Controllable precision of the projective truncation approximation for Green’s functions

Fan, Peng; Tong, Ning-Hua

doi:10.1088/1674-1056/28/4/047102

Cited by 7 publications

(6 citation statements)

References 44 publications

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“…PTA was proposed by Fan et al first for quantum GF EOM [31]. It is a systematic method for truncating the EOM and it has controllable precision [47]. Recently, this method is used in the study of phase diagram of two dimensional spinless fermion model [48].…”

Section: Projective Truncation Approximationmentioning

confidence: 99%

Projective truncation approximation study of one-dimensional $ϕ^4$ lattice model

Ma,

Guo,

Wang

et al. 2022

Preprint

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In this paper, we first develop the projective truncation approximation (PTA) in the Green's function equation of motion (EOM) formalism for classical statistical models. To implement PTA for a given Hamiltonian, we choose a set of basis variables and projectively truncate the hierarchical EOM. We apply PTA to the one-dimensional φ 4 lattice model. Phonon dispersion and static correlation functions are studied in detail. Using one-and two-dimensional bases, we obtain results identical to and beyond the quadratic variational approximation, respectively. In particular, we analyze the power-law temperature dependence of the static averages in the low and high temperature limits and give exact exponents.

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Section: Projective Truncation Approximationmentioning

confidence: 99%

Projective truncation approximation study of one-dimensional $ϕ^4$ lattice model

Ma,

Guo,

Wang

et al. 2022

Preprint

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“…The calculation of the equal-time spatial SSCF is challenging for most of methods used to investigate AIM, such as perturbative method and NRG approach. Recently, two of the authors of the present work proposed a many-body calculation method, PTA-EOMGF 32,33 and applied it to Anderson impurity model. In that work, the continuous bath degrees of freedom is discretized using the NRG discretization formula, which improves the energy resolution at the cost of losing the spatial resolution.…”

Section: Numerical Calculationmentioning

confidence: 99%

“…In this paper, we attempt to explore how the partially spinpolarized conduction bath (ferromagnetic electrodes) influences the equal-time spatial SSCF at zero temperature. We study the Anderson's impurity model (AIM) with a spin polarized conduction bath using the equation of motion of twotime Green's functions with projective truncation approximation (PTA-EOMGF) 32,33 . This method is a many-body numerical calculation technique recently proposed by two of the authors of the paper.…”

Section: Introductionmentioning

confidence: 99%

Spatial spin-spin correlations of the single-impurity Anderson model with a ferromagnetic bath

Fan¹,

Tong²,

Zhang³

2022

Preprint

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We investigate the interplay between the Kondo effect and the ferromagnetism by an one dimension Anderson impurity model with a spin partially polarized bath, using the projective truncation approximation under Lacroix basis. The equal-time spatial spin-spin correlation function (SSCF) is calculated. For the case of spinunpolarized conduction electrons, it agrees qualitatively with the results from density matrix renormalization group (DMRG). For system with partially spin-polarized conduction electrons, an oscillation in the envelope of SSCF emerges due to the beating of two Friedel oscillations associated to two spin-split Fermi surfaces of conduction electrons. The period is proportional to the inverse of magnetic field h. A fitting formula is proposed to perfectly fits the numerical results of SSCF in both the short-and long-range regions. For large enough bath spin polarization, a bump appears in the curve of the integrated SSCF. It marks the boundary between the suppressed Kondo cloud and the polarized bath sites.

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“…With this method, GF with correct analytical structure can be obtained with controlled precision for a general quantum many-body system. 65 For a given Hamiltonian H, we select a set of linear independent operators to form the vector A = (A 1 , A 2 , ..., A n ) T , which is supposed to include the most relevant excitations of the problem. A matrix of two-time retarded Fermion-type GF is defined as…”

Section: Introduction To Gf Eom Ptamentioning

confidence: 99%

“…It was confirmed on the Anderson impurity model that the precision of result improves systematically with enlarging basis size. 65…”

Section: Introduction To Gf Eom Ptamentioning

confidence: 99%

Interacting spinless fermions on the square lattice: Charge order, phase separation, and superconductivity

Ma,

Tong

2021

Preprint

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We investigate the phase diagram of spinless fermions on a square lattice with nearest-neighbor interaction, using the recently developed projective truncation approximation in Green's function equation of motion. For attractive interaction, the ground state is in an homogeneous p + ip superconducting (SC) phase at high or low electron densities. Near half filling is a phase separation (PS) between the SC phases. Allowing inhomogeneous solution, we obtain p-wave SC domains with positive interface energy. As temperature increases, the SC phases transit into normal phases above Tsc, generating an homogeneous normal phase (far away from n = 1/2), or a PS between normal phases with different densities (close to n = 1/2). Further increasing temperature to Tps, the PS disappears and the particle-hole symmetry of the Hamiltonian is recovered. For repulsive interaction, depending on electron filling, the ground state is in charge-ordered phase (half filling), charge-disordered phase (large hole/electron doping), or PS between them (weak doping). At finite temperature, the regime of charge order phase moves to finite V and extends to finite doping regime.

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Controllable precision of the projective truncation approximation for Green’s functions

Cited by 7 publications

References 44 publications

Projective truncation approximation study of one-dimensional $ϕ^4$ lattice model

Projective truncation approximation study of one-dimensional $ϕ^4$ lattice model

Spatial spin-spin correlations of the single-impurity Anderson model with a ferromagnetic bath

Interacting spinless fermions on the square lattice: Charge order, phase separation, and superconductivity

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