by 20 publications

(30 citation statements)

References 46 publications

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“…The sub-leading oscillations were studied in detail in Ref. [61]. Although resonant fermions are strongly coupled (the regime is non-perturbative and away from any regime with small dimensionless parameters), we can expect S n,A to follow a similar trend as the non-interacting gas, for the following reasons.…”

Section: Definitions: Hamiltonian Density Matrices and The Entamentioning

confidence: 99%

Entanglement spectrum and Rényi entropies of nonrelativistic conformal fermions

Porter

Drut

2016

Phys. Rev. B

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We characterize non-perturbatively the Rényi entropies of degree n = 2, 3, 4, and 5 of threedimensional, strongly coupled many-fermion systems in the scale-invariant regime of short interaction range and large scattering length, i.e. in the unitary limit. We carry out our calculations using lattice methods devised recently by us. Our results show the effect of strong pairing correlations on the entanglement entropy, which modify the sub-leading behavior for large subsystem sizes (as characterized by the dimensionless parameter x = kF LA, where kF is the Fermi momentum and LA the linear subsystem size), but leave the leading order unchanged relative to the non-interacting case. Moreover, we find that the onset of the sub-leading asymptotic regime is at surprisingly small x 2 − 4. We provide further insight into the entanglement properties of this system by analyzing the spectrum of the entanglement Hamiltonian of the two-body problem from weak to strong coupling. The low-lying entanglement spectrum displays clear features as the strength of the coupling is varied, such as eigenvalue crossing and merging, a sharp change in the Schmidt gap, and scale invariance at unitarity. Beyond the low-lying component, the spectrum appears as a quasi-continuum distribution, for which we present a statistical characterization; we find, in particular, that the mean shifts to infinity as the coupling is turned off, which indicates that that part of the spectrum represents non-perturbative contributions to the entanglement Hamiltonian. In contrast, the low-lying entanglement spectrum evolves to finite values in the noninteracting limit. The scale invariance of the unitary regime guarantees that our results are universal features intrinsic to three-dimensional quantum mechanics and represent a well-defined prediction for ultracold atom experiments, which were recently shown to have direct access to the entanglement entropy.

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Section: Definitions: Hamiltonian Density Matrices and The Entamentioning

confidence: 99%

Entanglement spectrum and Rényi entropies of nonrelativistic conformal fermions

Porter

Drut

2016

Phys. Rev. B

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“…Calculations of spatial Renyi entanglement with QMC include lattice calculations of topological systems [14] and continuum calculations of Fermi liquids [15,16] and molecules [17]. The Renyi entropies calculated in these works are generally determined with the Swap operator which can be applied to interacting systems.…”

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confidence: 99%

“…Thus whenever a system is only weakly interacting we expect the method to work especially well for generating basis sets. In the case of Fermi-liquids this means the basis sets are likely to be efficient in the high density limit [15,16]. For strongly interacting systems, such as transition metals molecules and low density Fermi-liquids, the spatial natural orbitals are likely to remain a good single determinant basis set for the expansion, but the number of basis elements required to converge the spectrum might be large.…”

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confidence: 99%

Calculating the entanglement spectrum in quantum Monte Carlo with application toab initioHamiltonians

Tubman

Yang

2014

Phys. Rev. B

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Several algorithms have been proposed to calculate the spatial entanglement spectrum from high order Renyi entropies. In this work we present an alternative approach for computing the entanglement spectrum with quantum Monte Carlo for both continuum and lattice Hamiltonians. This method provides direct access to the matrix elements of the spatially reduced density matrix and we determine an estimator that can be used in variational Monte Carlo as well as other Monte Carlo methods. The algorithm is based on using a generalization of the Swap operator, which can be extended to calculate a general class of density matrices that can include combinations of spin, space, particle and even momentum coordinates. We demonstrate the method by applying it to the Hydrogen and Nitrogen molecules and describe for the first time how the spatial entanglement spectrum encodes a covalent bond that includes all the many body correlations.Density matrices traced out in real space are becoming a fundamental tool in characterizing different states of matter in condensed matter systems [1][2][3][4][5][6][7]. While the interest in spatial reduced density matrices (RDM) is quite recent, the use of density matrices in general is quite ubiquitous [8]. The calculation and usage of particle RDMs in quantum Monte Carlo (QMC) simulations are quite extensive and many techniques have been developed to calculate such density matrices [9][10][11].Recent QMC entanglement studies have focused on determining the Renyi entropies [12,13]. Calculations of spatial Renyi entanglement with QMC include lattice calculations of topological systems [14] and continuum calculations of Fermi liquids [15,16] and molecules [17]. The Renyi entropies calculated in these works are generally determined with the Swap operator which can be applied to interacting systems. In the community of ab initio research, there has also been much recent work on using QMC to make highly accurate calculations of the momentum distribution of realistic materials [10]. It turns out the estimators used to calculate the momentum distribution can be seen as a form of the Swap operator. In this work we use the best techniques that have been developed from both of these communities to introduce a generalization of the Swap operator, making it an efficient tool to calculate the entanglement spectrum of spatial RDMs.The spatial entanglement spectrum is derived from a density matrix ρ A in which a system is split into two regions (A and B), and the degrees of freedom in region B are traced out. The matrix elements of such a density matrix can be expanded in any basis that is complete in region A. However, in our numerical calculations we in general can only consider a finite number of basis elements. Therefore practical calculations of the entanglement spectrum are basis dependent, and a carefully selected basis is required. The algorithm presented here is different from recent proposals [18][19][20][21] for calculating the entanglement spectrum in several ways. First, there is no calculation o...

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“…Logarithmic scaling of entanglement entropy at a quantum critical point in d = 1 (spatial dimension) is discussed in [7,8]. For the logarithmic modification of the area law in the presence of a Fermi surface see [9][10][11][12]. For a logarithmic prefactor coming from a "Bose surface" rather than "Fermi surface" see [13].…”

Section: Introductionmentioning

confidence: 99%