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Jorge Dukelsky

CSIC (Consejo Superior de Investigaciones Científicas-Spanish National Research Council), Theoretica Chemistry and Physics, Faculty Member

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Papers by Jorge Dukelsky

Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian

The Journal of chemical physics, Jan 7, 2017

Coupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic struc... more Coupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic structure theory. However, they are very different. Single reference coupled cluster is highly successful for treating weakly correlated systems but fails under strong correlation unless one sacrifices good quantum numbers and works with broken-symmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the mean-field level through multireference non-orthogonal configuration interaction wavefunctions, but unlike coupled cluster, it is neither size extensive nor ideal for treating dynamic correlation. We here examine different scenarios for merging these two dissimilar theories. We carry out this exercise over the integrable Lipkin model Hamiltonian, which despite its simplicity, encompasses non-trivial physics for degenerate systems and can be solved via diagonalization for a very large number of particles. We sh...

Staircase of crystal phases of hard-core bosons on the kagome lattice

Physical Review B, 2016

We study the quantum phase diagram of a system of hard-core bosons on the kagome lattice with nea... more We study the quantum phase diagram of a system of hard-core bosons on the kagome lattice with nearestneighbor repulsive interactions, for arbitrary densities, by means of the hierarchical mean-field theory and exact diagonalization techniques. This system is isomorphic to the spin S = 1/2 XXZ model in presence of an external magnetic field, a paradigmatic example of frustrated quantum magnetism. In the nonfrustrated regime, we find two crystal phases at densities 1/3 and 2/3 that melt into a superfluid phase when increasing the hopping amplitude, in semiquantitative agreement with quantum Monte Carlo computations. In the frustrated regime and away from half-filling, we find a series of plateaux with densities commensurate with powers of 1/3. The broader density plateaux (at densities 1/3 and 2/3) are remnants of the classical degeneracy in the Ising limit. For densities near half-filling, this staircase of crystal phases melts into a superfluid, which displays finite chiral currents when computed with clusters having an odd number of sites. Both the staircase of crystal phases and the superfluid phase prevail in the noninteracting limit, suggesting that the lowest dispersionless single-particle band may be at the root of this phenomenon.

0 50 70 38 v 1 1 4 Ju l 2 00 5 The β 4 potential at the U ( 5 ) – O ( 6 ) critical point of the Interacting Boson Model

Exact numerical results of the interacting boson model Hamiltonian along the integrable line from... more Exact numerical results of the interacting boson model Hamiltonian along the integrable line from U(5) to O(6) are obtained by diagonalization within boson seniority subspaces. The matrix Hamiltonian reduces to a block tridiagonal form which can be diagonalized for large number of bosons. We present results for the low energy spectrum and the transition probabilities for systems up to 10000 bosons, which confirm that at the critical point the system is equally well described by the Bohr Hamiltonian with a β potential.

Phase diagram of the 2D Bose-Hubbard model: Goldstone and Higgs

7th Workshop on Shape-Phase Transitions and Critical Point Phenomena in Nuclei; Universidad de Se... more

Critical points in the Interacting Boson Model

AIP Conference Proceedings, 2004

We study the quantum shape phase transitions in nuclei within the Interacting Boson Model (IBM). ... more We study the quantum shape phase transitions in nuclei within the Interacting Boson Model (IBM). The phase diagram for the standard IBM related to axial shapes is revised. The phase diagram of the IBM in relation to the recently proposed Y(5) critical point, connected to the change from axial to triaxial shapes, is investigated.

Density-matrix renormalization group approach to quantum impurity problems

Journal of Physics: Condensed Matter, 2004

A dynamic density-matrix renormalisation group approach to the spectral properties of quantum imp... more A dynamic density-matrix renormalisation group approach to the spectral properties of quantum impurity problems is presented. The method is demonstrated on the spectral density of the flat-band symmetric single-impurity Anderson model. We show that this approach provides the impurity spectral density for all frequencies and coupling strengths. In particular, Hubbard satellites at high energy can be obtained with a good resolution. The main difficulties are the necessary discretisation of the host band hybridised with the impurity and the resolution of sharp spectral features such as the Abrikosov-Suhl resonance.

Application of the density matrix renormalization group method to finite temperatures and two-dimensional systems

Journal of Physics A: Mathematical and General, 2003

The density matrix renormalization group (DMRG) method and its applications to finite temperature... more The density matrix renormalization group (DMRG) method and its applications to finite temperatures and two-dimensional systems are reviewed. The basic idea of the original DMRG method, which allows precise study of the ground state properties and low-energy excitations, is presented for models which include long-range interactions. The DMRG scheme is then applied to the diagonalization of the quantum transfer matrix for one-dimensional systems, and a reliable algorithm at finite temperatures is formulated. Dynamic correlation functions at finite temperatures are calculated from the eigenvectors of the quantum transfer matrix with analytical continuation to the real frequency axis. An application of the DMRG method to twodimensional quantum systems in a magnetic field is demonstrated and reliable results for quantum Hall systems are presented.

Density matrix renormalization group and the nuclear shell model

Physical Review C, 2006

We summarize recent efforts to develop an angular-momentum-conserving variant of the Density Matr... more We summarize recent efforts to develop an angular-momentum-conserving variant of the Density Matrix Renormalization Group method into a practical truncation strategy for large-scale shell model calculations of atomic nuclei. Following a brief description of the key elements of the method, we report the results of test calculations for 48 Cr and 56 Ni. In both cases we consider nucleons limited to the 2p-1f shell and interacting via the KB3 interaction. Both calculations produce a high level of agreement with the exact shell-model results. Furthermore, and most importantly, the fraction of the complete space required to achieve this high level of agreement goes down rapidly as the size of the full space grows.

The Density Matrix Renormalization Group in Nuclear Physics: A Status Report

arXiv (Cornell University), Jun 1, 2003

We report on the current status of recent efforts to develop the Density Matrix Renormalization G... more

Integrable model of a p -wave bosonic superfluid

Physical Review Research, 2019

We present an exactly-solvable p-wave pairing model for two bosonic species. The model is solvabl... more We present an exactly-solvable p-wave pairing model for two bosonic species. The model is solvable in any spatial dimension and shares some commonalities with the p+ip Richardson-Gaudin fermionic model, such as a third order quantum phase transition. However, contrary to the fermionic case, in the bosonic model the transition separates a gapless fragmented singlet pair condensate from a pair Bose superfluid, and the exact eigenstate at the quantum critical point is a pair condensate analogous to the fermionic Moore-Read state.

Number conserving particle-hole RPA for superfluid nuclei

Physics Letters B, 2019

We present a number conserving particle-hole RPA theory for collective excitations in the transit... more We present a number conserving particle-hole RPA theory for collective excitations in the transition from normal to superfluid nuclei. The method derives from an RPA theory developed long ago in quantum chemistry using antisymmetric geminal powers, or equivalently number projected HFB states, as reference states. We show within a minimal model of pairing plus monopole interactions that the number conserving particle-hole RPA excitations evolve smoothly across the superfluid phase transition close to the exact results, contrary to particle-hole RPA in the normal phase and quasiparticle RPA in the superfluid phase that require a change of basis at the broken symmetry point. The new formalism can be applied in a straightforward manner to study particle-hole excitations on top of a number projected HFB state.

An extended Agassi model: algebraic structure, phase diagram, and large size limit

Physica Scripta, 2019

The Agassi model [1] is a schematic two-level model that involves pairing and monopole-monopole i... more The Agassi model [1] is a schematic two-level model that involves pairing and monopole-monopole interactions. It is, therefore, an extension of the well known Lipkin-Meshkov-Glick (LMG) model [2]. In this paper we review the algebraic formulation of an extension of the Agassi model as well as its bosonic realization through the Schwinger representation. Moreover, a mean-field approximation for the model is presented and its phase diagram discussed. Finally, a 1/j analysis, with j proportional to the degeneracy of each level, is worked out to obtain the thermodynamic limit of the ground state energy and some order parameters from the exact Hamiltonian diagonalization for finite−j.

Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian

Physical Review C, 2017

The failures of single-reference coupled cluster for strongly correlated many-body systems is fla... more The failures of single-reference coupled cluster for strongly correlated many-body systems is flagged at the mean-field level by the spontaneous breaking of one or more physical symmetries of the Hamiltonian. Restoring the symmetry of the mean-field determinant by projection reveals that coupled cluster fails because it factorizes high-order excitation amplitudes incorrectly. However, symmetry-projected mean-field wave functions do not account sufficiently for dynamic (or weak) correlation. Here we pursue a merger of symmetry projection and coupled cluster theory, following previous work along these lines that utilized the simple Lipkin model system as a testbed [J. Chem. Phys. 146, 054110 (2017)]. We generalize the concept of a symmetry-projected meanfield wave function to the concept of a symmetry projected state, in which the factorization of high-order excitation amplitudes in terms of low-order ones is guided by symmetry projection and is not exponential, and combine them with coupled cluster theory in order to model the ground state of the Agassi Hamiltonian. This model has two separate channels of correlation and two separate physical symmetries which are broken under strong correlation. We show how the combination of symmetry collective states and coupled cluster is effective in obtaining correlation energies and order parameters of the Agassi model throughout its phase diagram.

Excited-state quantum phase transitions in the two-spin elliptic Gaudin model

Physical review. E, 2016

We study the integrability of the two-spin elliptic Gaudin model for arbitrary values of the Hami... more We study the integrability of the two-spin elliptic Gaudin model for arbitrary values of the Hamiltonian parameters. The limit of a very large spin coupled to a small one is well described by a semiclassical approximation with just one degree of freedom. Its spectrum is divided into bands that do not overlap if certain conditions are fulfilled. In spite of the fact that there are no quantum phase transitions in each of the band heads, the bands show excited-state quantum phase transitions separating a region in which the parity symmetry is broken from another region in which time-reversal symmetry is broken. We derive analytical expressions for the critical energies in the semiclassical approximation, and confirm the results by means of exact diagonalizations for large systems.

Generalized Br�ckner-Hartree-Fock theory and self-consistent RPA

Nucl Phys a, 1998

Nuclear structure insight from exactly solvable pairing models

Following a brief description of how pairing models can be solved exactly, we discuss two example... more Following a brief description of how pairing models can be solved exactly, we discuss two examples in which this exact solvability has been used to provide interesting insight into issues of importance in nuclear structure physics. One concerns the development of a new mechanism for sd dominance in interacting boson models of nuclei and the other concerns a mapping of nuclear pairing onto a classical electrostatic problem and the insight it provides into nuclear superconductivity.

Decoherence and quantum quench: their relationship with excited state quantum phase transitions

Beauty in Physics: Theory and Experiment: in Honor of Francesco Lachello on the Occasion of His 70th Birthday, 2012

We study the similarities and differences between the phenomena of Quantum Decoherence and Quantu... more We study the similarities and differences between the phenomena of Quantum Decoherence and Quantum Quench in presence of an Excited State Quantum Phase Transition (ESQPT). We analyze, on one hand, the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics and, on the other, we treat the quantum relaxation process that follows an abrupt quench in the control parameter of the system Hamiltonian. We explore how the Quantum Decoherence and the quantum relaxation process are affected by the presence of an ESQPT. We conclude that the dynamics of the qubit or the quantum relaxation process change dramatically when the system passes through a continuous ESQPT.

Exactly solvable Richardson–Gaudin models and their applications

Physica Scripta, 2006

We first show that the quantum pairing problem can be mapped exactly on to a classical electrosta... more We first show that the quantum pairing problem can be mapped exactly on to a classical electrostatic problem in two dimensions and then use this analogy to obtain a pictorial representation of how superconductivity arises in a finite fermionic system. Specific application to the nuclei 114−116 Sn suggests some new insight into the evolution of pairing correlations in a quantum system with few active particles. We also summarize other recent work on exactly solvable pairing models, including their applications in a wide variety of strongly correlated quantum systems.

The phase diagram of the Heisenberg antiferromagnet with four-spin interactions

Journal of Physics: Condensed Matter, 2009

We study the quantum phase diagram of the Heisenberg planar antiferromagnet with a subset of four... more We study the quantum phase diagram of the Heisenberg planar antiferromagnet with a subset of four-spin ring exchange interactions, using the recently proposed heirarchical mean-field approach. By identifying relevant degrees of freedom, we are able to use a single variational anzatz to map the entire phase diagram of the model and uncover the nature of its various phases. It is shown that there exists a transition between a Néel state and a quantum paramagnetic phase, characterized by broken translational invariance. The non-magnetic phase preserves the lattice rotational symmetry, and has a correlated plaquette nature. Our results also suggest that this phase transition can be properly described within the Landau paradigm.

Reply to the Comment by P. McCulloch and M. Gulácsi on “Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains”

Europhysics Letters (EPL), 2003