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Register a new userCombining symmetry breaking and restoration with configuration interaction: a highly accurate many-body scheme applied to the pairing Hamiltonian
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Background: Ab initio many-body methods have been developed over the past ten years to address mid-mass nuclei... As progress in the design of inter-nucleon interactions is made, further efforts must be made to tailor many-body methods. Methods: We formulate a truncated configuration interaction method that consists of diagonalizing the Hamiltonian in a highly truncated subspace of the total N-body Hilbert space. The reduced Hilbert space is generated via the particle-number projected BCS state along with projected seniority-zero two and four quasi-particle excitations. Furthermore, the extent by which the underlying BCS state breaks U(1) symmetry is optimized in presence of the projected two and four quasi-particle excitations... The quality of the newly designed method is tested against exact solutions of the so-called attractive pairing Hamiltonian problem. Results: By construction, the method reproduce exact results for N=2 and N=4. For N=(8,16,20) the error on the ground-state correlation energy is less than (0.006, 0.1, 0.15) % across the entire range of inter-nucleon coupling defining the pairing Hamiltonian and driving the normal-to-superfluid quantum phase transition. The presently proposed method offers the advantage to automatically access the low-lying spectroscopy, which it does with high accuracy. Conclusions: The numerical cost of the newly designed variational method is polynomial (N$^6$) in system size. It achieves an unprecedented accuracy on the ground-state correlation energy, effective pairing gap and one-body entropy as well as on the excitation energy of low-lying states of the attractive pairing Hamiltonian. This constitutes a strong enough motivation to envision its application to realistic nuclear Hamiltonians in view of providing a complementary, accurate and versatile ab initio description of mid-mass open-shell nuclei in the future.
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Background: Ab initio many-body methods whose numerical cost scales polynomially with the number of particles have been developed over the past fifteen years to tackle closed-shell mid-mass nuclei. Open-shell nuclei have been further addressed by implementing variants based on the concept of spontaneous symmetry breaking (and restoration). Purpose: In order to access the spectroscopy of open-shell nuclei more systematically while controlling the numerical cost, we design a novel many-body method that combines the merit of breaking and restoring symmetries with those brought about by low-rank individual excitations. Methods: The recently proposed truncated configuration-interaction method based on optimized symmetry-broken and -restored states is extended to the z-signature symmetry associated with a discrete subgroup of SU(2). The highly-truncated N-body Hilbert subspace within which the Hamiltonian is diagonalized is spanned by a z-signature broken and restored Slater determinant vacuum and associated low-rank excitations. Results: The proposed method provides an excellent reproduction of the ground-state energy and of low-lying excitation energies of various z-signatures and total angular momenta. In doing so, the successive benefits of (i) breaking the symmetry, (ii) restoring the symmetry, (iii) including low-rank particle-hole excitations and (iv) optimizing the amount by which the underlying vacuum breaks the symmetry are illustrated. Conclusions: The numerical cost of the newly designed variational method is polynomial with respect to the system size. The present study confirms the results obtained previously for the attractive pairing Hamiltonian in connection with the breaking and restoration of U(1) global gauge symmetry. These two studies constitute a strong motivation to apply this method to realistic nuclear Hamiltonians.
We study the entanglement of purification (EoP), a measure of total correlation between two subsystems $A$ and $B$, for free scalar field theory on a lattice and the transverse-field Ising model by numerical methods. In both of these models, we find that the EoP becomes a non-monotonic function of the distance between $A$ and $B$ when the total number of lattice sites is small. When it is large, the EoP becomes monotonic and shows a plateau-like behavior. Moreover, we show that the original reflection symmetry which exchanges $A$ and $B$ can get broken in optimally purified systems. In the Ising model, we find this symmetry breaking in the ferromagnetic phase. We provide an interpretation of our results in terms of the interplay between classical and quantum correlations.
Topological superconductors represent one of the key hosts of Majorana-based topological quantum computing. Typical scenarios for one-dimensional topological superconductivity assume a broken gauge symmetry associated to a superconducting state. However, no interacting one-dimensional many-body system is known to spontaneously break gauge symmetries. Here, we show that zero modes emerge in a many-body system without gauge symmetry breaking and in the absence of superconducting order. In particular, we demonstrate that Majorana zero modes of the symmetry-broken superconducting state are continuously connected to these zero-mode excitations, demonstrating that zero-bias anomalies may emerge in the absence of gauge symmetry breaking. We demonstrate that these many-body zero modes share the robustness features of the Majorana zero modes of symmetry-broken topological superconductors. We introduce a bosonization formalism to analyze these excitations and show that a ground state analogous to a topological superconducting state can be analytically found in a certain limit. Our results demonstrate that robust Majorana-like zero modes may appear in a many-body systems without gauge symmetry breaking, thus introducing a family of protected excitations with no single-particle analogs.
While coupled cluster theory accurately models weakly correlated quantum systems, it often fails in the presence of strong correlations where the standard mean-field picture is qualitatively incorrect. In many cases, these failures can be largely ameliorated by permitting the mean-field reference to break physical symmetries. Symmetry-broken coupled cluster, e.g. Bogoliubov coupled cluster, theory can indeed provide reasonably accurate energetic predictions, but the broken symmetry can compromise the quality of the resulting wave function and predictions of observables other than the energy. Merging symmetry projection and coupled cluster theory is therefore an appealing way to describe strongly correlated systems. Independently, two different but related formalisms have been recently proposed to achieve this goal. The two formalisms are contrasted in this manuscript, with results tested on the Richardson pairing Hamiltonian. Both formalisms are based on the disentangled cluster representation of the symmetry-rotated coupled cluster wavefunction. However, they differ in the way that the disentangled clusters are solved. One approach sets up angle-dependent coupled cluster equations, while the other involves first-order ordinary differential equations. The latter approach yields energies and occupation probabilities significantly better than those of number-projected BCS and BCS coupled cluster and, when the disentangled clusters are truncated at low excitation levels, has a computational cost not too much larger than that of BCS coupled cluster. The high quality of results presented in this manuscript indicates that symmetry-projected coupled cluster is a promising method that can accurately describe both weakly and strongly correlated finite many-fermion systems.
Applying a variational multiparticle-multihole configuration mixing method whose purpose is to include correlations beyond the mean field in a unified way without particle number and Pauli principle violations, we investigate pairing-like correlations in the ground states of $ ^{116}$Sn,$ ^{106}$Sn and $ ^{100}$Sn. The same effective nucleon-nucleon interaction namely, the D1S parameterization of the Gogny force is used to derive both the mean field and correlation components of nuclear wave functions. Calculations are performed using an axially symetric representation. The structure of correlated wave functions, their convergence with respect to the number of particle-hole excitations and the influence of correlations on single-particle level spectra and occupation probabilities are analyzed and compared with results obtained with the same two-body effective interaction from BCS, Hartree-Fock-Bogoliubov and particle number projected after variation BCS approaches. Calculations of nuclear radii and the first theoretical excited $0^+$ states are compared with experimental data.
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