Multiparticle spectral properties in the transverse field Ising model by continuous unitary transformations

Fauseweh, Benedikt; Uhrig, Götz S.

doi:10.1103/physrevb.87.184406

Cited by 15 publications

(14 citation statements)

References 55 publications

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“…A possible reason could be the enforcement of spherical symmetry in our calculations. Recent experiments have revealed the coexistence of spherical ground states and axially deformed states with excitation energies below 3 MeV in 68 Ni and its vicinity [183][184][185]. In the next subsection, we will discuss examples in which the MR-IMSRG(2) successfully deals with the presence of both spherical and deformed states in the spectrum of neon isotopes, but we note that the states in question have much larger energetic separations of 7 − 8 MeV.…”

Section: Calcium and Nickel Isotopesmentioning

confidence: 99%

“…In the solid-state physics literature, the approach is also known as continuous unitary transformation (CUT) theory, see [65][66][67][68][69]. When we discuss our decoupling strategies for the nuclear many-body problem, it will become evident that the IMSRG is related to CC [58,70], canonical transformation theory (CT) [71][72][73], and the Irreducible (or Anti-Hermitian) Contracted Schrödinger Equation (ICSE) approach [74][75][76][77][78][79][80], and there is even some overlap with purely variational methods (see section 4.3).…”

Section: Introductionmentioning

confidence: 99%

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In-medium similarity renormalization group for closed and open-shell nuclei

Hergert¹

2016

Phys. Scr.

145

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Abstract. We present a pedagogical introduction to the In-Medium Similarity Renormalization Group (IMSRG) framework for ab initio calculations of nuclei. The IMSRG performs continuous unitary transformations of the nuclear many-body Hamiltonian in second-quantized form, which can be implemented with polynomial computational effort. Through suitably chosen generators, it is possible to extract eigenvalues of the Hamiltonian in a given nucleus, or drive the Hamiltonian matrix in configuration space to specific structures, e.g., band-or block-diagonal form.Exploiting this flexibility, we describe two complementary approaches for the description of closed-and open-shell nuclei: The first is the Multireference IMSRG (MR-IMSRG), which is designed for the efficient calculation of nuclear ground-state properties. The second is the derivation of nonempirical valence-space interactions that can be used as input for nuclear Shell model (i.e., configuration interaction (CI)) calculations. This IMSRG+Shell model approach provides immediate access to excitation spectra, transitions, etc., but is limited in applicability by the factorial cost of the CI calculations.We review applications of the MR-IMSRG and IMSRG+Shell model approaches to the calculation of ground-state properties for the oxygen, calcium, and nickel isotopic chains or the spectroscopy of nuclei in the lower sd shell, respectively, and present selected new results, e.g., for the ground-and excited state properties of neon isotopes.Submitted to: Phys. Scr.

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Section: Calcium and Nickel Isotopesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

In-medium similarity renormalization group for closed and open-shell nuclei

Hergert¹

2016

Phys. Scr.

145

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“…Continuous unitary transformations (CUTs) or the flow equation method 35,36 represents the basis of various perturbative 7,37,38 and renormalization approaches 30,[39][40][41] . The basic flow equation reads…”

Section: Some Technical Aspectsmentioning

confidence: 99%

From gapped excitons to gapless triplons in one dimension

2015

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Often, exotic phases appear in the phase diagrams between conventional phases. Their elementary excitations are of particular interest. Here, we consider the example of the ionic Hubbard model in one dimension. This model is a band insulator (BI) for weak interaction and a Mott insulator (MI) for strong interaction. Inbetween, a spontaneously dimerized insulator (SDI) occurs which is governed by energetically low-lying charge and spin degrees of freedom. Applying a systematically controlled version of the continuous unitary transformations (CUTs) we are able to determine the dispersions of the elementary charge and spin excitations and of their most relevant bound states on equal footing. The key idea is to start from an externally dimerized system using the relative weak interdimer coupling as small expansion parameter which finally is set to unity to recover the original model.

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“…This effective model can then be used to calculate physical properties of the system. CUTs have been applied successfully in a variety of cases [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Effective one-dimensional models from matrix product states

Keim¹,

Uhrig²

2015

Eur. Phys. J. B

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In this paper we present a method for deriving effective one-dimensional models based on the matrix product state formalism. It exploits translational invariance to work directly in the thermodynamic limit. We show, how a representation of the creation operator of single quasi-particles in both real and momentum space can be extracted from the dispersion calculation. The method is tested for the analytically solvable Ising model in a transverse magnetic field. Properties of the matrix product representation of the creation operator are discussed and validated by calculating the one-particle contribution to the spectral weight. Results are also given for the ground state energy and the dispersion.

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Multiparticle spectral properties in the transverse field Ising model by continuous unitary transformations

Cited by 15 publications

References 55 publications

In-medium similarity renormalization group for closed and open-shell nuclei

In-medium similarity renormalization group for closed and open-shell nuclei

From gapped excitons to gapless triplons in one dimension

Effective one-dimensional models from matrix product states

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