Finite-size effects in canonical and grand-canonical quantum Monte Carlo simulations for fermions

Wang, Zhenjiu; Assaad, Fakher F.; Toldin, Francesco Parisen

doi:10.1103/physreve.96.042131

Cited by 20 publications

(13 citation statements)

References 27 publications

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“…Thus this method is particularly appealing within QMC and, quite recently, is becoming widely used for the study of strongly corre-lated systems. On the other hand, in a recent work [31], by using finite-temperature determinant quantum Monte Carlo without TABCs, the convergence of physical quantities to the thermodynamic limit have been examined for the canonical ensemble (CE) and the grand-canonical ensemble (GCE). It has been shown that GCE provides a convergence faster than CE.…”

Section: Introductionmentioning

confidence: 99%

Study of the superconducting order parameter in the two-dimensional negative- U Hubbard model by grand-canonical twist-averaged boundary conditions

2018

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By using variational Monte Carlo and auxiliary-field quantum Monte Carlo methods, we perform an accurate finite-size scaling of the s-wave superconducting order parameter and the pairing correlations for the negative-U Hubbard model at zero temperature in the square lattice. We show that the twist-averaged boundary conditions (TABCs) are extremely important to control finite-size effects and to achieve smooth and accurate extrapolations to the thermodynamic limit. We also show that TABCs is much more efficient in the grand-canonical ensemble rather than in the standard canonical ensemble with fixed number of electrons. The superconducting order parameter as a function of the doping is presented for several values of |U |/t and is found to be significantly smaller than the mean-field BCS estimate already for moderate couplings. This reduction is understood by a variational ansatz able to describe the low-energy behaviour of the superconducting phase, by means of a suitably chosen Jastrow factor including long-range density-density correlations.arXiv:1806.06736v1 [cond-mat.str-el]

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Section: Introductionmentioning

confidence: 99%

Study of the superconducting order parameter in the two-dimensional negative- U Hubbard model by grand-canonical twist-averaged boundary conditions

2018

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“…The charge gap ∆ C and the spin gap ∆ S , with ∆ C > ∆ S , are monotonically increasing with t ⊥ and U . Gapped systems exhibit, as a function of the linear size, a fast approach to the thermodynamic limit [44,45]. Figure 2 illustrates the temperature dependence of the nearest-neighbor hopping term t i,i+1 inĤ E for t ⊥ = 2 and 2.5 and fixed coupling constants t = 1 and U = 4.…”

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confidence: 99%

Entanglement Hamiltonian of Interacting Fermionic Models

Toldin

Assaad

2018

Phys. Rev. Lett.

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Recent numerical advances in the field of strongly correlated electron systems allow the calculation of the entanglement spectrum and entropies for interacting fermionic systems. An explicit determination of the entanglement (modular) Hamiltonian has proven to be a considerably more difficult problem, and only a few results are available. We introduce a technique to directly determine the entanglement Hamiltonian of interacting fermionic models by means of auxiliary field quantum Monte Carlo simulations. We implement our method on the one-dimensional Hubbard chain partitioned into two segments and on the Hubbard two-leg ladder partitioned into two chains. In both cases, we study the evolution of the entanglement Hamiltonian as a function of the physical temperature.Introduction.-The advent of quantum information techniques in the field of condensed matter physics has boosted a variety of new insights in old and new problems. In particular, recent years have witnessed a rapidly growing number of investigations of the quantum entanglement in strongly correlated many-body systems [1, 2]. The simplest approach is the so-called bipartite entanglement, where one divides a system into two parts, and a reduced density matrix describing one of the subsystems is obtained by tracing out the degrees of freedom of the other part. Arguably, the most studied quantities in this context are the entropies of the reduced density matrix, that is, the von Neumann and especially the Renyi entropies. In the ground state, the entanglement entropies generically satisfy an area law; i.e., to leading order they are proportional to the area between the two subsystems [3]. Among the many results, it is well established that in a 1+1 conformal field theory (CFT) corrections to the area law allow one to extract the central charge of a model [4].More information is contained in the entanglement Hamiltonian, also known as the modular Hamiltonian, which is defined as the negative logarithm of the reduced density matrix. Its spectrum, dubbed as the "entanglement spectrum," has been shown to feature the edge physics of topologically ordered phases such as the fractional quantum Hall state [5] as well as of symmetry-protected topological states of matter [2,[6][7][8][9]. The entanglement Hamiltonian also plays a central role in the first law of entanglement [10]. Beside the entanglement spectrum and the associated eigenvectors, the knowledge of the entanglement Hamiltonian opens the possibility of characterizing the reduced density matrix as a thermal state. Furthermore, the expectation value of the entanglement Hamiltonian equals the von Neumann entanglement entropy, a key quantity which is generically not accessible in numerical simulations of interacting models. Perhaps not surprisingly, compared to the computation of entanglement entropies, an explicit determination of the entanglement Hamiltonian has proven to be a considerably more difficult problem, and only a few solvable results are available. Aside from limiting cases,

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“…[22] for more details on the formulation. A similar technique can be used to simulate the canonical ensemble [34]. Simulations have been performed using the ALF package [35].…”

Section: Methodsmentioning

confidence: 99%

Mutual information in heavy-fermion systems

2019

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A key notion in heavy-fermion systems is the entanglement between conduction electrons and localized spin degrees of freedom. To study these systems from this point of view, we compute the mutual information in a ferromagnetic and antiferromagnetic Kondo lattice model in the presence of geometrical frustration. Here the interplay between the Kondo effect, the Ruderman-Kittel-Kasuya-Yosida interaction, and geometrical frustration leads to partial Kondo screened, conventional Kondo insulating, and antiferromagnetic phases. In each of these states the mutual information follows an area law, the coefficient of which shows sharp crossovers (on our finite lattices) across phase transitions. Deep in the respective phases, the area law coefficient can be understood in terms of simple direct product wave functions thereby yielding an accurate measure of the entanglement in each phase. The above-mentioned results stem from approximation-free auxiliary field quantum Monte Carlo

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Finite-size effects in canonical and grand-canonical quantum Monte Carlo simulations for fermions

Cited by 20 publications

References 27 publications

Study of the superconducting order parameter in the two-dimensional negative- U Hubbard model by grand-canonical twist-averaged boundary conditions

Study of the superconducting order parameter in the two-dimensional negative- U Hubbard model by grand-canonical twist-averaged boundary conditions

Entanglement Hamiltonian of Interacting Fermionic Models

Mutual information in heavy-fermion systems

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